The Quantum Tai Chi
(Gauge Theory: The Dance Of Mind Over Matter)
P. Stephen Petersen, PhD. (Philip Petersen)
Empyrean Quest Publishers
©1996 by P. Stephen Petersen
Library of Congress Cataloging-in-Publication Data
Petersen, P. Stephen
The Quantum Tai Chi (Gauge Theory: The Dance of Mind Over Matter)/P. Stephen Petersen
1. Quantum Theory (Physics) 2. Physics--Philosophy. 3. Quantum Interpretation (Physics)
First Empyrean Quest Edition 1996
Printed in the United States of America
PREFACE: No Footprints in the Snow
INTRODUCTION: Wu Hua: The Magic of the Tai Chi of Physics
Chapter 1 Chen: The Arousing THE BIRTH OF GAUGE THEORY
Part A. The Gauge: A Standard of Measure
Milne's Different Drum
Part B. Weyl's Relativity of Measurement
All Forces Are Gauge Forces
Chapter 2 Sun: The Gentle A CHILD'S VERSION OF THE NEW RELATIVITY
Playing Tai Chi Beyond Space and Time
Global and Local Tai Chi's
Chapter 3 Li: The Elegant QUANTUM GAUGE THEORY
Part A. Particles and No-Particles
Psi: The Quantum Tai Chi
Part B. Weyl's Quantum Theory of Electromagnetism
Chapter 4 K'un: The Receptive THE TAO AND THE QUANTUM GAUGE
Dr. Bertlmann's Socks
Karma and Wigner's Mind Waves
Sir Arthur's Comparison Tai Chi
Can the Tai Chi Collapse Psi?
Healing Schrödinger's Cat
The Gauge As A Hidden Variable
Chapter 5 Tui: The Joyous THE YANG-MILLS PARADIGM
Part A. Noether's Theorem: Global Tai Chi's
The Foundation: the Electromagnetic Gauge
The Nucleus as an Equal Opportunity Employer
Fiber Bundles: Natural and Real
Part B. The Electroweak Miracle
The Color Force and Grand Unification
Supersymmetry: Super 'Wu Hua'
Lao Tzu and the Tzupercollider
Chapter 6 Chi'en: The Creative INTERPRETING THE QUANTUM TAI CHI
Apparatus Tai Chi in Italian
A Watched Pot Never Boils
Pearle Dives into the Unknown
A Phase Transition in the Brain?
Chapter 7 K'an: The Toiling MIND OVER QUANTUM MATTER
The Tai Chi of Superconductivity
The Temperature of Consciousness
Quantum Gravity's Simplest of all Possible Worlds
Chapter 8 Ken: The Meditating TOWARD A GAUGE THEORY OF CONSCIOUSNESS
Wave Functions (Tai Chis) for Life Decisions
The Gauge Theory of Cycles
The Memory Tai Chi
Chapter 9 Chung: The Peaceful FOREVER JUNG (AND YANG)
The Tibetan Wheel of Time
Ezekiel and the Wheels
Healing Rivers: The Breath and the Blueprint of Life
Healing and the Quantum Tai Chi
Gauge Theory: A Proof of the Existence of God?
EPILOGUE: The Universe: Holographic or Phase 'Magnetic'?
Love and appreciation to Dr. Richard Puetter, astrophysicist and patient PhD advisor, who guided my thinking to shores of reason. Wonder at the genius and generosity of the artist and poet, Roseanne Walsh, who first saw that the clothespins in my model of gauge theory were really Tai Chi's. She gave me the thread I needed to tie the book together. I am eternally grateful.
I dedicate this book to my parents, whose love and faith in me has kept me going through difficult times. In some mysterious way I also sense and acknowledge the help of Fu Hsi and the Yellow Emperor, friends out of history, who are the earliest known formulators of the Tai Chi philosophy, perhaps the first 'Theory of Everything'.
Finally, 1 acknowledge the love of physics my faculty advisor and gauge theory instructor C. N. Yang expressed to me when I first dropped out of the PhD program at the State University of New York in 1968. His words came back to me when I reentered the PhD program in 1983: "I do it because I love it!" I did not know then how much my contact with the Nobel laureate 'father' of gauge theory would mean to me.
PREFACE: No Footprints in the Snow
Legend has it that the creator of Tai Chi Chuan lived 200 years. Chang San-Feng, the originator of the martial art of the inner force, was born April 9, 1247. He integrated the Tao and the Tai Chi with Shao-Lin Chuan, the ancient Chinese art of self-defense. Historians suggest Chang was responsible for many miracles. One particular miracle typifies his method. Those who frequented the Shao-Lin Temple during the winter recounted this remarkable ability.
Chang liked to walk in the bitter cold through the snowy landscape surrounding the temple. Neophytes saw he left no footprints in the snow. In present day instruction, "stepping on snow leaving no footprints" represents the highest level in Tai Chi Chuan. The snow does not change. The Tai Chi phase, symbolizing the cyclic nature of a master's steps, transforms as he walks.
In physics, certain properties of elementary particles 'leave no footprints'. An example is nuclear particle identity. The distinction between protons and neutrons is not noticible inside the nucleus, though it manifests when these particles are free. Inside the nucleus, the strong nuclear force overpowers the electric force exerted by the charge on the proton. The effect of a proton is the same as a neutron. The identity of a proton versus a neutron has no measurable effect on other particles in the nucleus. (Chang's footing had little effect on the snow.) Imagined changes of particle labels or properties, without measured effect, physicists call 'invariance'.
We can represent Chang's footsteps by a Tai Chi passing through its phases. Similarly, particle 'invariance' is 'embodied' in an angle of 'symmetry' representing a hidden particle property.
The 'symmetry' of 'the Quantum Tai Chi' (the wave function in physics) is different from the symmetry which elicits feelings of awe in the world of art. Nonetheless, it is 'beautiful' in the world of mathematics. The 'traceless' nature of this Tai Chi comes from the arbitrary nature of electrical voltage. Add a constant to all voltages in a problem, and the electrical force or resultant current does not change.
For example, consider labeling the voltage at the head of a chickadee 1 volt, and that at its feet 0 volts. We can understand why very little current will flow through its body. (Holding a flashlight battery with 1.5 volts difference between its terminals is not a shocking experience.) It is the voltage difference between the head and foot of the chickadee which causes current flow.
There is no reason we could not label the voltage at the bird's topknot 10,001 volts and that at its feet 10,000 volts. This is a common convention for a bird on a 10,000 volt high tension wire. It is not voltage itself which can 'fry' the bird, but voltage difference, and resistance to current flow.
The mathematical symmetry related to the zero for voltage is responsible for the existence of the electromagnetic force. The repulsive electric force, acting between atoms, keeps us from falling to the center of the earth.
Symmetry connects to force. Witness Chang San-Feng's light-footed passage over the snow. The symmetry of his 'walking Tai Chi' perhaps required a force to counteract gravity.
Describing how forces result from symmetries is one of the main purposes of this book. It is not easy without equations, but the challenge is stimulating. Is there a symmetry for every force? Is the symmetry of the Quantum Tai Chi related to the existence of all forces in the universe? Does the Quantum Tai Chi always leave no trace as it 'walks' through phase changes?
The answer most physicists give to all of these questions is a hopeful 'yes'. The word 'gauge', however, should replace 'Tai Chi' to match the language they use. 'Gauge' is the word for the central concept of a new relativity, proposed by Hermann Weyl in 1918. For him, 'gauge' meant the measure of time and space. These days, it signifies a hidden property, represented by an angle beyond time and space. In this, there is a strong resemblance to the Tai Chi.
Chen Ning Yang (aided by Robert Mills) tried to apply Gauge Theory to neutrons and protons in the nucleus in 1954. This effort opened the path to a pinnacle of achievement in physics. This peak is the hoped-for unification of the four forces (gravity, electromagnetism, weak, and strong nuclearforces). Gauge Theory, by proving the relation of force to symmetry, may scale this height.
However, what of the forces within the human psyche that shape events in the outer world? Is the application of the Gauge Theory limited to physics?
Jung and Yang
The Chinese system of the Tao, as revealed in the 'I Ching', fascinated western psychologist Carl Jung. He investigated its relationship to the unconscious mind. Chinese American, C. N. Yang, is the physicist-inventor of the modern Gauge Theory of elementary particles.
Both Jung and Yang went through humiliating experiences which prepared them for later success. Jung experienced a decade or more of rejection by the academic community because of differences of opinion between Freud and himself. Yang lived through the hardship of China's war with Japan, and nearly starved. As a child, he had to dig his schoolbooks out of the rubble of his bombed-out home.
The Tai Chi philosophy and Gauge Theory promoted by these two scientists are two independent, parallel understandings of nature. The Tai Chi represents the unfoldment of polar forces of yin and yang. So also the 'gauge' of Gauge Physics relates to forces generated by polar 'charges'. The Gauge Theory of physics now proposes to unify the 'four' forces by recognizing a unified symmetry related to them. It had as its precursor the Taoist Tai Chi philosophical system, at least 5,000 years old!
Gauge Theory suggests a 'Theory of Everything', as physicists now call it. The Taoist Philosophy of the yin-yang Tai Chi, is also a 'Theory of Everything', intended to describe more than just the physical. The content of consciousness, which envelopes and includes the physical, is the domain of the polar forces of Yin and Yang. This is pictured in ancient China as the whirling Tai Chi, the Ridgepole of the Universe.
The I Ching calls Yin and Yang the two 'Chi', or breaths of Heaven and Earth. The most ancient writer on the Tai Chi, The Yellow Emperor, lends a psychological twist: "Yin and Yang create desires and vigor in men and women." In other words, the Tai Chi 'creates' forces which operate in the psyche. Yin and Yang, characterized by their proportions, are alleged to magnetize life circumstances to us. The Taoist perspective on the Tai Chi is that it leaves 'footprints' as it 'walks' through the world.
We will adapt the Quantum Tai Chi, which leaves 'no footprints', to include the Taoist perspective on the nature of consciousness. This will become clear in the book's study of 'Symmetry Breaking'.
Symmetry breaking happens when you try balance a stick on end in your hand. Well-balanced, there is no telling which way the stick will fall. When it falls, directional symmetry is broken.
A menu on a computer also presents its operator with symmetry. There is a choice of several selections. The computer operator breaks the symmetry by selecting one option. The symmetry in the nucleus between protons and neutrons breaks when the bound nucleus becomes free protons and neutrons. Bombarding the nucleus can do that. The symmetry represented by quantum possibilities in an experiment similarly breaks when the state of consciousness changes. The state changes from that of the imagination to that of 'observation'. Man accomplishes this by 'bombarding' the 'nuclear matter' of the imagination with sensory data.
The Quantum Tai Chi claims that Gauge Theory contains the seeds of a mathematical theory of consciousness and its related forces. To support this claim, the book entertains a Symmetry-Breaking Theory of Quantum Measurement. It describes the so-called 'collapse' of the quantum wave function as a change in state of the 'substance' of consciousness. Such a change is similar to the freezing of randomly-oriented liquid water molecules into ordered crystalline ice.
This theory of quantum measurement appears 'between the lines' of a history of the Gauge Theory of Physics. We include excerpts from the literature describing the Tai Chi and related concepts in other Eastern philosophies. The purpose of this exploration of Eastern thought is to lay the groundwork for the symmetry-breaking of the Tai Chi of Consciousness. Like the mystic Tai Chi, it imitates a turning 'spindle' which 'weaves' the fabric of the universe. This 'creation' of the observed universe occurs by a twist of the dial (gauge) of that consciousness. It converts some of the myriad possibilities of imagination into reality.
This is a 'movement' of the Tai Chi which, unlike that of Tai Chi Master Chang San-Feng, does
leave 'footprints in the snow' of our physical world. The perceived world condenses from the 'Chi',
or potential energy of consciousness.
INTRODUCTION: Wu Hua: The Magic of the Tai Chi of Physics
Many years ago, I had a friend who recommended an interesting meditative practice. I could never identify its source. He suggested that by concentrating hard on a small cloud, one could make it disappear. I decided to try it. Lying on my back in a meadow nestled between the hills above Malibu California, I watched the clouds as they passed quietly overhead. At first, I observed a cloud without focusing full attention on it. It changed form or diffused slightly. Rarely would it disappear entirely.
However, I soon concentrated intensely on a small cloud with the express desire to dissolve it. The white misty vapor gradually disappeared into the blue background. I spent more time in this meditation. My awareness was changing. Colors were more alive and vibrant. I felt refreshed--more aware of beauty in the hills around me.
When I was introduced to this exercise, I believed that the universe available to our senses obeyed the laws of simple physics. However, I am now convinced that the current laws of physics cannot explain this experience. Because of the changes and dispersion a cloud undergoes, it is easy to begin to feel that consciousness is changing the shape of the cloud. The whole meditative experience was subjective. However, there was something about it that heightened the senses. At least it made me feel like a participant in the dissolution of a cloud. Seldom have I more deeply felt the sheer joy of the flow of consciousness.
The ancient Chinese called this energy of consciousness 'Chi'. The thoughtform for the source of this energy, seen at the entrances of oriental self-defense parlors, is called the 'Tai Chi'. The Tai Chi is considered the gateway between spirit and matter, the 'Ridgepole of the Universe'. The whirling form of the Tai Chi represents the constant change of polarities at each point in space. These polarities are 'yin' and 'yang', and represent opposing qualities in nature. Examples are hot and cold, day and night, love and hate, moist and dry, hard and soft. The Tai Chi is the 'model'
or symbol of the essence of the Tao, or the 'order of Nature'. Lao Tzu says in the Tao Te King,
"Returning is the characteristic movement of the Tao...
All things work together.
I have watched them reverting,
And have seen how they flourish,
And return again, each to its roots...
The Tao is a void,
Used but never filled,
Like an ancestor
From which all things come.
It blunts sharpness,
It tempers light,
Subdues turmoil." (1)
The mystery of consciousness and its interaction with the 'world' we experience with the senses has always stimulated the mind of man. Hippocrates, the first scientific healer, hypothesized, 'to consciousness the brain is messenger'. In his 1637 Discourse on Method, Descartes, the Physicist and Philosopher, also contemplated a mind-matter duality. He called the two: 'thought' and 'extension' (about matter taking up space). Modern quantum theorists like Wigner speculate on the role of consciousness in physical observations of particles. He and other physicists claim that some form of consciousness must play the role of selecting the microscopic states of electrons. These are taken from the possibilities which may appear as outcomes of an experiment.
One ancient who considered the influence of mind on matter was Huang Ti (the Chinese Yellow
Emperor). He is said to have written 'The Yellow Emperor's Classic on Internal Medicine' (see figure
2). This book which discusses the relationship of consciousness to health utilizing 'Chi'. This is the
potential for action of Tao that flows within the body in a way independent of the nervous system.
This book was written nearly 5000 years ago. In it, the spiritual teacher of the Yellow Emperor, Ch'i
Po, takes us back even further:
"'In ancient times those people who understood Tao (the way of
self cultivation) patterned themselves upon the Yin and the Yang
(the two principles in nature) and they lived in harmony with the
arts of divination.'" (2)
The Yellow Emperor's work is the most ancient on record describing the Tai Chi and the alternating
flow of yin and yang. It is of note to consider some of the legendary information we have about his
life. Herbert Giles, in his book, A Biographical Dictionary , describes the mysterious Huang Ti. This
sage used the knowledge of the Tai Chi as a part of his healing philosophy.
"He is said to have reigned 2696-2598 B.C. and to have been
miraculously conceived by his mother, Fu Pao, who gave birth to
him on the banks of the river Chi ( ) from which he took his
surname... The close of his long reign was made glorious by the
appearance of the phoenix and that mysterious animal, known as
Ch'i Lin (variously identified with the unicorn and giraffe) in
token of his wise and humane administration." (3)
The word 'Chi' signifies a whole complex of concepts. Chinese characters differ from most of our Western words which are left-brain oriented and represent one idea. They are right-brain oriented and intuitive. Many connected ideas may be represented by one pictorial symbol. For example, 'shu' which stands for tree, is used for 'history', 'planting', or 'propagating' the race. It is also an adjective in the phrase 'shu lin', a forest of trees.
A. F. P. Hulsewe, wrote an article on the art of divination called 'Watching the Vapors, an Ancient Chinese Method of Prognostication'. He mentions several connected meanings for the symbol 'Chi'. Hulsewe indicates that one could consider Chi to be a vapor or aura much like the corona around the sun. He also quotes from the Han Shu, 'The History ('tree') of Han', a Chinese astronomical and historical text over 2000 years old:
"An aura is like a cloud, but is not a cloud; it is like a fog,
but it is not a fog, misty, as if something were visible."
Ssuma Chien, the writer, says that these 'auras' may be 'seen'
around the earth, animals, cavalry, in sleet clouds, rainbows,
and oceans, and they may be read to determine the future.
In this picture of the universe, everything has an aura. (4)
Reading auras these days may sound non-scientific. However, it is enlightening to learn that in the new physics of Quantum Field Theory, particles also have an 'aura' or a forcefield. Although it cannot be seen, its presence is felt. It conveys forces from one particle to another as they interact. Nowadays, physicists are in the habit of calling these 'auras' around particles 'Gauge Fields'. In fact, we could extend the meaning of the Chinese 'Chi' symbol to include the modern physics term, 'field'. In the new 'field paradigm', the 'auras of particles' are responsible for all the forces we experience in nature. What is a field? A field carries the potential for manifesting a force. Particles or objects inside a field may change or move.
Human auras are said to influence one another, when people get close enough. J. H. Seipel studied electromagnetic fields generated by neuron impulses at appreciable distances from the body. He suggested in 1971 that those fields may be the means "of direct information transfer or signaling which avoids the usual sensory channels." In a fashion analogous to auric fields, particle fields influence certain particles when near them. Fields such as the field of gravity extend far into the universe. Massive distant objects experience each others gravity. In fact, the universe as a whole is assumed to obey gravitational laws. Fields similar to gravity in their reach are thus called 'long range' fields. The field that holds neutrons and protons together in the nucleus becomes almost non-existent when these particles are not far apart. Such a field is 'short range'.
Particles have 'auras'. This makes them like everything else in the universe, as the ancient Chinese
viewed it. However, the similarity of particles to living beings does not end there. The new physics
of particles, Quantum Mechanics, may be leading us to a greater understanding of 'life' in the universe.
As Physicist E. H. Walker speculates (although this is perhaps not a majority opinion among
"Consciousness may be associated with all quantum mechanical
processes... since everything that occurs is ultimately the
result of one or more quantum mechanical events, the universe is
'inhabited' by an almost unlimited number of rather discrete,
conscious... entities that are responsible for the detailed
working of the universe." (5)
Gary Zukav, in The Dancing Wu Li Masters, carries this idea even further, when he says that "...photons (light particles), do appear to process information and to act accordingly, and therefore, strange as it may sound, they seem to be organic." (6) This reference to the 'life' in light is something to contemplate when gazing at the beautiful green photons coming from the lettuce in your lunch! (The lettuce looks green because the white light hitting it contains all colors, and all but the green is absorbed in the 'greenery'.)
Walker indicates that particles are 'organic', in the sense that they behave like they have
consciousness. In fact, modern Quantum Field Theory suggests that what we call a particle is an
'energy knot' in the field, as Hermann Weyl describes it. (7) Thus, particles are a flow creating the
illusion of a form, made up of concentrated 'Chi'. In the Neo-Confuscian tradition, Chang Tsai
describes 'Chi' as similar to a cloud:
"When the Chi condenses, its visibility becomes apparent so that
there are then the shapes (of individual things). When it
disperses, its visibility is no longer apparent and there
are no shapes. At the time of its condensation, can one
say otherwise than that this is but temporary? But at the
time of its dispersing, can one hastily say that it is then
non existent?" (8)
'Chi' thus lies somewhere between consciousness and matter itself. However, is there is a reason 'Chi' or particle fields exist? Gauge Theory answers this question. How Gauge Theory provides the reason for existence of fields is not so easy to explain without math. However, we will try. Gauge Theory is an extension of Quantum Theory. To many, Quantum Theory is a mystery. Gauge Theory moves to the core of Quantum Theory and beyond into a realm of even greater mystery and adventure. This realm involves the 'angles of consciousness' which are behind the fabric of space and time.
We know that what we see depends on the angle from which our eye views it. A pencil seen from one end looks like an eraser. A cube seen from the side looks like a square. However, Gauge Theory defines freedom of perspective beyond ordinary angles in 'visual' space.
To make a pencil look like just an eraser, we may have to rotate it through an angle. The angle of rotation determines how we will see it. All possible orientations of the pencil may be visualized mentally. Each orientation in a plane can be defined by an angle. A point of view or perspective in that plane can be replaced by that mental angle. This is one type of 'gauge'--an angle of consciousness or imagination.
If the pencil is hidden from view by placing it in a paper bag, we have the freedom to imagine it at any angle we want. This is a simple illustration of a kind of 'Gauge Freedom'. It is the freedom to imagine the gauge angle to be anything we want. This freedom exists only under certain circumstances: in this case, the pencil in the bag.
We will find that the first full-fledged Gauge Theory proposed by Yang and Mills in 1954 uses a
similar picture to describe the inner workings of the nucleus. (9) The nucleus is like a paper bag in
that it tightly holds protons and neutrons together. However, the strong nuclear force doesn't
discriminate between the two. Thus, their separate identities are 'hidden' inside the nucleus. The two physicists tried to represent the two-fold identity of protons and neutrons by the orientation of a pencil-like object called an 'isotopic spin vector'. One viewing direction represents a proton, and the opposite, a neutron.
This type of freedom, where the disposition of a symbolic object like an imaginary 'pencil' doesn't matter, was applied to physics in a revolutionary way by Chen Nin Yang. It was called Gauge Freedom, and the corresponding Theory of particles Gauge Theory. Since then, every major theory of particles has been impacted by Gauge Theory. Even String Theory, a new unifying theory representing all particles as different vibrations of a string loop, has now become Superstring Theory. It includes Supersymmetry. In Supersymmetry Theory, constructed as a Gauge Theory, particles of different spin interchange identities. The many different types of theories which have sprung like branches from the 'trunk' of Gauge Theory will be discussed later.
Gauge Theory impels us to understand the representation of particle qualities by angles in the imagination. These angles are collectively called 'the gauge'. They are useful because characteristics of particles are concealed under many circumstances. Such is the case for neutrons and protons inside the 'paper bag' of the nucleus. These concealed characteristics are what are called 'symmetries' because changing them doesn't change anything to all 'outward' appearances.
One reason Gauge Theory uses angles is to make a connection with symmetry of rotation. This we often think of as a source of beauty, in art, for example. Rotating a symmetric Chinese vase about a vertical axis doesn't change its apparent form. Rotating a mental object representing a certain particle characteristic like neutron-proton identity doesn't change the manifesting forces.
Modern Gauge Theory is extremely sophisticated. It is phenomenal that the ancient Chinese also had a symbol for imaginary angles which represent our perspective on nature. They called it the 'Tai Chi', although the 'Chi' pictograph was also used as a shorthand for it. The 'Tai Chi' is the symbol of changes. In passing through various angles of rotation, different qualities or life experiences are said to be manifested.
In Chinese lore, the 'Tai Chi' whirls, and each angle it whirls through represents the transformations or phases of a quality. For example, the Tai Chi for 'hot' becomes the Tai Chi for 'cold' as it passes from yang to yin. The Tai Chi which represents a particular quality at a point in space or time may be at one phase of its rotation. The Tai Chi for that same quality at another point in space or time may be at another phase. To illustrate, it is hotter in one place or time than another. The Tai Chi representing local temperature would be at various phases of the balance of hot and cold (yang and yin).
The angle of rotation of the Tai Chi thus describes the varieties of experience spread throughout
space as well as time. In this ancient view of the universe, all our perceptions at a given moment are
given a 'mathematical' form. In fact, the mathematics and meaning of the angles of rotation of the Tai
Chi make up a 'Theory of Everything'. This is a phrase used by physicists to describe a theory that
includes all physical phenomena. As the Yellow Emperor says,
"Yin and Yang (represented in the Tai Chi) is the basic principle
of the entire universe. It is the principle of everything in
creation. It brings about the transformation to parenthood;
it is the root source of life and death; and it is also
found within the temples of the gods." (10)
The relationship of the mystic Tai Chi to Quantum Gauge Theory is worth celebrating. Thus, we will use the eight symbols for its phases, called trigrams, as chapter headings. We will interweave the physics of Gauge Theory with Psychology and Eastern Philosophy.
Like the eight phases of the moon, the Tai Chi is said to revolve through eight combinations of yin and yang. The symbols for these eight phases are called trigrams because they contain three horizontal lines. Each has a different combination of either a broken line for 'yin' or unbroken line for 'yang'. Starting in the East with the rising sun, the trigrams stand for the eight directions of the compass. They also represent phases in the cycles of all natural phenomena.
In a finer division, sixty four phases of the Tai Chi are given as 'hexagrams'. They are made of 6 lines, either unbroken (yang) or broken (yin), and are called 'changes' in the I Ching. They are used by devotees of Eastern philosophy to understand the 'gestalt' or life circumstance of the moment. In this book, we will use the word 'Chi' to stand for a forcefield or field. A particular phase of the 'Tai Chi' will represent a gauge angle.
A beautiful landscape, a bridge, or a colorful bird flying overhead all can be put into code. We can symbolize it by an uncountable number of Tai Chi's overlayed onto the space of perception. This is because there is one in a unique phase for each point in time and space and each quality.
This is reminiscent of Walt Disney Studios techniques for cartooning. Overlays represent a
character's position at each instant of time. However, it is more like putting all the information into
a computer code, using angles instead of '1's' and '0's'.
Leibniz, the co-inventor of Calculus, also invented the binary
number system now used as computer code. After his
invention, he claimed that the hexagrams in the I Ching were
an alternate way of representing the binary numbers. An unbroken
line (Yang) stands for '1', a broken line (Yin) stands for '0'.
According to Joseph Needham, a Chinese historian, this connection
was probably suggested to Leibniz by a Jesuit missionary.
The reality, however, was that Fu Hsi, the father of the
hexagrams, did not have binary numbers in mind when he invented
them. Nevertheless, a base 5 number system may have been in use
then. The broken lines had a value of 1. The unbroken lines a
value of 5. This is not surprising since the Chinese also invented
the beginnings of algebra, which we also use in our modern
computing machines. (11)
Imagine a 'computer' code for a changing visual landscape using angles instead of binary numbers. There would be a corresponding set of Tai Chi's for each point in space and time. The Gauge Theory of physics doesn't concern itself with this type of picture of the overall universe. However, this book's chapter on the Gauge Theory of Consciousness proposes that it could. It also seen later that gauge 'coding' suggests a model for the recording and retrieving of human memory.
A variety of angles throughout space and time is also the nature of the local Gauge Theory. This
version originated with Chen Ning Yang (who likes to be called 'Frank', in honor of Ben Franklin).
The local theory was the most important advance in the history of Gauge Theory. It says there are
circumstances in which the angle of a given type of 'Tai Chi' is 'hidden' in influence. It isn't specified
by physical circumstance. The angle is free to be set differently at each point in the space-time
continuum, while this angle differs only slightly from its neighbors. The changes in gauge from point
to point must be continuous. These minutely-differing, adjacent 'Tai Chi's' in Gauge Theory are like
an outpicturing of psychologist William James's concept of the 'stream of consciousness':
"Consciousness then does not appear to itself chopped into bits.
Such words as 'chain' or train' do not describe it fitly, as it
presents itself in the first instant. It is nothing jointed, it
flows. A 'river' or 'stream' are the metaphors by which it is
naturally described. In talking of it ..., let us call it
the stream of thought, of consciousness, or of subjective life."
The 'Tai Chi' is a more general version of the 'gauge' in Gauge Theory. What corresponds to the yin and yang in the Tai Chi? We will find that for each force in Gauge Theory there is at least one type of 'charge' which comes in two varieties. They are 'positive' and negative', thanks to Ben Franklin, who discovered polarity in electrical charges.
Opposite charges repel and like charges attract. Thus, we could say that the yin phase of the 'Tai Chi' corresponds to the repulsive force. The yang is the attractive force for the characteristic the particular 'Chi' represents. However, the relation of the Quantum Tai Chi to polarity is more subtle.
We will also discover that these ideas apply to sense perceptions as well as the Gauge Theory. For example, if the quality is the amount of green tint in a landscape, the yang phase attracts it. The yin phase repels it. This attracts 'antigreen' or purple. Thus, the color in the visual field can be represented in code by angles of the Tai Chi which represent mixtures of yin and yang. In the landscape example, this would provide varying percentages of green and purple at each point in space.
It is interesting that a widely accepted theory of the strong nuclear force called Quantum
Chromodynamics uses the words 'color charge' to describe a hidden quality of quarks. Quarks are the
smaller particles of which neutrons and protons are made. The Gauge Theory of Chromodynamics
proposes that quark 'color' is nearly analogous to the colors on a painter's pallette.
It takes three quarks, one of each 'color', to make up a proton or
neutron. These particles aren't like marbles painted blue,
pink, and yellow. However, they do have qualities
analogous to the primary colors. Quark 'color' is an 'invisible'
characteristic. Quarks are never seen by themselves, manifesting
a single 'color'. This is like the requirement that sunlight or
white light contain all the colors of the rainbow. Whirl three
tiny flames of blue, pink, and yellow close to one another. The
effect creates a pure white light composed of all possible
Gauge Theory has only been used for the properties of particles like quarks. However, we will see many indications in this book that the potential uses for the Gauge concept can be extended. It could go far beyond the particle domain into the realm of perception, thought, and consciousness itself. This fulfills mathematically the ancient Chinese inner vision beyond the physical universe.
We begin our journey to the new world of Gauge Theory with a children's story. It illustrates the
power of the paradigm which may well eventually describe the 'magic' of parapsychology (ESP).
A well-known magician was known for pulling rabbits and
doves from his hat. However, no one could ever tell ahead
of time which one it would be, a rabbit or a dove. One day,
a little boy watching the show had a hunch. He knew the next
animal that would emerge from the magician's hat would be a
rabbit. He was so sure of himself that he could actually see the
rabbit's cottony tail, and nibbling nose moving around inside the
hat. He was startled when the rabbit he saw clearly in his
imagination suddenly transformed. It became a dove as it was
pulled from the hat. To this day the little boy believes that the
magician can change rabbits into doves with a magical transforming
The theories that describe how distinct particles came to be, very early in the history of the universe, utilize Gauge Theory. This is in much the same way that the magician pulled rabbits and doves out of the hat.
Inside the 'hat' of the early universe, electrons and quarks may have been 'invisible'. They were like the rabbits and doves in our story. When pulled out of the 'hat' as the universe expanded and changed its phase (in a way analogous to water changing from liquid to steam), this 'symmetry' was broken. Indistinct particles became either electrons or quarks, manifesting electrical and nuclear forces respectively. Similarly, the hidden animal in the hat emerged as a rabbit or a dove. This is like the magic of the Grand Unified Theory (GUT). This theory grandly suggests a unifying principle for all the forces but gravity. It may prove to be one of the major triumphs of Gauge Theory.
Transformation' or 'wu hua', is also part of the Taoist Philosophy. Chuang Tzu, Chinese philosopher
of the 4th Century BC, describes the transmutation of one's identity:
"Once, I, Chuang Chou (Chuang Tzu), dreamt that I was a butterfly.
Flitting about at ease and to my heart's content,
I indeed was a butterfly. Happy and cheerful,
I had no consciousness of being Chou. All of a sudden, I awoke,
and lo, I was Chou. Did Chou dream that he was a butterfly?
Or did the butterfly dream that it was Chou? How do I know?
There is, however, ... a difference between Chou and
a butterfly. This situation is what I would call the
transmutation... (wu hua)." (13)
In light of such everyday occurrences, two identical particles changing their nature, one becoming an
electron and one becoming a quark, is not such a surprising transformation. We will see that Gauge
theory is capable of describing all such 'magical' transformations. It doesn't matter whether they are
transmutations of consciousness or so-called 'physical reality'.
1. THE BIRTH OF GAUGE THEORY
"Cheng of the North Gate inquired of the Yellow Emperor: 'When your Majesty performed the music of the Haien-ch'ih in the wilds of Lake Tung-t'ing, the first time I heard it I was afraid, the next time I idled through it, the last time I was confused.'
'I was afraid you might find it like that', said the Yellow Emperor. 'First I played it as a work of man, but attuned to heaven... Yet nothing can be depended on to last. Next I played it as the harmony of Yin and Yang (the Tai Chi), illumined by the torchlight of sun and moon. Its notes
Can shorten, can lengthen,
Can weaken, can harden,
Altering and transforming it evens out in oneness
Does not submit to precedents and norms ...
You were veering with the line of least resistance, that is why you idled through it. Next I played it
with notes which never idled, and tuned it to the spontaneous course of destiny... You were trying
to listen to it, but there is nothing to perceive in it; that is why you were confused."'
Chuang-Tzu, Chapter 14
Gauge Theory was born in 1918, the same year as Einstein's General Relativity. Herman Weyl, a pupil of Hilbert, the famed mathematician, first published Space-Time-Matter. In it, he explored what he called 'gauge invariance'. Transformed over the decades until it became almost unrecognizable. the 'gauge' idea has sparked such excitement. It has unified the weak nuclear and electromagnetic forces. This was marked by the 1983 discovery of the 'W' and 'Z' particles intermediating the weak force.
In this chapter we discover the ability of Weyl's 'gauge' to shorten and lengthen our perception of time and space. It shares this ability with the yin and yang of the Tai Chi. The above statement of the Yellow Emperor illustrates this.
However, the similarity of the gauge to the Tai Chi phase won't be clear until we discuss the quantum version of Gauge Theory. This we save for a later chapter. Weyl's earliest concept of a gauge dimension is linear and spatial. His later quantum version suggests an angular dimension as an extension of Quantum Theory.
A decade earlier, William James anticipated Weyl's loosing of the bonds of space and time. Witness
his description of a 'psychological' space and time:
"Cosmic space and cosmic time, so far from being the intuitions that Kant said they were, are
constructions patently artificial as any science can show. The great majority of the human race
never use these notions, but live in plural times and spaces, interdependent and durcheinander
(disordered)... We assume for certain purposes one objective time that flows evenly, but we don't
livingly believe in or realize such equally-flowing time." (1)
In a physicist's view of space, objects themselves do not normally change in size like shrink-to-fit jeans. However, we may conceive of clocks and rulers that represent changes in the scale of time or space. We are free to set units of measurement. This is the first glimpse of 'gauge freedom' provided by Herman Weyl. It is a freedom of perception or consciousness.
Weyl's ' gauge freedom' was part of a theory he intended as an alternative to Einstein's General
Theory of Relativity. This chapter looks forward to the extension of gauge freedom to aspects of
consciousness. We examine the idea that all forces may depend on our perspective. This we meet on
the road to a new relativity of consciousness--the thesis of this book.
The Gauge: A Standard of Measure
Model train enthusiasts have a built-in grasp of the word 'gauge'. Manufacturers construct the coach, caboose--even the scenery--to scale. This cuts reality to an exact fraction. Take, for example, Abraham Lincoln's campaign train. A good model would be complete down to the future president's eyelashes. Someday scale models will be authentic even at the microscopic level. This will be a product of the 3-D holographic revolution.
The standard gauge for American railroads provides 4 feet 8 1/2 inches between the rails. Broad gauge trains, however, have a wider rail gap. Narrow gauge trains have closer rails. Gauges for most model railroads are taken from these three standards.
The American College Dictionary defines 'gauge' as, "a standard of measure." For model railroads, the standard is set relative to a full-scale version. Generally, this unit of measure (distance between rails) differs for different gauge trains. There is a 'gauge' for these models of the 'real' world.
The philosophy of yoga says that the outer world is like a scale model of the inner world. It is a coarse 'materialization' of mind-stuff. 'Real' trains are but lower vibratory manifestations of patterns that relate to 'train-ness' in the mental world. We will explore this mode of thought in the chapter on the Gauge Theory of Consciousness.
As Swami Vivekananda, a 'yogi' who visited the U. S. during the early 20th century, said,
"It is not that some forces are physical, some mental; the physical forces are but the gross
manifestations of the fine forces, just as the physical world is but the gross manifestation of the
fine (mental or etheric) world." (2)
There are other areas of life (besides model trains) with varying standards of measurement. The standard unit of length, for example, may be different in two countries. Thus, some means of translating is necessary. The average person in the United States still uses the''foot' as a unit of distance. A conversion factor is needed to the European 'meter'. The conversion factor (1 m = 3.281 ft) provides a connection between the standards or gauges in two countries.
The word 'connection' is key in Gauge Theory as well as General Relativity. It describes how the way we view space and time changes. It may differ, not only from place to place, but also from time to time. A connection in Gauge Theory is a formula or log (listing), which describes how a gauge varies with position in space-time. Matter curves space-time. A connection in Einstein's Theory of General Relativity describes how space-time curvature varies in different locations. In both theories, Gauge Theory and Einstein's Theory, a connection is a prescription for changes in space-time.
A person has freedom to choose their standard of measure at any time and any place. We don't have to use rulers with inch divisions to measure length. This understanding of the arbitrary means of measurement is the basis for gauge freedom in physics. However, unless we know how to connect one measure to another, communication is difficult.
Imagine Jonathan Swift's Lilliputians (little people) and Brobdignagians (big people) making contact for the first time. Suppose they try to sell each other 'yards' of cloth material. Without knowing how many Lilliputian 'yards' were in a Brobdignagian 'yard', exchange would be challenging.
Relating to standards of measure is vital. Even in ancient cultures, this was so. As Kuan-Tzu, a
contemporary of Confucius remarked,
"A bag too small cannot hold something big, a well-rope too short cannot draw from deep
The need for a connection also becomes clear in the measurement of time. For example, you can take a jet from New York to Chicago's O'Hare Airport. From there, you can go on to Denver the LA Airport. To keep a wristwatch in time with the clocks in each airport, however, you must adjust it back one hour for each stop. This relationship between time zones is a connection. Before the adoption of time zone system, Local Time was in use. Timekeeping was even more complex. Every small change of longitude required a well-defined change in time. At least there was a system for keeping track of the changes. This is a connection more like that in local Gauge Theory.
Robert Ornstein, who wrote the classic Psychology of Consciousness, tells a story of an unusual
connection in timekeeping.
The legendary 'guru' Nasrudin was enroute to London with his disciples in a twin engine plane. They were four hours away when a frantic disciple burst into the cockpit to report, "The right engine has gone out!" "That's allright," Nasrudin replied, we will get there in two hours." A few minutes passed and the distraught follower returned screaming, "Master, Master! The second engine has gone out!" Nasrudin winked, twirled his mustache, and pointed out, "No problem. We should be arriving any minute." (4)
In this humorous example, we see a 'standard of measure' which changes with position in space and time. What about those which vary with time alone? We are free to reset standards of measurement as time passes. For example, someone could heat the iron bar standard meter in Paris.It would expand, and present a gauge that varies with time, if they did the experiment carefully, the expanding rod could be used to measure distance. Its extension would be dependent on temperature. To relate the meaning of our measurements, we would have to set up a connection. This would be between the rod at the standard temperature and the rod at the new temperature. This is an artificial example of the freedom to choose a gauge in time. However, it shows that gauges can vary continuously with time.
In the usual conception of the Tai Chi, the yin and yang 'fishes' are rotating uniformly in time. Although Chinese philosophy says that it changes in space as well, a time-varying Tai Chi is the focus. It gives the picture of a gauge changing cyclicly as time passes.
In the chapter on the Gauge Theory of Consciousness, we will use this notion to give a left-brain understanding of events which connect between our inner and outer world. In that chapter we will suggest that a cyclic occurrence in the outer world corresponds to a cycle in the world of the mind.
This is not hard to grasp for the sun. Many of us rise and begin our day when sunlight hits our eyes. This is a stimulus for the mind. Both the solar cycle and the associated mental cycle can be represented by a single Tai Chi with a one-day cycle. This is an example of a 'cycle gauge'.
We will suggest the that the right-brain, intuitive part of our nature works with many non-linear
clocks clicking off the phases of memory. It is not 'timeless' as many have claimed. The balance of
the right and left brain--linear and cyclic time--brings the experience of time transcendence.
Milne's Different Drum
Long before venturing fully into the world of 'cycle time', we examine an example of unusual timekeeping from the archives of physics. E. A. Milne wrote about it a decade after Weyl's Gauge Theory. Weyl's theory is the main thrust of this chapter. However, Milne's ideas prepare us for that theory by giving us a specific case of it.
This example will break us free from the concept of a clock which ticks off even seconds. It will give us a new gauge for the measurement of time quite different from the gauge for the mantlepiece clock.
There is a deeper motivation for exploring this example. It is that the universe itself will appear simpler. This happens if we constrain time to slow down in a certain way.
We also desire the simplification of the equations of physics. Allowing clocks which run differently leads to a 'static' universe. This freedom to let time flow differently also builds a base for our later discussion of 'cycle time'.
Milne introduced 'expanding time' in the 1930's as a cosmological theory. (5) He noted that we
are free to have clocks speed up or slow down. We can build clocks differently from the standard.
They could even match a momentary subjective sense of time. This is like Henry David Thoreau:
"If a man does not keep pace with his companions, perhaps it is because he hears a different
drummer. Let hime step to the music which he hears, how ever measured or far away." (6)
Milne's idea also echoes William James' discourses on the 'plural' nature of time:
"That one Time which we all believe in and in which each event has a definite date, that one
Space in which each thing has its position, these abstract notions unify the world
incomparably; but in their finished shape as concepts how different they are from the loose,
unordered time-and-space experiences of natural men. Everything that happens to us
brings its own duration and extension, and both are vaguely surrounded by a marginal
'more' that runs into the duration and extension of the next thing that comes." (7)
Milne's 'deviant clocks' (deviating from a steady flow of time) are a way of picturing freedom of consciousness. Each adjusts the flow of our 'psychological' time to the need of the moment. However, Milne wasn't trying to make James' notion of time mathematical. Rather, he sought to simplify the laws of physics by changing how we represent time.
Milne limited his fanciful timekeeping by allowing only one time for each event. It would be absurd to say, 'I got married at 3, 4, and 7 o'clock', unless each time referred to a different marriage. (We will relax this requirement in our study of 'cycle time'.)
Milne realized that we could build clocks which speed up or slow down--without running backward. This prevents events which are not simultaneous from reading as the same time. The drive mechanisms of Milne's 'deviant clocks' were thought to accelerate or deccelerate from a smoothly flowing 'time'.
This relativity of timekeeping is more challenging to conventional thinking than Einstein's Special Theory of Relativity. We never keep time in any other way than with a smooth-running clock. However, it is reasonable that we may see clocks differently when 'moving'--as in Einstein's Theory.
Evenly running clocks are merely conventional, not descriptive of the essence of time itself. Stuart Edward White in The Unobstructed Universe, published in 1940, calls the essence of time 'receptivity' to experience. This leaves room for James' psychological time. The speed of the reception of events may vary, and suggests Einstein's space-time continuum. In it, events are 'received' as the signposts of the measure of time.
Milne's 'freedom of time' (freedom to conceive of 'deviant clocks') suggests 'receptivity'. However, he applies it to the expansion of the universe. We believe that the universe is expanding, because of the redshift. This we think of as a lowering of frequency because the source is receding.
In the same way, the pitch of a siren is lowers as it moves away from us. The 'redshift' refers to the changing of color of visible light because of its relative motion. It moves toward the red end of the rainbow.
Milne showed that, by slowing down a clock in the right way, its units of time would get longer
and longer. We could match the expansion of the units of space. Such a clock wouldn't measure any
Nowadays, physicians say that the expanding universe is conformally' flat. This means that space and time expand uniformly together, when time flow is changed. The purpose of Milne's suggestion was to simplify the equations describing the universal expansion.
Milne applied his time change to an example of a cosmological theory with constant expansion speed. He wanted clock-based measurements to see the universe at a standstill. To do this, they would have to mete out a new logarithmic 'time'. The logarithm of time increases more slowly than linear time. Thus, Milne's clock slows.
Each cosmological theory would require clocks which slow down differently. This could 'halt' expansion. Milne used Just one model of the universe as an example.
The time on Milne's clock for a day to pass would be much shorter now than it would be 10 years from now. This is an example of 'subjective' time. Of course, such a time system doesn't help us tell time on earth. However, it does exhibit an imaginary 'cosmic' clock that is unique. It slows down so the universe is calculated not to expand at all. Physicists call such a new time 'universal proper time' or 'cosmic time'.
Newton's laws of motion depend on time. Thus, the new clock requires a new form for Newton's equations. The speed the new clocks run create new forms of the laws of motion. Material objects will still move the same, however.
On the other hand, we may want to stick to Newton's Laws in their usual form. For this, time must be linear, and the measure of space must be in fixed units. This opens a new understanding.
It allows us to see that our usual form for physical laws depends on our usual way of measurement. Thus, there is a relationship of physical law to the manner of measurement of time and space. Convention accustoms us to linear time and Newton's Laws. For example, we find it hard to conceive that it might be useful to have clocks run differently. However, equations may be simpler for a transformed definition of time. They were for Milne and the expanding universe.
In effect, Einstein did this for rapid relative motion. He compared time measured by a stationary observer to that measured by a moving observer. This effect is 'time dilation', and time measured 'on board' the 'moving' object we call 'proper time'. The use of proper time simplifies many calculations in Special and General Relativity.
Time flow transforms physical laws. Thus, Milne concluded that fixed laws of the universe don't
exist. These laws may depend on how we measure quantities at each point in space-time. This
measurement mode is a 'gauge'. Although Milne's argument is mathematically correct, the
conventional point of view did not change. As the mathematical physicist Walter Thirring points out:
"In physics, ...the way yardsticks and clocks behave... is determined by the equations of motion.
It is this reasoning which gives a concrete significance to the mathematical structure of our
Milne, however, was not the only one who held the more radical point of view. This was that we should not consider physical laws to be 'set in cement'. As physics evolves, its future depends more and moreon new perspectives of measurement. We envision a new relativity--a relativity of measurement.
Gauge Theory provides a transforming power ('wu hua'): that of perspective. As pointed out in
the ancient Lu Shih Chhun Chiu:
"If a man climbs a mountain, the oxen below look like sheep and the sheep like hedgehogs. Yet
their real shape is very different. It is a question of the observer's standpoint." (9)
In Milne's example, the laws of physics change with a change in perspective. Richard Bach's
Jonathan Livingston Seagull also shows, in an imaginative way, how the laws of physics change with
changing perspective or gauge. His 'lifestory' is a preview of the new alchemical 'Gauge Age'
envisioned in the chapter on the Gauge Theory of Consciousness. Jonathan is the first seagull to fly
at terminal velocity. He possesses the ability to transport himself instantly from one place to another.
With this power in his wings, he announces his secret:
"Each of us is in truth an idea of the Great Gull, an unlimited idea of freedom (gauge freedom?)...
and precision flying is a step toward expressing our real nature. Everything that limits us, we
have to put aside. That's why all this high-speed practice, and low-speed, and aerobatics..." (10)
Up to this point, we have been discussing Milne's relativity of time. In it the laws of physics change with our way of measuring time. However, we may change some ways of measuring without changing these laws. For example, I drop a pen to the second floor of the Park Plaza Hotel. There are equations describing how it falls. They give the same result whether I measure its height from the rug on the second floor, sea level, or the center of the earth, for that matter. This type of irrelevant change of measurement physicists call gauge invariance, or 'gauge freedom'. However, we will also use the words 'gauge freedom' to denote the general freedom to measure in different ways, without concerning ourselves with changes in the laws of physics.
1.THE BIRTH OF GAUGE THEORY
1B Weyl's Relativity of Measurement
Partly because they both attempted a theory of relativity, Weyl and Einstein were fast friends. So close were they, that Weyl or his wife often attended Einstein's lectures. Weyl recalls that Frau Weyl accompanied Einstein to one of his presentations in Zurich in 1919. Tickets were limited because of a wartime coal short-age. Though Frau Weyl had a ticket, she misplaced it.. Ticket-takers tried to prevent her from attending. Einstein refused to give the lecture. After a 'scene', she was allowed to attend. Later, the world-famous Einstein was given a reprimand for standing up to the rules.
Weyl and Einstein were on excellent terms, but their theories of relativity were in competition. Einstein was the main opponent of Weyl's version, which for many years stood in disfavor with physicists. It is only in the last few decades that Weyl' original idea has been validated.
Hermann Weyl's ground-breaking idea was gauge symmetry or invariance. Though we may change our way of measuring, some of these changes do not affect the laws of physics. These changes with 'no footprints' are 'gauge invariant'. Physicists also call them 'symmetries'. Symmetries are the reason for the existence of forces. You might call them the realization of the quest to find out "what God is thinking". This was Einstein's view of the goal of physics.
Milne's idea of the gauge freedom of time was enlightening. However, it was not useful. It did not include gauge invariance. The laws of physics changed form with his change in gauge. Thus, he was given a lot of fleck for his claims, because they required rewriting well-established physical laws.
The freedom to reformulate physical laws by redefining physical quantities is called 'Gauge Freedom' in this book. Redefinition accompanies a change in the mode of measurement. Thus, Gauge Freedom involves a new relativity of measurement.
Later we shall see that time dependent gauges are useful in understanding the impact of cycles of events. Instead of setting clocks to halt the expansion of the universe, we will set imaginary clocks differently for each cycle. This approach is useful because it involves a new type of gauge invariance or symmetry. Cyclic laws don't. change with time translation by one period.
This symmetry is expressed by the periodic rotation of a time-varying Tai Chi. Crystals have a similar periodic symmetry in space. Locations of atoms are spaced in a regular pattern. 'Cycle time' is a mathematical description of periodic symmetry in time. It is an extension of the symmetry principles now being used to unify the forces of physics. Like those principles, it requires the existence of forces.
However, it is a quantum leap into this new application of Gauge Theory. We first examine 'classical' (pre-quantum) Gauge Theory, first introduced by Herman Weyl.
The earliest attempt at a general theory of gauge relativity was proposed by Weyl in 1918. It included the relativity of the measure of both space and time. He claimed it to be more 'general' than Einstein's General Theory of Relativity. Weyl unveiled the theory in his classic work, Space-Time-Matter. In it, he indicated that we can measure the size of objects differently at different times and locations.
Thus 'size' may differ from one place and time to another. A 'six foot cow' in Texas is a 'two meter cow' in France. This is the process of unit conversion. We also could change our measure of the cow from two meters to eight meters by redefining the meter. As long as we multiply all sizes by four, classical physics doesn't change. This Weyl called 'scale invariance'. It is now called 'conformal invariance', if an equal stretching of time is allowed.
Units of space and time could also change with location and time. For example, Americans could
redefine a second of time to be twice as long as it is now. Perhaps the French might stick with the old
In our dreams, objects may appear to change size. However, in waking life, solid objects
don't normally shrink or grow. In a way, this is a conditioned patterning of our conscious-ness. It is
a comforting one at that. Imagine living in a world like Alice's Wonderland, where size is subject to
whim. We are comfortable, however, with the scaling of pictures of objects. It is useful to 'blow up'
photographs or computer models, for example.
The freedom to reset scale is a property of consciousness. This property is beyond space and time. With scale freedom in mind, we might easily take the point of view of the sage, Chuang Tzu:
"Nothing in this world is bigger then the tip of an autumn hair, and Hount Tai is small; no one
lives longer than a doomed child, and Peng-Tzu (the Chinese Methuselah) died young; heaven and
earth were born together with me, and the myriad things and I are one." (11)
The freedom of spatial scale is also well expressed in the following Zen verse:
"A long thing is the long body of the Buddha,
A short thing is the short body of the Buddha." (12)
In a way, Weyl brought psychological space and time into physics. His formulation requires 'imagined' changes in space-time measure. However, his contemplated scheme required the existence of a force. He had to compensate for the freedom to reset the scale of space and time. Weyl proposed that variations in unit size were made up for by a force which behaved exactly like electromagnetism.
To get a sense of this by way of illustration, consider a version of Chinese Baseball. It is different from its American counterpart. While the pitch is in the air, players may move the base pads to any position on the field. Talk about gauge freedout The player running the bases must exert additional forces to touch all of them. Thus, those forces come about from a change of gauge, and compensate for it.
To understand mathematically the need to compensate for gauge freedom, a 'connection' is required. This connection relates unit variations at different points in space and time. Weyl identified the connection in his theory with the electromagnetic potential. This is the 4-D analogue of electric voltage.
There is a reason the connection must be 4-dimensional. Space and time make up 4 dimensions.
The connection describes the changes in scale in the 4 directions of space-time:
Consider an analogy. Suppose I want to describe how Temperature changes throughout space and time. I might use the following 4-D connection. Temperature is what is called a 'scalar field'. A scalar field assigns one number (in this case, a temperature) to each point in space-time. We want to relate temperature at one position in space-time to any other nearby position. Thus, we need to know how temperature changes in each of the four directions or dimensions:
Dimension 1--change in temperature as one moves in the x direction,
Dimension 2--change in temperature as one moves in the y direction,
Dimension 3--change in temperature as one moves in the z direction, and
Dimension 4--change in temperature as one moves in the time direction.
Each of these would have to be recorded for each position in space-time. We would have four connection numbers assigned to each point. This connection is called the temperature gradient. It is also a field. A connection on a acelar field with four components is called a 'vector field'
We could also represent temperature by Tai Chi's placed throughout. space and time. We would need a formula like %Yang / % Yin = hot / cold. It is proportional to temperature. Again, we want a four dimensional connection or vector field (Chi) to describe the relationship between these Tai Chi's. The temperature 'gradient' is the directed rate of change of the field values for temperature. It is like the slope of the temperature 'terrain' in various directions from each point.
As with temperature, Weyl suggested that. the electromagnetic potential is the connection for scale. It is the gradient of the field of scales, or space and time sizes at each point.
It may help to describe the mathematical situation in words. When the gauge or size scales are changed or 'transformed', the connection for size scales also transforms. This transformation looks like the E-M potential. The transformation is an 'electromagnetic gauge change'. The 'gauge' is in an arbitrary quantity in Electromagnetic Theory. Weyl found the change in electromagnetic gauge identical to the change in the gauge of space-time scale. The 4-D electromagnetic potential is thus the prescription for the freedom to change units of space-time in different locations.
Weyl's idea was a stroke of genius. His theory is widely recognized as the true beginning of Gauge Theory. The time component of the connection between space-time scales just happens to be the electric potential or voltage. This is the quantity from which electrical forces between charges are computed. The three space components of the connection happen to be the magnetic potential. it determines the nature of magnetic forces. Thus, electric and magnetic forces are 'connected' with freedom to choose scales for measuring space and time. To have change, we must have freedom.
We can picture the relationship of the gauge to force with the following schematic diagram. Arrows indicate that the quantity to the right may be mathematically derived from the quantity to the left.
Gauge (consciousness, or Tai Chi)
---- > Connection or Field (potential or 'chi')
---- > Force (changes or 'wu hua').
This relationship of the three levels--consciousness, force, and the connection between them--will be the same in all later discussion of Gauge Theory. The parallels between Gauge Theory and Chinese Taoist philosophy will also remain intact.
The term 'gauge transformation' was first used by Weyl to indicate a change in space-time scale. These scales may vary from place to place and time to time. However, I should not think that my car could shrink to the size of a scale model, because I drive it five blocks. That is a form of 'level confusion'. The level of scale changes is the level of the consciousness of the observer, not the level of the object observed.
An artist portrays a road in perspective. Though the entire road may be the same width, it appears to be smaller when more distant. It trails off almost to a point as it crosses the horizon. This is a matter of perspective. It's similar to the freedom employed in choosing a 'scale' with which to measure time and space.
Weyl did not went to describe a crazy world where people could shrink or grow, as in Alice's
Wonderland. He wanted to complete the relativity of measurement begun by Einstein. Weyl's writings
clearly indicate that he hoped his theory would extend Einstein's Theory of General Relativity. He
wanted it to extend into the realm of relativity of scale or gauge.
"To be able to characterize the physical state of the world at a certain point of it we must
not only refer the neighborhood of this point to a coordinate system but we must also fix on
certain units of measure. We wish to achieve just as fundamental a point of view with regard
to this second circumstance as is secured by the first one, namely, the arbitrariness of the co-
ordinate system, by the Einstein Theory... " (12)
Instead of looking at conversions from meters to centimeters, Weyl explored the point of view that rulers and clocks could be flexible. My car may not shrink when I drive it to a new position. However, the tape measuring the car might stretch (cloth garment tapes are notorious for that). If the tape stretches, the "I" mark, standing for one meter at one time, may stand for 1.01 meters later on. The car would thus measure shorter.
In the same way, potential disciples may have varying measures of the worth of the guru. Chuang
Tzu was respected as a master teacher of the Tao (the Way). However, some did not that opinion of
him. Hui Tzu took the academic approach to enlightenment.
"Hui-Tzu said to Chuang-Tzu: 'I have a big tree of the kind men call shu. Its trunk is too gnarled and bumpy to apply a measuring line to, its branches too bent and twisty to match up to a compass or square. You could stand it by the road and no carpenter would look at it twice. Your words too, are big and useless, and so everyone alike spurns them.'
Chuang Tzu said, '...Now you have this big tree and you"re distressed because it's
useless. Why don't you plant it in Not-Even-Anything Village, or the field of Broad-And-Boundless, relax and do nothing by its side, or lie down for a free and easy sleep under it? Axes
will never shorten its life, nothing can ever harm it. If there's no use for it how can it come to
grief or pain?"' (13)
Like Hui Tzu, we have fixed ideas about the universe. They are influenced and crystallized by convincing individuals (scientists, artists, philosophers, etc.) who have viewed it in limited ways. It is possible that the conventions which have 'created' our reality may not always be the most 'useful'. Francis Bacon clearly recognized this in the 17th century.
Recognizing the freedom to choose units and making that freedom mathematical was not enough for Weyl. He went on to claim the world was scale or 'gauge' invatiant. Consider a change in scale of space and time. There is an appropriate change in the field ('chi') which compensates. This allows the laws of physics to maintain the same form. These changes have the character of changes in the electromagnetic field. Thus, the gradient of the field of scales can be identified with the electromagnetic field.
From the study of scale changes Weyl derived a supposedly unified theory of gravity and electromagnetism. This was possible because gravity could already be described by the curvature of space-time. Weyl added to curved space-time that fact that electromagnetism was related to the 'scale' of space-time. Gauge invariance, for Weyl, meant that the laws of physics don't change with changes in units of space and time.
It is unfortunate that Milne didn't. relate his theory of 'cosmic time' to Weyl's Theory of gauge relativity. In Milne's day, though, Weyl's original proposal of gauge invariance was thought to be faulty. This was because of a conflict with the mass concept in Quantum Field Theory.
Critics were quick to recognize apparent difficulties with Weyl's Theory. Weyl was the 'Moses' of Gauge Theory. He was not given the opportunity to realize his dream of reaching the 'promised land' of Gauge Relativity.
His friend, Einstein, had an objection. Consider two observers with synchronized clocks in the same location. One observer moves to another place where time is faster. He then comes back to the place where the second observer has remained. The two clocks will no longer display the same time.
Another apparent problem with Weyl's theory was the impact of scale changes on mass. This argument involved deBroglie wavelengths. DeBroglie wavelength is a characteristic wavelength of matter in the theory of Quantum Mechanics.
DeBroglie considered material objects and particles as waves (see Chapter 3). These wavelengths (sizes of matter waves) are inversely proportional to mass in deBroglie's formula. This means that for their size to vary throughout space-time mass has to vary in the opposite direction. If the size of units of length are cut in half, the deBroglie wavelengths double. Mass is cut in half. To Peter Bergmann, Einstein's student, this was nonsensical. It made the usual Quantum Field Theory, where mass is a standard of measure, invalid. (14)
Though it seemed to fail, Weyl's first version of Gauge Theory was valuable because it contained within it the seeds of full-blown Quantum Gauge Theory. His insight was correct on the level of the imagination instead of physical changes in scale. Weyl didn't fully realize that gauge invariance of space-time scale was to be found in the mind.
This fact was clear to Arthur Eddington in 1952. It was also clear to C. N. Yang a few years later.
He said that the quantum gauge represented "an imaginary scale change". However, he did not
elaborate on any possible metaphysical interpretation of it. (15)
Weyl's theory required mass to change with a change in the scale of space and time. Thus, Hoyle and Narlikar, the proponents of Steady State Cosmology, have more recently pursued a revitalized scale relativity. In it, mass is allowed to vary. (16) This was allowed so as to save the essential idea of Weyl's relativity. They reformulated Quantum Field Theory to accomodate units of mass which can change.
One possible frame of reference, in their view, is to imagine rulers growing with the expanding universe. The universe doesn't expand when measured by them (Milne revisited). Instead of slowing down time, the scale with which we measure space is made to expand. In such a case, atoms, mass, and the space between them would shrink relative to a stationary grid of galaxies.
Hoyle and Narlikar's Theory provides an unusual perspective. It is another example of a unique gauge. Like Milne's, this theory has not achieved notoriety. Their theory provides a new way of measurement, but no new facts. A non-expanding universe violates 'common sense'. However, the idea that the universe is expanding or, alternatively, that atoms are contracting, could be considered a matter of convention.
We are used to picturing galaxies rushing away from one another. We also measure objects with non-rubbery rulers. These are conventions. You may still say the expansion of the universe is a 'fact'. However, this 'fact' only becomes real when we set up rules for measuring universal expansion.
Our conception that the universe is expanding is a conditioned response. It is generated by observations that the universe has an outward velocity away from us. We don't normally see objects around us shrinking or growing. Thus, there is an underlying sense that we and the Earth have a stable 'size'. That is, size is always considered relative to ourselves. Similarly, before Copernicus, the motion of the solar system was considered relative to our Earthbound perspective.
Hoyle and Narlikar'a point of view is just one of many possible, where man's perspective on size
is destabilized. We may consider different perspectives in which the Earth is shrinking or growing at
different rates to be valid frames of reference.
Man found by direct observation that an Earth-centered solar system was just one
perspective, when he travelled out into it. Someday, we may be capable of freeing ourselves from
size limitations. We may travel in dimensions of scale. Will we then see the galactic clusters as
cells in some gigantic body of which we are yet unaware? Will we twist the dial of the Tai Chi
of scale and travel into the very depths of the minute dimensions of the quantum foam? Could
we directly observe the beauty of superstrings?
What if Hoyle and Narlikar had presented their theory right after Hubble and Humason discovered the expansion of the galaxies? Their unconventional cosmology could have taken hold. They could have said that Hubble and Humason really found that the atoms and people are shrinking with respect to the fixed universe. This is an allowed point of view in the relativity of measurement.
To go to extremes, one could pick a gauge with rulers growing even faster. In it, Chicken Little
could be considered correct in saying, 'the sky is falling'. However, this statement would have little
significance. We could pick any speed we like for the fall. The stars would never hit him on the head.
He could be shrinking even more rapidly. Chinese history records the story of a human 'Chicken
"There was a man in the state of Chi who was so afraid that the universe would collapse... that he could neither sleep or eat. Another man, pitying his distress, proceeded to enlighten him. 'Heaven', he said, 'is nothing more than an accumulation of chi and there is no place where this chi is not... Why then should you be afraid of a collapse?"' Master Lieh heard of these discussions, smiled, and said, 'He who maintains that heaven and earth will pass away, and he who maintains the contrary are both at fault. Whether they will or not is something we can never know. If they go, we shall go with them; if they stay, we shall stay and not know the end."' (17)
Lieh Tzu cuts to the very core of the conditioning which forces us to view the world in a particular way. Our conditioning predisposes us to measure. We predict from these measurements in a left-brain fashion. On the other hand 'non-measurement' is a state of perfect receptivity or enlightenment. To see the world as it really is, we must overcome our conditioning to measure continually.
'Measurement' is an attitude that Zen, for example, helps us transcend. No measurement--Zen enlightenment. We go into the center of the 'size Tai Chi', beyond phases, beyond yin and yang. This breaks our tendency to think of objects as big or small.
Our obsession with classification and measurement of objects prevents us from seeing the whole reality. We can be blind to how objects relate to myriad parts of the universe. Weyl's Gauge Theory is an attempt to break free from perceptions limited by our conditioned sense of size and time.
What is the goal? Weyl's Space-Time-Matter is a trail-blazing exploration of Gauge Theory. It
ends with a vision of self and nature uncharacteristic of scientific writings:
"Whoever looks back on the ground that has been traversed (in Weyl's book) ... must be
overwhelmed by a feeling of freedom won--the mind has cast off fetters which have held it captive.
He must feel transfused with the conviction that reason is not only a human, a too human,
makeshift in the struggle for existence, but that, in spite of a disappointments and errors, it is yet
able to follow the intelligence which has planned the world, and that the consciousness of each one
of us is the centre at which the One Light and Life of Truth comprehends itself in Phenomena."
We have complete Weylian freedom to choose how we measure quantities or perceive the universe
(gauge freedom). However, there comes a time, as for Hoyle and Narlikar, when we have to measure.
Then, we must choose our methods of measurement. The gauge is the method expressed
mathematically: like a table of time zones, or a clock calibration. It represents the way we measure
something. Thus, in Gauge Theory, specifying how we measure is called 'fixing the gauge'. Once all
the gauges are fixed, the form of the laws of physics related to the measurement are fixed. Or if the
situation doesn't depend on how we measure, any choice of gauge will do.
Freedom of choice of gauge is reminiscent of the whole concept of free will. In the Gauge Theory of Consciousness, we find that free will and predestination or 'karma', as it is expressed in Eastern philosophies, can be made compatible by using restricted gauges.
An example of the blending of limitation and freedom is involved in the decision of the hero of the
Bhagavad Gita, the Hindu 'Bible'. Arjuna is faced with fighting his brothers who have wrongfully
taken his kingdom. The events are set up by karma or the necessity of facing issues to learn a lesson
(a narrowing of gauge freedom). He must decide whether to fight and possibly kill his brothers and
relatives. This is a decision he must make in the context of the remaining gauge freedom. Thus Arjuna
experiences free will (freedom to choose a gauge) within the gauge conditions arranged by his karma
or predestination, and chooses to fight.
All Forces Are 'Gauge' Forces
If we change the gauge, the laws of physics may change. New forces may come into play to make up for it. This freedom from rigid forms of the laws of physics is a kind of 'Copernican' revolution. Perhaps our laws of physics are as complicated as Ptolemy's epicycle system for describing the notion of the planets. With a new perspective on measurement, the laws of physics may change to a simpler, more rational form. This they did for Kepler when he recognized the Sun to be at a focus of the elliptic motion of the planets.
Forces with different forms and relationships may come from the mathematics of new perspectives. Some may call these forces 'fictitious'. However, if we believe in the relativity of measurement, who is to say one way of measuring a quantity is 'real' and another 'unreal' or 'fictitious'? One method of measurement is just more accepted or 'conventional' than another.
Consider an example from elementary physics. For the moment, we leave behind rubbery rulers and slowing clocks. We observe a child on a merry-go-round, our own feet on the ground. From that perspective, many physics texts say there is a 'real' force necessary to keep the child from moving in a straight line. This is called the centripetal force, and points toward the center of the disc 6).
On the merry-go-round watching the child, there is a 'fictitious' or 'unreal' force which makes him spin away from the center of the wheel. This force is apparent because the perspective from which we measure or the 'gauge' (in a loose definition) has changed. The force is called the 'centrifugal force' 7). The centrifugal force is more commonly known than the centripetal force. This is because the person undergoing circular motion 'feels' it.
There is a relativity of perspective involved here. The forces accounting for the motion in the two observer perspectives are in opposite directions. The centrifugal force is called'fictitious' only because the so-called 'stationary' observer has the more commonly-held point of view. We don't usually ride a merry-go-round. Or do we? Recognizing that we live on a rotating earth forces us to change our viewpoint.
The perspective that identifies the centripetal force as 'real' is the more conventional one. It is conventional in part because the observer of the force is not moving with respect to an earthbound observer. Looking at it in the relativity of measurement--probably Weyl's and Einstein's greatest contribution to physics--neither of these perspectives is more 'fictitious' than the other.
Consider scale changes which alter the laws of physics. We recognize that Einstein did not use
anything but clocks running in local linear time (unlike Milne'& clocks which slowed down). He also
did not allow scale to vary with position (as did Weyl). We see now that Einstein's was merely a
conventional point of view.
Let's examine an example which highlights the freedom of measurement explored by
Herman Weyl. It is the notion that we could measure a bed using the height of a person named
'Charlie'. We begin with a baby Charlie and end with an adult. A given bed might be 7 Charlies
long when he is a toddler, and 1.2 Charlies when he is an adult. Is this merely unintelligent way
measuring things? Not if one were interested in the space that Charlie had to move around on
in his bed and how it affects his psychological sense of well-being. This example demonstrates
that using flexible units of measurement can be useful in science.
Transformations in size to emphasize a point are also taken to extremes in Taoist literature. For
example, Chuang Tzu confutes the pride of elected officials:
"In the northern darkness there is a fish and his name is K'un (the tiniest fish imaginable).
The K'un is so huge I don't know how many thousand li he measures. He changes and becomes
a whose name is P'eng. The back of the P'eng measures I don't know how many thousand
li across and, when he rises up and flies off, his wings are like clouds all over the sky... The little
quail laughs at him saying, 'Where does he think he's going? I give a great leap and fly up, but
never get more than ten or twelve yards before I come down fluttering among the weeds and
brambles. And that's the best kind of flying anyway'... Such is the difference between big and
In Weyl's relativity, as in the parables of Chuang Tzu, size and time are a matter of perspective. Scale invariance was first shown to disagree with the simple notion that masses don't vary with location. The conflict was between the theory and the conventional form of the laws of motion. These laws result from the conventional way of measuring space and time.
It has taken a long time to appreciate the virtue of Weyl's relativity. In the study of superstrings, physicists have finally recognized the value of Weyl's notion of scale invariance.
The impact of scale changes could be further investigated. Can we find useful new forms for old laws? Could these new laws describe experiments and data previously unexplained, as Kepler's did for planetary motion? In Einstein's Special Relativity, the mathematics which describes motion changes for a moving observer.
Along the same line, such fruitful work is being accomplished in gauge relativity. It examines how
the way we measure affects the form of the laws of physics. Thus, the relativity of measurement
begun by Einstein and extended by Weyl promises formalization of complete freedom of
To understand freedom of measurement, think of the analogy of the mind to a graphic
computer. We can construct models of 'real' objects on the screen with some software. However,
we are not limited to making these images a certain size. They can be contracted or expanded as
fast as we can type in instructions. 'Real time', or simulation programs have also been invented
for analysis of the flight of a space shuttle. Nevertheless, it is possible to program a flight in
another gauge or 'scale' of time. General Relativity says that time slows down in a strong
gravitational field, for example. This effect can be 'gauged' into 'real' time. It is a change in
gauge from 'linear' time. The mind possesses the same freedom as graphics programs (and much
more). This will become clear in our study of Quantum Gauge Theory and the Quantum Tai Chi.
Why limit the freedom of the mind to set scales and perspectives by calling one force 'real' and another force 'fictitious'? Why not call the new forces that result from fixing either the frame of reference or scale 'gauge forces' rather that 'fictitious' forces. All forces are real. 'Gauge force' is a term normally reserved for forces resulting from gauge invarience. However, it deserves this wider usage. The word 'gauge' is applied in its wider sense as a 'perspective of measurement'. When the measurement changes, new forces may appear.
This concurs with a unified Relativity of Measurement. Einstein's and Weyl's theories of relativity are thus united. After all, somewhere someone could be using Milne's logarithmic clocks or Hoyle's rubbery rulers. They could make the mistake of calling the expansion of the universe 'fictitious'. A similar error was made by the critics of Copernicus. They lampooned, murdered, and imprisoned those who supported Sun-centered motion for the planets. Galileo, for example, was imprisoned for writing in support of Copernicus' views.
In beginning physics classes, it was hard for me to understand why forces like the Coriolis Force were labeled 'fictitious'. The Coriolis Force is responsible for certain weather patterns. This force causes air masses on earth to circulate in giant storm-like vortices. I couldn't see why a 'fictitious' (made up) force could cause a real effect. The Coriolis Force is an influence, seen by an observer on the earth. It is a result of the rotation of the planet on moving objects, like air molecules or clouds. These objects are, to a degree, free of the Earth's rotation.
One can give an example of the Coriolis force on a single object instead of an air mass. For example, an object dropped from a tower on the equator will fall slightly to the west of where it is released. This is because the earth rotates underneath it. To an observer not rotating with the earth (in space) the object falls in a straight line. Another observer on the earth may postulate a force to account for what he sees as a curved path for the fall. His point of view, though, doesn't make the Coriolis force any less real in its effect. Thus, it is a gauge force. It is related to a frame of reference. Using the gauge terminology in this expanded sense will help to clarify the issue of the 'reality' of forces.
Of course, it then becomes our prerogative to call all forces related to a mode of measurement 'gauge forces'. The gauge or perspective of measurement isn't clearly understood in every case. This doesn't prevent us from using the term, 'gauge forces'. All forces may be understood as gauge forces. 'Gauge forces' arise when the gauge or perspective of measurement changes. Later in the book, we will leave physics to discuss Psychology and Consciousness. We will expand the conventional notion of the gauge to a perspective in consciousness. We will learn how freedom is defined and limited in measuring or perceiving quantities.
Forces come from gauge freedom. This is the method of the Gauge paradigm. Understanding that
forces are related to the gauge, helped bring about the unification of the Weak nuclear force and the
Electromagnetic force. This is a phenomenon for which Yang and Hills, and later Glashow, Weinberg,
and Salan are largely responsible.
In this chapter, we have explored the gauge as fixing a perspective of measurement. The perspective of measurement, since it may change with location or time, requires a connection or a means of relating the changes. We examined the connection idea. We then discussed Weyl's identification of the connection for space-time scale with the Electromagnetic potential. This opened the way for correlating electric and magnetic forces to such scaling. Though Weyl's theory suffered from apparent difficulties, we will see in Chapter 3 that Quantum Theory resolved those difficulties. This was by a reinterpretation of scale changes. First, however, a deeper mathematical insight will be developed in the next chapter.
Weyl's theory was the beginning of the recognition--in mathematical form--of the freedom to change our physical reality by viewing it differently. This wider relativity one might loosely call the relativity of physical law itself.
In a succeeding chapter, we will find that Quantum Theory clearly can be interpreted in a new way.
This new understanding allows us to distinguish the levels of physical reality and consciousness. In
addition, consciousness may be hierarchical in structure, as Jungian Psychology claims. If so, its levels
may also be delineated by a new type of Gauge Theory.
2. A CHILD'S VERSION OF THE NEW RELATIVITY
"All the time that has passed from antiquity until now is called 'chou'; all the space in every
direction... is called 'yu'. The Tao is within them, yet no man may say where it dwells." (1)
Hui Nan Tzu (120 BC)
"The way eternal has no name.
A block of wood untooled, though small
May still excel the world...
He who is intelligent is like a little child,
His vitality is intact." (2)
In the last chapter, we explored Weyl's original theory of Gauge Relativity. We considered variations in the measure of space and time. Weyl's first version was an attempt to derive the forces of electricity and magnetism from geometry. He saw them as a result of the freedom to rescale the size of space and time.
Similarly, Einstein's General Theory of Relativity characterized the force of gravity as a produce of curved space-time. The mathematical nature of both theories is the outcome of a 20th Century program to see physics as geometry.
It was soon discovered that four-dimensional space-time was not adequate for geometrizing the four forces of physics. These are gravity, electromagnetic, weak, and the strong nuclear force. This chapter explores the geometric solution that Gauge Theory brings to this area of research.
However, we will not plunge directly into the Quantum Gauge Theory. First, we will construct
a preliminary picture of the extra dimension beyond space-time. We will explore the significance of
the phase dimension (angle) of the Quantum Tai Chi. This will clarify the differences between 'global'
and 'local' changes in the phase or gauge. This distinction is comparable to the difference between
'global warning' and the local variations in Earth temperature.
Looking back, my interest in simple geometry began early in life. Now I realize that this relates to Gauge Theory. I have a photo of myself at age 3, sitting on an overturned stew pot with crayolas in hand, meditating on a clothesline. As I contemplate the child in this photograph, I recall the fascination this preschooler had the clothesline and clothespins. The clothespins were the kind with rounded ends, made entirely out of wood. To me, they looked like carved imitations of circus performers straddling a high wire.
At age 5, I was tall enough to reach the line and move the mysterious wooden clips. First, I bunched the clothespins together on one line. Then I straightened then all up in the same direction. This was a child's version of a 'global gauge' (see figure 8)
Next, I ran my hand over the pins as I moved along the clothesline. I gradually adjusted their angle to vary along the line. In this way, I had created something analogous to a 'local gauge'. This is a concept explained in this chapter. It is the basis of modern Gauge Theory (see figure 9).
As an adult, I repeated my childhood game. This time, I realized the connection between Gauge Theory and my childhood 'experience'. I set up a clothesline with old-fashioned clothespins. I took a fresh look at the childhood images that now invoke the angles beyond space and time we call the 'gauge'.
When I described the Gauge Theory to an artist friend, I used the clothesline as a visual aid. She commented that the angles beyond space and time reminded her of Tai Chis. In time, I saw I could use the Tai Chi as a symbol for gauge angles. It gave a familiar visual picture of 'Local Gauge Freedom'.
Thus, I was led, in spite of myself, to study Tai Chi Yin-Yang philosophy. I was also prompted to learn some of the movements in the meditative exercises. This book integrates both of them in the study of Gauge Theory.
I had my own idea of how to present this book. However, the natural flow of the 'Teo' had
another idea for me. The Zen master, Nan-in, also had another idea for a university professor who
came to him for instruction:
"Nan-in served tea. He poured his visitor's cup full, and then kept on pouring. The professor watched the overflow until he could no longer restrain himself.
'It is overfull. No more will go int'
'Like this cup,' Nan-in said, 'you are full of your own opinions and speculations. How can I show you Zen unless you first empty your cup?"' (6)
Muju (13th century Japan)
In the next chapter, we will show the quantum wave function can be represented by extending the
meaning of the Tai Chi. The Tai Chi can: (1) be exhibited in varying sizes, to match quantum
probability, and (2) have different phases to picture a free angular dimension in Quantum Theory. For
simplicity, we can first overlook the size of the Tai Chi (1) and examine only the phase or angle (2).
Playing Tai Chi Beyond Space-Time
The various meditative movements of Tai Chi Chuan are called "playing Tai Chi." This means that to be "conformed to the Tao," the player' must become "as a little child." This has the effect of connecting the adult logical, left-brain mind with the intuitive, right-brain spontaneity of the inner child.
In one 'form', or series of movements, the Tai Chi 'player' visualizes a large ball of energy between his hands. He notes the sensation of its energy as he moves. This can be thought of as a three-dimensional version of the Tai Chi symbol. One can see a flowing teardrop shape. Its angle changes to represent the balance of yin and yang.
Gauge Theory uses as many dimensions beyond space and time as necessary. These dimensions represent the symmetries of nature. Changing the 'angles of imagination' of these symmetries is like "playing Tai Chi".
Chang-Sang Feng, the founding master of Tai Chi Chuan, played Tai Chi 'without leaving footprints in the snow'. Similarly, in Gauge Theory, local changes in gauge angles are possible without affecting physical observations.
Such a concept has unified two of the four forces of physics. These are the weak and electromagnetic forces. We want to build an understanding of the local nature of this Gauge Theory. To do so, we should first comprehend the four dimensions of space and time. The gauge angles are 'pinned' to these dimensions, like pins on a clothesline.
Albert Einstein, the author of Special Relativity, showed that three-dimensional space was not a suitable 'background' for physics. Thus, one dimensional time was introduced as if it were an additional single spatial dimension. He accomplished this by making time space-like. He multiplied it by the speed of light (distance = speed x time). Physical quantities could then be varied over a fourdimensional space. Distances were measured with rods and clocks.
Relativity pictures events on a four-dimensional grid. Their location on the grid is 'relative' to the
notion of the observer. Thus, Western 'devotees' of science began to realize the illusory nature of
space and time pointed to by Eastern sages and mystics. In Einstein's Theory of Special Relativity,
the present moment may be different for different observers. This echos Padma Karpo, chief authority
on Tibetan Tantric teaching (1600 AD):
"The present thought cannot be fixed as being the present... All things have no existence
in themselves; it is the mind which giveth them being." (3)
The new Relativity of Gauge Freedom goes beyond the relative nature of space and time. It considers the impelling theoretical description of dimensions beyond space and time. These dimensions are associated with qualities in the material world. This suggests a Relativity of Perception.
Like the imaginary 'ball' of Tai Chi energy, these angles beyond space-time way correspond to events in time and space. This happens if symmetries are broken. All the qualities exhibit polarity, as in the Tai Chi. They share opposing qualities, i.e., positive (yang) and negative (yin). Examples are hot and cold, light and dark, and hard and soft. As in the Tai Chi, gauge angles represent polarities at each space-time point.
Thus, Gauge Theory suggests the world has a dual nature. Hermes Trismegistus, identified by
Plato as an ancient Egyptian sage, expresses this nicely:
"Everything is dual; everything has poles; everything has its pair of opposites like and unlike are the same; opposites are identical in nature, but different in degree; extremes meet; all truths are but half-truths; all paradoxes may be reconciled." (4)
Fragments of the Kybalion
This is reminiscent of the Yellow Emperor's understanding that the universe is composed of various yin and yang combinations.
The space-time over which the Gauge Tai Chis vary can be a challenge to visualize. To help 'see' it, we can reduce its 4 dimensions a single-dimensional 'clothesline'. Any point on a physical object leaves a one-dimensional 'track' in the space-time continuum. The center of a Tai Chi master standing still, for example, traces out a line in four dimensional space-time. Though he is not moving in space, he is 'moving' in time. The three space positions remain the same while the time position changes. However, this line traced by a 'stationary' point is only one particular line in space-time. A line representing the motion of a point in space-time is known as a 'world line'. For example, simple motion in one direction could be represented by a line in two dimensions. 'x' is the distance dimension, and 't', the time dimension. Charlie Chaplin, pacing back and forth in his room, has a world line in two dimensions. It resembles two sides of an isosceles triangle. It could start at x = 0, move to x = 20 feet, and return to x = 0, while the time ordinate is increasing ).
It is hard to visualize Tai Chis at every point in four dimensions. Thus, we imagine an arbitrary
jouney through space-time, an arbitrary world line. This world line may be curved. Imagine
straightening this curved line. At each point on this 'clothesline', we visualize a Tai Chi centered on
the line. Its phase tells us something, in code, about how we are going to measure or label some
quantity at that place and time. For example, we could use the Tai Chi of Chinese lore to represent
space-time scale. Yin expands scale, and yang contracts it. Similarly. when 'playing', the yin-yang
proportion is related to position and movement.
In Tai Chi Chuan, the student 'visually' refocuses his energy as he shifts weight from one
foot to another. He imagines pouring water from one hollow leg to another as weight is
transferred. The proportion of 'water in the leg' is the 'yang'. It is related to the percentage of
weight placed upon it. Thus Tai Chi instructors speak of the 70-30 position. This is one phase of
the Tai Chi yin-yang balance. 70% of the weight is on one foot, 30% on the other ).
As the Tai Chi master moves from place to place, the Tai Chi the change is gradual. If we represent location by a 'clothesline', the Tai Chi's in adjacent locations vary only slightly.
A 'clothesline' represents an arbitrary one-dimensional journey through four-dimensional space-time. Imagine Tai Chi's strung through their centers and moved closer and closer together. They represent variations in some natural quality throughout space-time. If an arbitrary choice of Tai Chi's does not impact material observations, we call nature 'symmetric' in that quality.
The Tai Chi could be considered an additional two-dimensional space (angle and radius) beyond each space-time point. This is indicated by the plane in which each rotates. The angle of the Tai Chi represents what is called the 'gauge'. This is a mathematical construct which can represent measurement, or perception itself.
The picture of the 'clothesline' and Tai Chi's turned to various phases creates an impression. There is a free angular dimension beyond space and time into which we can code information about our physical world.
Both of Einstein's theories, Special Relativity and General Relativity, present new conceptions of
space and time. Special Relativity deals with space and time as a unity, without matter in it: flat
space. This is an approximation to General Relativity, which postulates that matter curves space-time.
Matter's gravitational attraction makes objects move in curved paths. Like a car on a roller coaster,
mass follows the 'track' of space-time curvature. The new relativity of Gauge Freedom doesn't bend
space-time, but deals with angular dimensions beyond space and time. These picture the freedom we
have to measure or perceive objects differently. As Albert Einstein said,
"When you sit with a nice girl for two hours, it seems like two minutes; when you sit on a hot
stove for two minutes, it seems like two hours. That's Relativity." (7)
Einstein, of course, knew that his relativity was different from that implied by his light-hearted example. The type of relativity he was describing has to do with Weyl's Relativity of Measurement. Our ever-changing, subjective sense of time flow could be mathematically pictured by Weyl's gauge transformations. These can be converted into Tai Chi's which spin faster or slower, depending on the individual's momentary time perspective.
In physics, dimensions represented by the Tai Chi's of Gauge Theory are called 'internal dimensions'. In its most useful form, Gauge Theory adds 'internal dimensions'. These dimensions represent aspects of consciousness, measurement, or perspective. Often, they are related to polarities (like positive and negative charge), similar to yin and yang. To represent particle fields or 'chi', particle 'location' in these extra dimensions must be included.
The arbitrary nature of the angle of an Electromagnetic 'Tai Chi' is a good example of Gauge Freedom. In this case, only one extra dimension is mathematically required. This is because only one type of polarity,is represented, that of electric charge. Thus, to describe electrical force in Gauge Theory, we need a space of 4 dimensions for space-time plus 1 dimension for the gauge. 4 + 1 = 5. The gauge freedom in this case is a representation of the arbitrary selection of the 0 point of voltage. A choice must be made, but it does not affect the forces, which depend on voltage differences.
The Polish physicist, Theodore Kaluza, was the first to recognize that the electromagnetic force could be represented by extending space-time to five dimensions (8). In 1921, he claimed that gravity in five dimensions included both the electric and magnetic forces. This differs, however, from the Gauge Theory of electromagnetism, which does not include gravity. At first, Kaluza's 5-dimensional theory was ignored as unphysical. We do not ordinarily recognize an extra spatial dimension. We think of space as being 3, not 4-dimensional.
Oscar Klein, from Sweden, resolved this problem in 1926. He suggested that the extra spatial dimension is curled up into a tiny circle much smaller than a proton. Minute, curled-up dimensions such as this are said to be 'compacted' or hidden. They are so small that they cannot be measured with our present technology.
The dimensions of the universe change with each century. A 3-dimensional world was the domain of the 19th century. Einstein's 4-dimensional space-time occupied popular fancy during the 20th century. Now Kaluza's and Gauge Theory's fifth dimension may be the inspiration for the 21st century. Perhaps this was anticipated when a '60's singing group named themselves 'The Fifth Dimension'. If the addition of a dimension of a century continues, in a million years, we may look on our ancestors as residents of some proverbial 'flatland'!
In Gauge Theory, the added 5th dimension could also be described as a circle. However, the extra dimension is not considered to be like a dimension of space. Thus, it doesn't have to be microscopic like Klein's.
We can make the dimension 'feel' more spatial. To do this, we can convert the angle of the gauge into the length of arc intercepted out of a unit circle. This can be represented as the circular arc through which a reference point on the unit circle of the Tai Chi is free to rotate. This is like twisting a clothesline, and watching the effect on the tip of a clothespin.
Alternatively, one could think of a gymnast whose feet are rotating in a circle as he does one revolution around a horizontal bar. This is like a Tai Chi. Right side up is 'yang', and upside down 'Yin'.
We are ignoring the size of the Tai Chi for now. Thus, we can convert angles to length of arc by calling its outer circle a circle of unit radius. The circumference of a circle is 2R. R is the circle's radius. If R = 1, the circumference is just 2. This is also the angle in radians (about 57 degrees) which corresponds to one 360 degree rotation.
The simplest Gauge Theory has only one extra dimension. It is portrayed by the phase or angle of a single Tai Chi. However, the number of additional dimensions in a Gauge Theory depends on the nature of the particle symmetry portrayed. Quark color is an example of a 3-dimensional quantity requiring three 'Tai Chi's' at each point in space-time.
Why has the symbol of the circle been so important throughout antiquity? Is it because the gauge dimensions of reality can be represented by circles? Hermes Trismegistus, in The Divine
Pymander, describes God's awareness of circles,
"He willed to break through the circumference of the circles, and to depress the force of
His resting on the fire (Chi). And He having all dominion over the mortal living things of the
world, and over the irrational, looked obliquely through the Harmony (Tai Chi). breaking through
the might of the circles, and showed to the downward borne Nature the beautiful form of The God
(Tao in Nature)... " (9)
It is interesting that Hermes uses the word 'force' in connection with the circles. The gauge has a similar connection to force. Gauge invariance or symmetry is the reason for the existence of forces.
As it stands, the Gauge Theory of physics always involves potentially measurable quantities. In Chapter 1, we freed ourselves from measurement which uses unstretchable rulers, uniformly ticking clocks, and non-adjustable mass scales. The freedom to measure a quantity in different ways without affecting perceptions is called gauge invariance.
In this book, we will distinguish gauge invariance from gauge freedom. Gauge freedom is defined
as the freedom to measure quantities in any way we choose. This is regardless of changes in
perception of force and notion. Thus, gauge invariance is a more restricted form of gauge freedom.
Physicists have used the two interchangeably. However, making this distinction will help us realize
alternate, useful ways of formulating physical laws. This is an important byproduct of the study of
Gauge Theory. It will become clearer as the discussion of Gauge Freedom unfolds.
Global Vs. Local Tai Chi's
In physics, gauge invariance is also called 'gauge symmetry'. A 'symmetry' is a set of ordered changes that do not affect the appearance or measurement of a particular object. We can rotate a plain rubber ball without changing the way it looks. This indicates that some physical quantity related to rotation does not vary with time.
In this case, rotational symmetry implies that the ball's spin (angular momentum) is conserved. Thus, unless influenced by another force, the ball continues to spin about the same axis at the same rate. This makes sense because there is no disturbance to the uniform rotation caused by the ball's shape.
We could represent the angle of the ball by a rotating Tai Chi. Thus, we could say that the physical circumstance is invariant under Tai Chi rotations. That is, the angle of the Tai Chi may change, but the ball's appearance remains unchanged. This 'invariance under Tai Chi transformations' is directly parallel to the concept of inverience under the Gauge Theory. It is called 'symmetry' in physics.
Consider the ball moving in space as it spins. A second 'reference' Tai Chi could be used to represent the starting angle relative to which the rotation takes place. The rotational angle of the ball is then measured from the same 'reference' Tai Chi direction everywhere it moves. The invariance of the motion to change in starting angle physicists call a 'global symmetry'. It is convenient to have the same reference direction throughout the universe. This is like defining 'up', or 'north'. That is why we call the symmetry .*global'.
Global symmetry is the simplest type of gauge invariance. We can represent it by clothespins or Tai Chi's all lined up at the same arbitrary angle. This is rotational symmetry in a two dimensional space beyond apace and time. In the Quantum Gauge Theory (described in the next chapter), it corresponds to the conservation of electric charge. Charge can be neither created nor destroyed (see Figure 8).
Such a correspondence has been shown, but without a lot of math, it must be taken on faith. The connection of global gauge symmetry to conservation of a generalized charge-like quantity is a vital relationship in elementary particle physics. This is the first discovered connection of symmetry to a conservation law. It is part of the 20th century program to convert physical laws into geometrical properties.
Rotational symmetry is the simplest form of global gauge symmetry. Electromagnetic gauge
symmetry is only one example. To picture global rotational symmetry, imagine Tai Chi's in a line.
Each is turned to the same phase or blend of yin and yang. The arbitrary angle in the theory of
electromagnetism is related to the arbitrary 'ground' voltage (a global concept).
If we didn't know about this freedom to choose a ground voltage, it would be suprising that a
chickadee could survive sitting on a high tension wire at 30,000 volts. Because the air is normally
a poor conductor, current can only flow through the bird. It cannot flow to the ground through
the air. It is not the voltage assigned to the wire that counts. It is the difference between the
voltage at the bird's head and the voltage on the wire. To picture this difference, it is convenient
and pernissable to reset mentally the voltage of the wire at zero volts. In this case, the head (or
tail) of the bird would be at some small voltage relative to the wire. Electrons in the bird's body
adjust somewhat to the electric forcefield. Thus, very little harmful current would flow through
its body. Some corona discharge of electrons may take place (this is like mini-lightning), but not
enough to kill the chickadee.
Misconceptions sometimes arise because of the subtlety of global invariances. The 'bird on the wire' is an example. Some may think that it is a given voltage (electron pressure) alone that causes current to flow through a high tension wire. They note that the high voltage at a power station can kill. A given voltage, however, has its effect only when measured relative to another lower voltage.
A current of water doesn't flow just because it is raised to a great height. It flows because that height is greater than some other point in the water's course. In the example of water flow, we can explore the analogy of voltage to height. Both may be set to zero at any given point.
This is a form of gauge invariance. It is a very simple form of 'relativity' (using the word
unconventionally). This type of gauge invariance requires only differences in some quantity to be
We could use global Tai Chi's to represent arbitrariness of the zero for pressure in osmotic flow.
An analogy to gauge invariance can be seen when nutrients in the blood stream flow through a
permeable capillary wall. When the same substance is at a different pressure on either side, osmosis
occurs. We could add an arbitrary constant amount to the pressure on both sides. This would not
change the predicted amount of osmotic flow. Global Tai Chi's could be set to represent the
arbitrary value of some reference pressure. It is pressure difference that causes osmosis, not the
actual value of the pressure itself.
Electric current, water flow, and osmosis require a gauge that is universal or global. This is not so for certain other physical circumstances. Electric and magnetic forces manifesting together require a 'local symmetry'.
We are used to measuring the same way everywhere we go. However, we have the freedom to measure differently at each point on the space-time 'clothesline'. Thus, the measurement Tai Chi will vary along it. We can define a more subtle type of gauge freedom, that of local variations in the gauge.
'Local' gauge freedom is the next level of refinement. It is represented by the freedom to twist each Tai Chi at an angle minutely varying from its neighbors. This holds to a clothespin representation. Varying the angle locally varies the 'gauge' of measurement with position in time and space. This gauge freedom 'local' because you can twist each Tai Chi in a given location independently.
However, a continuous blending of angles is required. This continuity is necessary for the mathematics of Gauge Theory to work. Without it, there would not be continuity in the imagination, a 'stream' of consciousness. As Robert Ornstein notes in his Psychology of Consciousness (echoing William James),
"The contents of consciousness vary, and expectations are transitory and fleeting. They move from one idea, object, or image to another; yet it is always the same consciousness that flows from experience to experience." (10)Local gauge invariance of electromagnetic potential, for example, is pictured in variously rotated clothespins. One might see each clothespin at a different angle as a Tai Chi. Each is rotated to a given phase ). Because the gauge is arbitrary, this Tai Chi can be turned in any direction locally. However, neighboring Tai Chi's are at almost the same phase.
These varying Tai Chis have no effect on the electromagnetic forces. (Turning a rubber ball produces no apparent change in appearance.) Thus, local invariance of the electromagnetic gauge or Tai Chi is the symmetry that physicists describe as the reason for the existence of both electricity and magnetism.
The electric and the magnetic force were once considered separate forces. Gauge Theory is one way of expressing their unity as the electromagnetic force. This was the first unification of forces in the history of Gauge Theory. This is related to the combination of electric and magnetic forces. A detailed picture of why this is so will be given in Chapter 3.
Another example of local gauge invarience is the freedom to measure size differently. This could have been discovered by the Lilliputians and Brobdignagians in Swift's Gulliver's Travels. The cubit or forearm length in one land would be different from what a cubit is in the other. Differences in measurement methods may relate to physical differences (the size of the Lilliputiens versus the Brobdignagians). However, the fundamental nature of freedom of measurement of time and size provides gauge dimensions which are dimensions in 'consciousness'. These involve potential choices by conscious beings.
'Fiber bundle' is a term used by mathematicians for the association of an imaginary gauge space (Tai Chi) with each point in space-time. Imagine the clothespins getting thinner. They begin to look like filaments or fibers. This allows us to picture the mathematics of Gauge Theory with greater precision.
The clothesline ties the fibers together tightly in a row. This can be compared to a portion of a fine Japanese bamboo screen. Adjacent strands can be twisted minutely from their neighbors.
'Fiber bundle' also describes the connection of the strands of the spinal cord to small adjacent portions of the brain. Without. stretching such, the term could also be applied to bundles of 'microtubules' within each neuron of the brain. Later in the book we will see that these microtubules may be responsible for a choice of gauge. The interactions between the fibers might hold the key to the choice of one world from the many possible quantum worlds.
Clothespins on a clothesline are a child's version of mathematical fiber bundles. However, Tai Chis will be used instead of clothespins to provide a more complete picture of the quantum gauge as a feature of the quantum wave function.
Certain types of local gauge changes (like that related to the electromagnetic potential) do not affect physical laws. This has been the key to unifying the electromagnetic force and the weak nuclear force. This avenue of research presents hope for the unification of all the forces in physics.
Unification is similar to that expressed in the words to the old spiritual song: "The leg bone connected to the thigh bone, the thigh bone connected to the hip bone..." In each case, the 'separate' plans of creation are connected by an overall scheme. For the forces of physics, the overall plan seems to give mankind the freedom to measure the cosmos differently at each point in space and time: Gauge Freedom.Modes of measurement are the 'language' of science. This 'language' can vary from experimenter to experimenter and from time to time. However, it expresses the same 'meaning' or experimental results. This is the perspective of local gauge freedom. The quantum 'gauge' freedom of measurement permits man (and possibly a higher consciousness in a hierarchical relationship), to redefine the universe continually by perceptions and thoughts. The freedom to adjust the Tai Chi from different levels of being is the connection between the distinct levels of thought (or imagination) and experience. This will lead us to an impelling interpretation of Quantum Theory, harmonizing with the Philosophy of the Tao.
The utility of the fiber bundle concept of gauge freedom has become gradually evident over a long time. It also took time for non-Euclidean geometry (curved space) to permeate physics via Einstein's General Theory of Relativity. It is exciting that the Gauge Theory paradigm is still in its early stages of application. Perhaps it will tie all the strands of physics together, like fibers in a bundle. In particular, the four forces of physics may be seen as the product of one universal symmetry. In the process one 'superforce' will be realized.
Someday, Gauge Theory will be expanded to include more than just a description of the four forces. We seek to capture the deep essence of the theory in this book. Thus, we will develop concepts and points of view that may lead scientists in many fields (including psychology and metaphysical science) to discover other uses for the gauge idea.
3. QUANTUM GAUGE THEORY
"The Tao does have a reality and its evidence. But this does not imply that it does something intentionally. Nor does it possess any tangible form. So it may be transmitted from heart to heart among the 'true men', but cannot be received as in the case of a thing having a true form. It may be intuited, but cannot be seen. Itis self-sufficient. It has its own root in itself." (1)
In this chapter, we discuss the quantum gauge. This is not a gauge on the dashboard of the Volkswagen Quantum. It is a gauge on the 'control panel' of the consciousness of the physicists who observe elementary particles. One might easily call this gauge 'The Quantum Tai Chi'.
To get at the quantum gauge, we first recall Quantum Theory says particles are made up of 'chi'. 'Chi' we identify with the quantum field or 'wave function'. Thus quantum waves are the mathematical description of 'chi' or fields. They have reality on the level of consciousness.
At times, this wave function forms a lumpiness we call a 'wave packet'. When it does, we may observe a particle in physical reality. A particle is a lump of 'chi'. 'Chi' carries energy, but is more than energy itself. Waves carry energy. However, they cannot be considered energy alone. Waves transport energy. Quantum waves are not made out of physical substance. They are waves of probability. This is in contrast to ocean waves, for example. Those are made of seawater.
Ocean waves are generated by the force of wind or tides. In standard Quantum Theory, there is no physical force generating quantum waves. However, energy can move from place to place. In David Bohm's interpretation of Quantum Mechanics, there is a quantum force described by a 'quantum potential'. This we will discuss in the following chapter. The quantum potential acts instantly across the universe to inform particles that they must behave in certain ways. This behavior violates the rules of pre-quantum or 'classical' physics.
Classically, a particle is a bundle of matter or mass. In Quantum Theory, a particle is a 'quantum'
or bundle of chi. Chi is composed of probability waves, extends everywhere, and is 'self aware'. The
'quantum potential' says it has knowledge of itself throughout the universe. A quantum has energy
and may have mass, charge, spin, etc. These quantities come in certain well defined, small units.
If Gulliver's Lilliputians were small enough to see elementary particles, they would 'see'
blue photons (light quanta) in particular sized energy bundles. Yellow photons would have
other-sized energy bundles. These tiny people could 'view' electrons and quarks spinning with the
same unit of spin. (However, spin actually has a different dimensionality from ordinary physical
reality.) All electrons would have the same amount of electric charge. Quarks have 1/3 or 2/3rds the
charge on the electron. To 'experience' quarks directly, they would have to penetrate the surface of
neutrons or protons. They would peer into that 'undiscovered country, from whose bourne no
traveler returns'. Quarks can never be found outside the protons, neutrons, and mesons which make
up the nucleus.
These particle characteristics come only in certain units. This is specified by the mathematics of Quantum Theory, the most precisely- demonstrated physical theory in history. Some quantities have been found by experiment to match predictions, accurate to the 15th decimal place! Quantum Theory and the wave function, 'Psi' or 'chi', will be around (in some form) for many years to come. The quantum mathematical function, Psi, describes the probability of various possible results of experiments. It does not directly describe the result of single experiment. Thus, like the Tao, the wave function is elusive. It does not directly relate to form or matter. It does not "do something intentionally" as Chuang Tzu intimates in the chapter heading. It is a tool for describing matter, rather than a description of matter itself. It provides a 'map' of the possibilities, rather than some reality that is 'out there'.
Fritjof Capra similarly describes modern physics in his book The Tao of Physics:
"Modern physics has confirmed most dramatically one of the basic ideas of Eastern mysticism; that
all the concepts we use to describe nature are limited, that they are not features of reality, as we
tend to believe, but creations of the mind; parts of the map, not of the territory." (2)
When mathematically describing the wave function, its phase (similar to timing) is like a 'Tai Chi'. It generates alternating yin-yang probability waves or 'Chi'. In matter, we think of the timing of ocean waves, for example, as being physically important. Ask any surfer. However, in the current interpretation of Quantum Theory, changing the phase of its probability waves has no impact on physical manifestation.
Quantum waves exist only in consciousness. 'Quantum surfing' is an imaginary sport. The arbitrary nature of phase is called 'gauge invariance'. It makes certain mathematical changes in the Quantum Tai Chi have no bearing on the state of matter.
The arbitrary nature of the gauge or phase of the Quantum Tai Chi has profound implications for
physics. This arbitrariness is the reason the forces of electricity and magnetism are necessary to
describe the world. It is the reason that light exists, as we know it in the physical world. This chapter
explains why the Tao, or the Natural Way, of the Quantum Tai Chi requires the existence of light and
"That which lets now the dark, now the light appear is Tao... The Master said: Whoever knows
the Tao of the changes and transformations (forces), knows the action of the gods." (3)
The 'classical' Gauge Theory of Hermann Weyl (described in Chapter 1) was not adequate as a relativity of space-time scale changes. Physicists such as Einstein strongly criticised Weyl's theory of gauge invariance. Gauge Theory appeared to reach a dead end. Few physicists wanted to give up the concept that mass remains the same when an object moves from place to place.
Classical Mechanics is basically the study of Newton's Laws of motion. It is based on 'inertia'. By changing the stabilized definition of inertia--resistance of mass to motion--wouldn't we be throwing the baby out with the bath water?
In Weyl's theory, the mass of a football in one place could differ from its mass in another. Can you imagine a place kicker breaking his leg just because he had to kick from ten yards farther back? However, even in Weyl's theory this wouldn't happen. The football could be 'measured' (mathematically) as very heavy at the ten yard line by redefining the meaning of a pound. It's just that the laws of physics would have to change radically to keep everything normal. It was much later that Hoyle and Narlikar showed they knew how to perform such mathematical magic.
A quest to escape Weyl's 'dillemma' took place during the 1920's. Physicists began to consider how the new theory of quanta might shed light on an important issue. When people measure differently, physical laws must be reformulated. The mistake Weyl originally made was formulating the way we measure space and time within space-time itself. This chapter describes the proper perspective of measurement provided by the Quantum Theory.
The description of measurement belongs outside of space and time in an imaginary dimension, a dimension of the Quantum Tai Chi. This new mathematical perspective was provided later (also by Weyl). However, before we can understand the 'holy grail' of this quest--the quantum gauge--we need to understand more about the quantum.
The quantum or particle nature of light was first discovered by Max Planck in 1900 12). He said
that photons are made up of certain well-defined or 'discrete' units of energy. These bundles of
energy are proportional to the frequency of light observed. He used this discrete nature of light to
derive the energy spectrum of a perfectly radiating, hot object in equilibrium. The sun is an example.
The discovery of Quantum Theory was by accident. Planck was trying to fit a theoretical curve
to the radiation observed from a radiating hole in a box. He used the standard mathematical
procedure of using finite quantities, and then letting them become very small. However, in
completing the calculation, he forgot the lest step. He found it unnecessary. The curve was fit by
assuming the finite quantities to be real. Later, these finite bundles of light were called 'quanta'.
Planck foresaw the impact that his discovery would have, when he said, "The greater (the)
difficulties (of establishing a Quantum Theory), the more significant it finally will show itself to
be for the broadening and deepening of our whole knowledge of physics." (4)
'Quantum Mechanics' describes the workings of small particles which have well-defined bundles of energy, charge, etc. Planets could conceivably be bound with any arbitrary amount of energy around a star. This depends on their velocity. Electrons, bound to atoms by electrical force, can take on only certain energies. For example, an electron in the hydrogen atom takes on only energies inversely proportional to the squares of integers. These energies are 1, 4, 16, etc. times some quantum unit.
In an atom, when an electron changes energy states, it emits a photon or light particle. Light particles emitted by an atom may have only certain energies. These energies are differences in the energy levels of the electron in the atom. The particles with these unique energies are called 'quanta', or singularly, 'quantum'. Thus, in atomic and particle experiments, energy is often exchanged or released in well-defined bundles or amounts. This process is commonly known as the 'quantum leap'. The theory that describes this world of discrete energies is called Quantum Theory.
The mathematics which structures the world of quanta revolves around finding the 'wave function', symbolized by the Greek letter Psi. The wave function, Psi, relates to physical reality indirectly. it includes all possibile measurements of physical reality. A possible measurement is like a picture of a house from one perspective. The wave function is like the total house. Many perspectives or views are possible. Psi usually represents more than one possibility. However, a physical measurement select only one.
This process of selection is called 'wave function collapse'. When one function representing one
possibility is selected in an experiment, the functions representing the other possibilities disappear.
The wave function in an 'instant' collapses from a sum of functions to a single function. To
understand collapse, and the subtle information Psi contains, we will explore 'the wave-particle
duality.Particles and No-Particles
All known microscopic experiments obey the rules of Quantum Mechanics. In them, particles have been found to behave either like particles or waves, but never like both together. This is because Quantum Theory, or 'Wave Mechanics', describes all of matter as being made up of waves of probability. These are represented by the wave function, Psi. These waves of probability collect in clumps of different frequency waves called 'wave packets'. These have particle properties under some circumstances. However, those circumstances require that the observer cannot detect the wave character of the 'quanta' at the same time.
This is similar to the dualistic nature of dust particles indicated by Gautama Buddha. He speaks
to a disciple about particles existing from one perspective, and not another:
'When, Subhuti, you consider the number of particles of dust in this world system of 1,000 million
worlds, would they be many? Subhuti replied: Yes, oh Lord. Because what was taught as particles
of dust by the Tathagata (Buddha), as no-particles that was taught by the Tathagata. Therefore,
they are called 'particles of dust.' And this world-system the Tathagata has taught as no-system.
Therefore, it is called a 'world system'. (5)
In an experiment where you can measure the wave properties of quanta, the particle properties cannot be investigated simultaneously. We must look for either 'particles' or 'no-particles'. The two perspectives were called 'complementary' by physicist Neils Bohr.
This is analogous to a leaf being a leaf when we look at it without a microscope. Under a microscope it looks like a collection of cells. The 'cell' and 'leaf' properties are complementary descriptions. They are exclusive, one of the other. What you see depends on how you look at it. If we shoot a beam of electrons at two slits and examine the screen behind the slit, we find that the 'particles' have produced an interference pattern. This is much like the convergence of two ocean waves. It is a wave property.
However, if we examine a single electron by measuring its speed, we are observing a particle
property. We cannot detect a wave property at the same time.
A particle is like a double agent. At one time the agent can act like a spy for the enemy. At another
time, he can act like a spy for the home country--never both at once. The reality is the spy's home
allegiance. For a quantum, though its true identity as a wave packet is sometimes hidden, it is
nonetheless a wave packet. The particle nature is a 'false' identity. As most spies would not hold
allegiance to two nations at once, no particle can be a particle and a wave at the same time.
The particle view of matter is left-brain oriented, and the wave point of view is right-brain oriented. Particles approach, collide, and then recede. These are processes which take place in time. They are logically analyzable as causally connected events. This type of temporal, logical perspective is rooted in the left brain.
Quantum waves, on the other hand, are cyclic or repeating. One part of the wave form does not 'cause' the other. We can picture a wave instantly as a form of oscillation extending throughout all of space. The right brain sees the whole picture throughout space. it identifies repeated patterns. When the left, more logical side of the brain is resting, the right brain sets up 'alpha waves'. These are electrical repeated wave patterns. Buddha described dust as.'particle' and 'no-particle'. Perhaps this is a way of saying that particles are particles when understood by the left brain. They are waves (no-particles) when perceived by the right brain.
Quantum Theory is thus the first theory of physics to recognize the dual perspective of perception suggested long ago by the Buddha. In the Western world, we are conditioned to think about the world in a very left-brain, logical, temporal fashion. It is this conditioning that Zen Buddhism, for example, seeks to break down.
Thus Eugen Herrigel, while practicing Zen archery, looses his logical left-brain perspective. He
transcends the idea that something has to cause every event, and gains another point of view, under
the discipline of his Master:
"How can the shot be loosed if 'I' do not do it?"
"It shoots," he (the Master) replied.
When he finally got 'it', Herrigel said, "How it happened that (the shots) loosed themselves
without me doing anything, how it came about that my tightly closed right hand suddenly
flew back wide open, I could not explain then and I cannot explain today. (6)
Zen rids the practitioner of Western logical conditioning. It helps us see objects as they are. So
also Quantum Theory has the effect of ridding us of the conditioning of hundreds of years of thinking.
We begin to see matter as something other than particles. Thus, QuantumTheory can be called the
'Zen' of Physics.
Psi: The Quantum Tai Chi
Particles can be considered to be made up of probability waves. Electrons are possibly the most important Zen 'wavicles' (probability wave packets that act like particles) in our immediate experience. They are the vehicles for the chemistry of life, 'inorganic' matter, and the forces we experience every day. The 'electronic' force acts when we hit a baseball, for example. Electrons can also be considered in a right-brain fashion, as if they were waves.
They are quite elusive characters, obeying quantum rules which do not. allow us to represent them by stating exactly how many of then will be in some small region of space. We cannot give them a perfectly well-defined density. Thus classical predictions employing their initial speed and location are inaccurate in describing where electrons are. In the atom, the electron must obey quantum rules of probability and uncertainty.
Psi, the wave function which describes the electron, is a collection of probability waves. Thus, it is a Quantum Tai Chi'. In the previous chapter, we found the simplest kind of gauge can be represented by the angle of twist of a clothespin. In the 'Tai Chi' point of view, the angle of twist becomes the 'Tai Chi' phase.
In Quantum Theory, the radius of the quantum Tai Chi also has a significance. The radius tells us the probability of finding one electron throughout space-time. One electron is the simplest case. The radius of the quantum Tai Chi squared is called the 'probability density' of the electron. It is the probability of finding the electron within a unit volume anywhere in space and time. The square of the length instead of the length itself is chosen for mathematical reasons.
The equations of Quantum Theory imply that the angle of the quantum Tai Chi (quantum gauge) is arbitrary. It may depend on what we are measuring, and where. To see how this works, let's examine an analogy. Look at a peculiar way of finding directions on the surface of the earth.
Imagine what would happen if everyone on earth were to choose a direction to call 'North' without consulting anyone else. Imagine no one knows how to use a compass or a map. North would be unique to each person. To describe the entire 'field' of directions for North, we might use an angle relative to true North for each person' definition of North. The set of angles defining 'North' along an arbitrary line on the earth's surface could be represented by Tai Chi's on a line. The angle of twist would represent the angle of deviation from true North. This is a 'gauge' representation of locally varying direction.
We will see in later chapters that we are free to use more than one gauge angle to represent particle properties. To prepare us for this extra challenge, here is an example of local gauge invariance with three dimensions.
The direction we call 'up' is arbitrary. The local freedom of choice of an 'up' direction is illustrated by different solar systems having the their planets' orbits oriented in different directions. In our solar system, we measure a planet's axis of spin with respect to a direction perpendicular to the ecliptic plane. The ecliptic is the plane of the planets. Thus, Uranus is tilted at an angle of 105o with respect to that 'up' direction. In another solar system, however, with its planets in a different plane, it is convenient to change the reference 'up'.
Also, on each planet, 'up' is different. On earth, because of the tilt in its axis, 'up' is 23 1/2 o off from what 'up' is for the solar system. This variation in possible definitions of 'up' can be accounted for by allowing a free angle, like a three dimensional gauge. The direction is chosen as 'up' depends on the directions to be compared.
Quantum Gauge Theory has a structure freely associated with certain properties of matter. There is an angle or angles for each 'hidden' particle property, as there is a Tai Chi for each quality in Chinese Philosophy.
The wave function which represents 'wavicles' in Quantum Theory is two dimensional. Since a line may represent space-time, the space quantum Tai Chi's are free to rotate through is identical to the space the wave function 'lives' in. That is, a point on the circle of the quantum Tai Chi can be described by two coordinates. One is its distance from the arbitrary space-time line. Another is its angle of twist.
Thus, the wavefunction is represented by 'Tai Chi'' of varying sizes and phase. This is an excellent way of visualizing the wave function with the gauge angle freedom included.
The 'Tai Chi'' in this picture also are given the 'magical' property of taking on different radii. This happens as the probability of finding the particle at that point in space changes. Thus, statistical laws govern the quantum 'uncertainty' in location of a tiny particle. They are related to the radial coordinate for the wave function.
This means the 'length' of Psi may be different at each point in time and space. It depends on where the particle is most likely to be sitting. This makes it a 'field', since it has varying values over the entire field of space and time (it varies over an infinite ballpark).
Some descriptions of 'Chi' sound very similar to those for a quantum wave function. Take, for
example, that of eighteenth century painter, Chang Keng:
"Chi is something beyond the feeling of the brush and the effect of the ink, because it is the
moving power of heaven, which is suddenly disclosed (as in the collapse of the wave function from
various possibilities to one possibility). But only those who are quiet can understand it." (7)
What kind of field is 'Chi' or the quantum wave function? Psi--the quantum field--is a two dimensional or 'complex' field. It is set up so its length squared describes the probability of locating a particle at a given place. To find the probability over an extended region, we would have to add up all the little probabilities in each little piece of space. On an expanded scale, for example, this may turn out to be like the particle having a 63% total probability of being in New York City. Thus. it will 37% probability of being anywhere else. A prime goal of using the equations of Quantum Mechanics is to find the length of the two-dimensional vector we call the wave function 'everywhere and everywhen'. This corresponds to the distance from the central space-time line threading the quantum Tai Chi's.
The quantum Tai Chi is a 'Western', left brain perspective on the Tai Chi of antiquity. The Taoists viewed the outer circle of the Tai Chi in an 'Eastern', right-brain way as an eternal symbol of cyclic manifestation, transcending size. However, the point of view in this book is that the size of the Tai Chi can be given an interpretation as quantum probability. This is a logical, analytical perspective, related to left-brain scientific reasoning.
In the 'Western' view of the Tai Chi in this book, the angle of the quantum Tai Chi has no influence on the results of physical experiments. In the Eastern view, the Tai Chi determines the mixtures of polar qualities in matter and consciousness. In the Gauge Theory of Consciousness developed later in the book, the interpretation of Quantum Theory will be extended to include this ancient perspective as well as the 'quantum Tai Chi'.
Probability, related to the radius of the quantum Tai Chi, is what is important in our world of observation. Probability-related predictions are not limited Quantum Theory. For example, random distrubutions of chance event about a mean produce a predicted bell curve in Psychological experiments.
We could also picture the probability that a quarterback is in each area on a football field by something like a wave function. The Tai Chi's would be larger in the center and shorter out to the sides, where the probability is smaller. Such a prediction could come about by observing the quarterback position in many games. However, in a given game, the exact location at a given time could not be predicted from this field of probabilities. In Quantum Theory the prediction comes from mathematics like that which produces the psychologist' bell curve.
Though the first dimension of the wave function relates to a precise probability at each location in space-time, the second dimension of the wave function is a free quantity. It doesn't matter what angle Psi (the quantum Tai Chi) is turned in wave function space. It doesn't affect material observations. You can think about quantum Tai Chi's in different positions. However, their phase presumably won't affect the results of a ballgame. The angle or gauge can represent how we set up arbitrary quantities in a measurement, like the '0' of Voltage.
The angle of the wave function is called its 'phase'. This is similar to the phase of a physical wave. That phase has to do with its timing. It has to do with the part of the wave being observed: whether the crest or the trough. The timing of the impulse creates the phase passing a giving point in a physical wave. The timing of several waves can add up constructively or destructively:
If soldiers march with their steps in time (in phase) across a bridge, the size of the oscillations in the bridge is greater than if they marched out of step. This is because the waves each soldier create in the bridge are in phase with the others. Their amplitudes add. Thus, a marching garrison break its gait as it crosses a bridge. This is to keep from disturbing or even collapsing the bridge.
Quantum phase is not significant when considering the overall wave function of an isolated particle. With no other 'wave' to compare it to, the quantum equation requires it to be arbitrary. The timing of one soldier marching across a bridge can be chosen arbitrarily. This is because there are no other marching soldiers with whom he has to be out of phase. In the same sense, the angle of the wave function, or gauge, is arbitrary.
The mathematics of Quantum Theory allows for an extra, free angular dimension. We will see later that levels of reality other than the physical may have a lot to do with choosing the 'gauge' of the wave function. The angle of the wave function is a connecting link between levels of consciousness.
The connection between levels of the mind can be thought of as a 'Tai Chi'. It works from a level of consciousness requiring polar forces in the next level of consciousness outward. For example, a Tai Chi could relate forces in the collective unconscious mind to forces in the conscious mind. Such a picture has its psychological implications, particularly for the male and female parts of our psyche.
The Tai Chi can thus be a bridge between one level of reality and another. One could symbolize it by a man and woman, hand in hand, crossing a bridge over a precipice. This is symbolic of the unity of the male and female sides of ourselves, which occurs when we step through the center of the Tai Chi into a higher consciousness. As Dr. Heinrich Hackmann says,
"Tao is the key to the mysterious mingling of 'Heaven and Earth', Tao (and the Tai Chi)
means the way and the method of maintaining the harmony between this world and beyond, that is
by shaping earthly conduct to correspond completely with the demands of the other world." (8)
Weyl's Quantum Theory of Electromagnetism
The magic begins when we recognize that if we change the free angle of the wave function, the laws of physics might change their form. The gauge or angle can encode information about how we measure particle characteristics. Although a change in mode of measurement may change the mathematical laws, the predicted observations don't change. An example we have already seen is the difference in the equations for force on a rider on merry-go-round when viewed by an observer on and off the rotating platform. By changing perspective, we get a new view of a given experiment. The equations of physics may change with a change in phase. This is because a change in a gauge variable may change the measurement of some other physical quantity. Changing size scale related to changing mass scale in Weyl's Theory (see Chapter 1). In Weyl's Theory a football weighs more as it is moved to a position on the playing field where the basic unit of size is larger.
How did a quantum-based understanding of gauge changes in the mathematical formulation of physics come about? The focus was on the theory of electricity and magnetism. Weyl first proposed his 'classical' gauge measurement theory in 1918. This 'gauge relativity' gave an interesting, but supposedly flawed, derivation of electromagnetism from geometry.
Shortly after that, electromagnetic theory merged with Quantum Theory. In 1927, Vladimir
Alexandrovich Fock inserted an electromagnetic term into the Schrödinger equation of Quantum
Theory. (9) He adjusted the momentum by a term proportional to the electromagnetic potential. In
this way, he could reproduce the behavior of particles like electrons in the presence of electric and
magnetic fields. In these fields, the momentum will change because of the forces the fields apply to
the particles. Momentum represents movement.
It's like getting into the aura of a happy person on a train. Your own 'momentum' may change. You might feel happy too. The field or 'chi' of the person's aura produces a force on your nervous system. It changes your 'momentum'. Similarly, electric or magnetic fields can accelerate the motion of an electron.
Fock's quantum electromagnetic equation included the strength of the electromagnetic force. To
do so, it had to contain the quantum of electric charge, symbolized by the letter, 'e'. His rewriting
of the quantum equation was done without any justification, except that it gave the correct
experimental predictions. Thus, this is writing it in 'by hand'. He did this, instead of deriving what
quantum electric and magnetic behavior should be like from Quantum Theory alone.
Writing it in 'by hand' is like the laborious task of scribes and monks. Before the invention
of the printing press, they copied every book in existence. The process of putting a term into a
physics equation to fit a separate theory can be a laborious task as well. Fock had to be sure that
all the relevant variables in the new term were correctly included. The old theories had to fall out
of the new combination. The term also had to have the same units as the other terms in the
The Fock term in the Schrödinger equation contained the connection between gauges of measurement of space and time in different space-time locations. This connection was noted by Weyl originally. The connection is the electromagnetic field, sometimes called 'A'. (The Yang-Mills theory used 'B' for a different gauge field.) The new quantum equation, with electromagnetism included, described electromagnetic interactions of particles with each other. This it did as well as describing interactions of particles with fields.
The theory's relativistic (high speed) version is capable of describing, for example, the motions
of charged particles in particle accelerators. Any charged particles under the influence of electric or
magnetic fields are covered by this theory. The theory is called 'Quantum Electrodynamics'.
The late Richard Feynmann, originator of an insightful formulation of Quantum
Electrodynamics, used to call this theory 'QED'. This is the signet placed at the end of a
mathematical proof. It means, 'I have demonstrated that which was to be demonstrated'--quad
erat demonstrandum. Some still think that the QED theory of physics is as exact as a
mathematical proof. The resulting evidence is good to beyond 15 decimal places. It provides
a value for a constant, related the charge on the electron, which can be tested to at least that
We want to illumine the original Fock version of electromagnetic Quantum Theory in the light of Weyl's original gauge theory. To do this, a connection is needed. It describes how the gauge or measurement changes from place to place and time to time. A table of time changes for time zones around the world is an example of a connection.
The electromagnetic connection for the gauge is a vector field. It is defined as a set of four quantities for each point in space and time. To the theorists, the connection was a vector field. It meant the particle representing the field had a unit of quantum spin. It was a light particle, a photon. It is now recognized that charged particles create a field of light ('virtual' photons) around them. This 'chi', 'aura', or 'field of light' transfers energy to other charges entering its domain. Thus, the photon's existence is a prescription for insuring gauge invariance in Quantum Theory.
Charged particles have an 'aura' of light. This somewhat like Eastern 'enlightenment'. In Tibetan
lore, enlightenment is a process of bringing to 'light' the true nature of the Self. It is a condensation
of the cloud of virtual 'photons' of being into a concentrated forcefield. It is an illuminating 'cloud'
which, for the initiated, condenses into the 'Clear Light' behind all manifestation.
"It has been said that the True State of the mind, the Thatness of all things, inseparable from the Voidness, beyond the domain of phenomena, while experiencing the thought-transcending Great Bliss, is the primal Clear Light." (10)
The Guru Padma Karpo
Physicists could comprehend the fact that light itself from a gauge connection in Weyl's Theory. However, there was one incomprehensible fact. The connection (the field) had to be-multiplied by -1 often called 'i'. This requires that small changes in the measurement gauge between nearby locations not be a real number. It doesn't obey the laws of elementary arithmetic. The 'physical' parts of the equation are real numbers. However, the gauge term in the Schrödinger quantum equation is 'imaginary'.
Imaginary numbers were invented by Raffaele Bombelli in 1572. At the time, the real numbers covered all physical quantities. Since these numbers were distinct from real numbers, they were termed 'imaginary'. The implication was that they were non-physical.
Leibniz, the philosopher-mathematician, called 'i' the "portent of the ideal world." Arthur Paul,
a modern writer, has said that the multiplication by 'i' turns a "real number, which is the symbolic
representation of an object, into an 'imaginary' number, which is the symbolic representation of
an imagined object.
Thus small changes in gauge in nearby space-time locations are mental adjustments of measurement.
Fritz London from Stuttgart came up with a further understanding of the imaginary gauge term. This was the same year as Fock's suggestion. It was based on Carl Friederich Gauss' interpretation of 'i times a real number' as a rotation of that real number by 90 degrees. New numbers could be made by adding real numbers to imaginary numbers. Call them 'complex' numbers. They express rotation through an arbitrary angle. This converts a line to a rotating Tai Chi.
London revealed that the electric-magnetic term in the quantum equation came from the phase of wave function, Psi. It could have an arbitrary phase factor multiplying it. (12) The phase is the free angular dimension of the quantum Tai Chi. Thus, the freedom to choose a gauge or phase at each location requires that the electric and magnetic forces exist.
Gauge freedom requires the existence of the term Fock tacked on to the quantum Schrödinger equation. Quantum Theory alone, with no additional postulates, mandates the existence of electromagnetic fields.
Units of electric charge are known not to change. Also, associated particles do not change their motion unless acted on by a force. However, the quantum Tai Chi phase (specification of the location of crests and troughs in space-time) can change. The ability to accomodate such changes must be accounted for by a field or 'chi'. This field is a 'cloud' of photons around an electron, for example. This cloud of light particles is responsible for electric and magnetic forces. Charged particles exchange the chargeless, massless bundles of light we know as photons.
Consider the Chinese baseball example given in the previous chapter. The freedom to move the bases while the ball is in the air implies that the base runner must use different forces. These are applied from foot to field, when the bases are in different positions. In the 'game' of Quantum Electrodynamics, we are free to set the phase of the quantum Tai Chi. This means electric and magnetic forces must exist to compensate for local variations in that Tai Chi. These are analogous to changes in the positions of the bases in.Chinese baseball. This freedom of phase is 'phase symmetry' or 'gauge symmetry'.
However, as C. N. Yang pointed out, a change in phase is an imaginary change in gauge. It is not only women who are allowed to change their minds, particularly where measurement is concerned.
'Phase' refers to the timing of waves. The phase factor is allowed to have freedom in dimensions other than time, if desired. In fact, it was eventually seen that phase freedom was realized as Gauge Freedom (standard definition). Gauge Freedom allowed free choice of angles in any dimension set up to picture how we measure.
The phase factor was known to be 'connected' to the electromagnetic potential. However, it was not yet clear what it meant. This was left for Weyl to tie together in 1929.
A brief analogy way help us get an idea of how the phase factor relates to the connection. A standard clock is a type of Tai Chi. At each successive hour, the 'clock Tai Chi' has a phase corresponding to one of the twelve numerals on the clock face. A phase factor can be used to rotate mathematically the hour hand on an imaginary 'Tai Chi clock'. The rotation of the phase factor can be represented by an angle. Thus, the connection in the time direction is the rate of change of that angle with time. The angle of the hour hand on the 'clock' changes by 360/12 = 30o every hour. Thirty o/hour is the time component of the connection. If we change the gauge by doubling the speed of the clock, the connection would double. The mechanism which keeps the clock running would have to produce different forces.
The mathematical reason for the existence of electric and magnetic forces can be explained as follows. The quantum gauge can depend on space as well as time. Its connection is the rate of change, with respect to space and time. Thus, we need 4 numbers to specify the electromagnetic field. This is because the connection is related to four different rates of change of the gauge.
The connection must describe how the gauge changes as one moves in each of the 4 directions in space-time. There has to be a rate of change of the gauge with respect to x, y, z, and t. For a one number gauge you get a four number field, and a four number field is an electromagnetic field. The electromagnetic field's existence implies that forces like the electric and magnetic forces must exist. They require the existence of a photon field around charged particles.
This understanding of the relationship of the quantum gauge to force was momentous for the progress of physics. Weyl indicated the imaginary scale change suggested by Fock and London was related to a certain arbitrariness in the potential. This is represented by a 'gauge transformation'. (13)
To understand gauge transformations, consider an example. Change the zero point for measuring height. An object is dropped in the presence of a gravitational field. With a change of the position of zero height, there is no change in the physics of the particle's fall. This is gauge invariance.
Weyl's study showed that the angle of the wave function could be arbitrarily chosen at each position in space-time. This is like twisting the clothespins smoothly to different angles.
Freedom to rotate all the quantum Tai Chi's to the same angle (global symmetry) implies conservation of electric charge. However, global symmetry alone does not imply the existence of magnetic force. Weyl showed electricity and magnetisn could only be motivated from Quantum theory in a unified way by a local gauge symmetry. The wave function Tai Chi's are free to be rotated differently from place to place and time to time.
In a similar way, anyone is free to set the hour hand on clocks at. at any angle at different locations
and times. This is a freedom you might call 'freedom of time' (a freedom of consciousness). It is a
type of gauge freedom. An angle is involved. These freedoms do no affect the physical world. They
merely involve a change in perspective. The following Zen poem illustrates in word pictures how one
level of reality does not affect another:
"The bamboo shadows are sweeping the stairs,
But no dust is stirred.
The moonlight penetrates the depths of the pool,
But no trace is left in the water." (14)
Gauge Freedom is illustrated by the example of a pen dropped by a secretary in an office. This demonstrates limited global gauge invariance. The object falls the same no matter where we measure its height from. It is change in height, not height itself, that determines the motion. The zero of height could be assigned to the floor or the top of a desk, for example. However, we cannot define height differently in different places. This is because 'place' enters into the notion of the object. The pen drops from one place to another. Therefore, height must be defined 'globally' in a given experiment measuring gravitational fall.
Similarly, the electric potential is globally invariant. Its zero can be set arbitrarily. Ground does
not have to be zero potential. However, it is customary to say the earth has zero potential. Set a
ground potential or voltage for the Earth. We are setting it relative to everywhere else in the universe.
Venus probably has a different ground potential than the Earth. While in a sealed spacecraft on
Venus, we would probably refer to its ground as zero potential. This is changing the gauge
globally, or universally. Setting Venus ground as zero, fixes potentials all over the universe. This
is 'fixing' the gauge. The symmetry for electric voltage is global because the definition of potential
itself is tied to place.
In another electrical illustration, a battery has a potential difference across its terminals of 1.5 volts. We measure the potential of each terminal relative to say some point on a charged plate. Thus, one terminal may measure 75 volts, the other 76.5 volts. The difference between the two is 1.5 volts. This is much like time zones. The laws of time zone changes don't change with what time it is. That is a global definition we set by defining Greenwich Mean time. The laws of time change are represented by differences in time as we cross zone boundaries.
The contrast between 'global' and 'local' gauge invariance has been rarely described in laymen's
terms. Robert Crease and Charles Mann do an excellent job in their book, The Second Creation. This
is an instructive review of the personalities who have made the revolution in 20th century. They draw
an example of global symmetry.
"from the world of high finance... If the income of every person and the price of every commodity
suddenly increased tenfold, nothing would happen. People would still spend their wages on the
same things in the same way, except now paychecks and prices would have an extra zero. The
supply and demand of every commodity would be undisturbed and, in the jargon of economists,
all markets would still 'clear'. The forces of supply and demand can be said to be globally
symmetric with respect to a change in the economic measuring stick--money." (15)
Crease and Mann then describe local symmetry in economic terms,
"Now imagine that incomes and prices were to jump around randomly, some rising, some falling
by different chance amounts. The situation should then change dramatically: supply and demand
would be out of whack. Some people would be clamoring to buy more than is currently offered
for sale, while others would be unable to afford their previous standard of living. This state of
affairs, according to classical economists, brings into play the 'invisible hand' of market forces.
Prices adjust, decreasing in one place, increasing in another, until once again all markets clear.
Automatically compensating for each random change in the system, the invisible hand maintains
the original symmetry, which in this case is a local one." (16)
It was clear to Weyl that local gauge invariance was responsible for the very existence of both electric and magnetic forces. (Similarly, price changes are responsible for forces which change supply and demand.) This is because the connection--the electromagnetic potential--creates a term for itself in the energy equations of Quantum Theory. The form of the connection can be mathematically derived from the quantum gauge. Thus, electromagnetism falls naturally out of the more inclusive theory of Quantum Mechanics.
It is almost incredible that the formalism of Quantum Mechanics had electricity and magnetism hidden in it for Weyl to discover. This was the beginning of a true Quantum Theory of electricity. It also eventually stimulated the quest for a 'holy grail' in the imaginations of physicists. It is that all the forces might fall out of the hidden gauge dimensions of Quantum Theory. Were this true (and this must include the force of gravity), Quantum Theory would be the Theory Of Everything. This the ancient Chinese had already seen, from a different perspective, in their universal Tai Chi. Gravity is the most difficult force to fit into the gauge description. Therfore, unifying Quantum Theory and gravity has been the passionate goal of many a theorist. A gauge theory of Quantum Gravity would be highly prized.
Electromagnetic gauge freedom became the archetype or model for all future gauge theories. However, there is a primary difference in the gauge for forces other than electromagnetism. It is that the gauge can be constructed to express other dimensions than that of the electromagnetic gauge. All gauge theories have charges and currents that are conserved. Also, each Tai Chi in Taoist Philosophy is related to a type of yin and yang. The sum of yin and yang is always conserved. This can be geometrically determined from the diagram of the Tai Chi. In Gauge Theory, conserved charges and currents may not be just electric charges and electric currents. We call other 'charges' by different names. However, they behave similarly, in that they display polarity, like yin and yang.
In the next chapter, we will find the wave function in a given location behaves like a highly
conscious being. It knows what all the other Tai Chi's are doing. It represents the Tao. In so doing,
the quantum Tai Chi--and related material existence--takes on dimensions of cosmic consciousness.
4. GOD AND THE QUANTUM GAUGE
The disadvantage of regarding things in separate parts is that when one begins to cut up and analyze, each one tries to be exhaustive. The disadvantage of trying to be exhaustive is that it becimes mechanically exhaustive. One goes deeper and deeper, forgetting to return, and only sees the ghost of external things.Chuang Tzu
Dr. Bertlmann's Socks
An illustration of Chaung Tzu's critique of cutting up and analysing is the 'strange case of Dr. Bertlmann'. This is an anecdote used by quantum physicists to clarify 'quantum wholeness'. Like some quantum experiments, Professor Bertlmann has a predictable unpredictability. His students observe he always wears color-mismatched socks. If he walks into a lecture with a pink sock on his leading foot, he is not wearing pink on his trailing foot. Also, the color of a sock on a given day is hard to guess. Yellow for the leading sock is as likely as blue or green. His students, however, are ignorant of one important fact. Mismatched socks are Dr. Bertlmann's non-conformist intention. Like Professor Bertlmann's socks, separate 'particles' often behave as if they were coordinated in their properties. Alain Aspect, a physicist at the University of Paris, demonstrated such 'quantum wholeness' in 1982. Pairs of photons emitted from an atom in opposite directions were found to have their polarizations opposite one another. This occurred more often than one would expect by chance. 'Polarization' is when light waves vibrate in a plane.
Quantum Theory predicted the Aspect result. However, there was no rational way to explain how one photon 'knew' what the polarization of the other was. Before the observation, each photon's polarization was supposed to be random. Aspect made sure that they couldn't signal each other at less than light speed by measuring their polarizations simultaneously.
Physicists interpret this experiment in several ways. One view is that we must give up the existence of particles. Another view is that signals are not limited by the speed of light. The more revolutionary perspective reminds one of Dr. Bertlmann. Perhaps there is an unbroken whole with a plan, a 'quantum interconnectedness'. In this plan, particles are capable of instant telepathy. They are unpredictably coordinated, like Dr. Bertlmann's socks.
Confucius was asked about the sage Wang T'ai. This teacher had his legs cut off and did not
speak. Confuscius' followers wondered how he managed to reform others without speaking.
"From the point of view of the differentiation of things, we distinguish between the liver and the gall, between the Ch'u State and the Yueh State. From the point of view of their sameness, all things are One. He who regards things in this light... beholds the unity in things, and does not notice the loss of particular objects. And thus the loss of his leg is to him as would be the loss of so much dirt."
In Quantum Theory, the 'unity in things' is specific. The two polarizations in the Aspect experiment are instantly connected. To explain, we don't have to give up the 'common sense' notion that a photon always has a definite polarization. The 'hidden variable' hypothesis makes this claim. However, Quantum Mechanics is usually interpreted as denying the polarization exists before it is observed.
What if we didn't know Dr. Bertlmann's feet belonged to one body? We might think that one foot
always 'knew' not to wear the color sock the other was wearing. However, we are dealing with the
whole of Dr. Bertlmann, not just his feet. Before observing one of his feet on a given day, we
wouldn't say that his socks didn't exist. We would, however, probably want to know why his socks
were uncoordinated. A similar curiosity motivates 'hidden variable' theorists.
"Reaching from the Mystery into the Deeper Mystery
is the gate to the Secret of All Life."
Dr. Bertlmann's choice of sock color is like a particular choice of gauge in Quantum Theory. We will see that choices of gauge (or modes of measurement) which influence quantum results might be made.
In some 'hidden variable' theories it is assumed that particles exist classically. They have positions and speeds as in classical theory. However, they move in unexpected ways, hidden from our perception. Their unfamiliar motion comes about because they 'partake' of what is going on in the rest of the universe.
This chapter will discuss ideas like the above in the context of Gauge Theory. Without considering the gauge, this interconnectedness (like Taoist 'oneness') is not fully explained by Quantum Theory. The gauge is like the vehicle for a consciousness beyond space and time. It may work to bring about results in quantum experiments.
To reach this conclusion, we need to understand current views of quantum 'consciousness'. Thus,
we explore several widely-accepted interpretations of Quantum Mechanics. Then we will integrate
our knowledge of the quantum gauge with these interpretations.
Wigner's Mind Wave Philosophy
We have seen that electromagnetic force is intimately related to the quantum gauge. Gauge Theory is used to 'derive' other forces as well. Physics formerly sought to define the nature of 'force'. Now the quest is to define the quantum gauge symmetry 'causing' each force. Once you define the right gauge, the theory is simplified. Everything can be described by probability waves and a measurement prescription.
These waves are complex fields (chi). They are made up of a probability and an angle at each point in space-time (a quantum Tai Chi). They involve imaginary numbers and relationships.
One interpretation is promoted by Arthur Paul and the mathematician Charles Muses. It is that the 'i' in imaginary involves the human imagination or mind. (1) Muses quotes H. Stanley Redrove, mathematician and chemist:
"If some 'real' number be regarded as representing a certain material thing, then the corresponding
'imaginary' quantity, i.e, the product of this real number and i (the square root of -1) may be
regarded as representing the ideal prototype of this thing."
For example, if the number 3 represents three apples, the number 3i can represent three imaginary or 'thought-picture' apples. Three real apples plus three imaginary apples can be written, 3 + 3i. This is what is called a complex number. It is 'complex' because it is the sum of two different types of numbers: real and imaginary. Wave functions are complex. Thus, they represent the 'interface' between consciousness and physical 'reality'.
In this view, the complex wave function is in the mind of the observer. It also represents physical reality. Before measurement, the prototype consists of a set of quantum possibilities. After measurement, only one possibility is realized. In this 'philosophy', everything is based on mind waves of possibilities and the actualities resulting from measurement.
Quantum Theory is like a complicated 'miniature golf course' embodying quantum possibilities and measurements. There are often several routes leading to the same 'hole'. Miniature golf has channels, rebounds, and underground tunnels. A choice is necessary. A given choice is like a quantum measurement. However, the selection in standard Quantum Theory is ruled by statistical probability. The experimenters who set up the possibilities are like the builders of the 'golf course'. They have gauge freedom: the freedom to decide how to measure.
Gauge Theory is an extension of Quantum Theory into an extra free dimension, the quantum phase. Quantum waves are not only waves of probability. They have a freedom, allowing imaginative ways of observing and experimenting. You might call the extra quantum phase angle a 'twist of the imagination'. Every good mystery has a 'twist'. The 'twist' in the quantum mystery is how we measure. This has been hinted in previous chapters. However, we described only space-time scale changes and electromagnetic potential changes. We will now see that any decision or measurement can be given meaning in Gauge Theory.
Quantum 'reality' is in the consciousness of the observer. This idea was first championed by John
Von Neumann in 1932. He laid the rigorous mathematical basis for Quantum Theory in his book, Die
Grundlangen. (2) He showed there is no ordinary world out there, if one believes Quantum
Mechanics. Eugene Wigner, a life-long friend of Von-Neuman, later extended this to mean: "the
content of consciousness is an ultimate reality." (3) This he claimed because, "If one speaks... of the
wave function, its changes are coupled with the entering of impressions into our consciousness." (4)
"The myriad things take shape and rise to activity,
But I watch them fall back to their repose.
Like vegetation that luxuriantly grows
But returns to the root (soil) from which it springs."
It is as if the tree falling in the forest does not exist unless there is 'someone' there to perceive it. The perception of its fall is registered in some kind of 'consciousness'. The question whether this 'someone' could be an animal or a computer is still under debate. However, some 'living' being has to observe the results registered in a computer for them to exist. It could even be argued that it is 'God' within a living being who lends reality to the data by perceiving it.
Because of this 'consciousness' interpretation, Wigner predicted that "physics and psychology...
may yet be united into a common discipline without overtaxing our mind's capacity for abstraction."
(5) We can get a glimpse of this when we transcend the limitation of a single observer.
The 'mind-wave' viewpoint finds its mystical adherents. More than one observer can share wave
functions. This means imagination can be shared. This is like the collective unconscious of the
Psychologist Jung, the cosmic consciousness of Walt Whitman, and the universal mind of
Hinduism. All potential perceptions are shared at some inner level of human consciousness.
If we believe in such an interpretation, the Quantum Gauge Theory of Everything (QGTOE) seals the victory of the quantum mind revolution. This revolution promotes an 'internalized' world picture. Perception comes out of universal mind waves with a free dimension. We have freedom of choice to observe the world as we wish. This suggests 'free will'. Also, the belief there is a world out there is a cosmic 'trick' or 'Maya' (Hindu for 'delusion').
There are several loose ends in such an imaginative picture. First, is there any way to avoid 'God' merely playing dice with the universe? Einstein posed this question. After all, Quantum Mechanics is the best theory of everything we have. It requires a picture of possibilities, not absolutes. One could claim that it is not a dice-playing God. We could say 'God within' or the 'cosmic mind', as the shared imagination, creates the quantum possibilities.
However, the equations of Quantum Theory do not tell us which of their solutions will be achieved in a given experiment. They don't tell us what the result will be. Quantum Theory does allow for freedom, through the quantum gauge, to set up these 'quantum golf courses'.
Instead of rolling dice, this hidden reality or 'cosmic mind' could make the quantum choice. Karma, retribution, mercy, or a combination may select which quantum states are possible. This sets bounds of limitation. Such 'meta-physics' suggests a preliminary collapse of the wave function to a subspace of quantum states.
Within these bounds, the individual ego consciousness might choose further collapse. This is what happens when a quantum experiment is set up, or when a life choice is made. The final collapse to a single possibility is up to statistics, karma, God, mercy, or grace. We must recognize, however, that karma is usually made with macroscopic beings or objects. Single microscopic events may not be strongly influenced by it.
Thus, free will can go hand in hand with the dictates of karma. Could there be a quantum gauge or gauges that do this? Could we insert the very notion of quantum measurement into the gauge? These are some of the concerns of this book.
The second loose end in the quantum mind-wave philosophy is a more difficult challenge. How
is one wave function possibility chosen? How does the wave function collapse? Its collapse during
measurement has been under hot debate since Bohr and Einstein stayed up late sharing second-hand
We think of Einstein as a serious and moral person. However, in at least one case, he exhibited
almost an impish behavior... He was working in the same building with Bohr. He ran out of pipe
tobacco, and contrived to steal some from his colleague. Bohr had his back turned. He was
looking out the window. Sneaking into his office on tiptoe, Einstein went to Bohr's desk. He
opened a pouch in his drawer, before he heard him. Both Bohr and Einstein were soon rolling in
Bohr and Einstein often wrangled over Quantum Theory. The theory assigns probabilities to possible observable quantities. Like a pair of dice before you throw them, there are probabilities for each number to appear. However, only one possibility is selected. The quantum equations do not describe how the wave function collapses from many possibilities to one.
Gauge Theory may provide a solution to the collapse problem. This solution first suggested itself
while I was considering the work of Sir Arthur Eddington.
Sir Arthur Points The Way
What is the meaning of this imaginary gauge freedom? Is it a freedom to conceive of measuring time and space (and other quantities like spin and particle identity) differently? Is it in the imagination, because of the 'i' factor? Does it say that time and size are all in the mind? Sir Arthur Eddingtion, the master of the mysteries of the evolution of stars, had what I believe are the beginnings of a reasonable response.
Eddington was like Dr. Bertlmann in some ways. An excellent speaker, he popularized the Big Bang Theory in the lecture hall. However, in his later years, he kept to himself. He worked on theories in directions no one else considered. Eddington did most of the work he is recognized for in the 1920's and 30's. However, his most mysterious work was published posthumously from his notes in 1953. This leaves a 20 year gap in progress on the Gauge Theory. The theory needed time for experimental particle observations to catch up. It needed time for Eddington to come to the penetrating viewpoint expressed in his Fundamental Theory. (6)
This work is full of complex 'number magic'. His derivation of Hubble's constant scaling the expansion of the universe is a factor of about 15 off. However, he has an interesting interpretation of the quantum phase factor. It is surprising this description lies buried and unrecognized in his work. In fact, the only reference to it I know of is in Arthur Young's writings. The Geometry of Meaning is an example. (7)
Eddington's goal in his Fundamental Theory was to calculate the values of natural constants from universal principles. For instance, he derived mathematically the ratio of the mass of the proton and the electron. He also derived the value of the fine structure constant, which gives the relative strength of the electromagnetic force. There are many errors and obscurities in his notes. This is expected for a manuscript not ready for publication at his death. Perhaps this explains why his contribution to Gauge Theory and the theory of measurement has gone unnoticed.
However, Eddington had something important to say about the quantum gauge. This is the quantum Tai Chi angle x 'i'. We include the 'i' to keep Weyl's original gauge relativity intact. In explaining the nature of quantum measurement, Sir Arthur considered measuring one quantity for a single particle. He said the experimental equipment and the particle can be represented by an imaginary 'comparison particle' and 'object particle'.
The object particle is an image of that which is to be measured. The comparison particle is an
imaginary standard particle for which the quantity to be measured is known. Each has a wave
function, and the wave function for the combination is the product of the two (Psi comparison x Psi
object). This is always true for two non-identical particles considered as a 'system' in Quantum
Measuring the height of a growing child can be accomplished in a similar way. We can compare
it to the height of an adult who has stopped growing. The child is like the object particle, the
adult the comparison particle. The key is, that though the child's height is unknown, the adult's
height is. It is interesting that people can probably be represented by wave functions, as particles
The comparison particle wave function can be expressed simply as a quantum phase factor involving a gauge angle. It embodies the gauge or the standard of measurement. This is like a father who is a stable 6 feet 1 inch tall. He is an excellent gauge for measuring the variable height of his children. (Sometimes this is done by determining how many hands short of his height the child is.)
Eddington's proposal is a precursor of a Gauge Theory of quantum measurement. However, how
does a quantum gauge produce a result by collapsing the wave? He left this vital question
How Does Consciousness Collapse Psi?
Consciousness can collapse the wave function. Let's take Eddington's description a step further, in a direction he didn't consider. All the quantum possibilities exist in a space which we can make into a gauge space. We can associate it with each point in space-time. This is called 'Hilbert Space'. It is named after the mathematician, Hilbert, who invented it. The equations of Quantum Mechanics don't change with rotations in this imaginary space. This is Hilbert gauge symmetry. Though the full picture is presented in Chapter 7, we can begin by giving a preview here.
Rotating the wave function in Hilbert space is like viewing the same object from a different angle.
Specified views of Psi give a different value for the measurement. Thus, quantum measurement is like
taking a unique perspective on the wave function in the space which contains the quantum
In a similar way, an architect can use a 3-D computer software to create a detailed picture of a
house. He can rotate the house to see it from various perspectives on his computer monitor: the
front, the back, the sides. He can then print out any of these views by typing in the 'print'
The software the architect puts into his computer is like a portion of the superconscious mind or Hilbert Space. This has programmed into it the quantum possibilities in the experiment. Designing the house is like setting up the experimental details: the dials, and meters, counters, etc... This tells us what possibilities will be included in the wave function. It also determines what their relative probability will be.
The house is like the wave function. Printing out a view of the house is like performing the experiment. The result is only one perspective on the wave function in superspace. The view of the house on the page is something 'physical', like the result of a quantum measurement.
Before the measurement, one quantum possibility is as good as another. This is a type of gauge invariance. The 'stickler' is that all possibilities don't have the same probability. However, changing from one possibility to another doesn't alter the quantum Schrödinger equation.
Thus, consciousness is the domain in which the gauge doesn't matter. However, 'physical' reality is not gauge invariant in this sense. 'Physical' reality does not 'exist' before the measurement. Thus, consciousness is free to choose a gauge which rotates the wave function to one possibility. How is this choice made? Chapter 7 shows how the brain may accomplish this task.
Wave function collapse is like jumping up another level of reality. Superconscious gauge transformations leave that part of consciousness which represents physical 'reality' unchanged. Superconsciousness is the 'software'. In it, changes programmed by consciousness don't affect the physical until they are 'printed out' by observation. A gauge choice can rotate the wave function and reduce its components. Thus, it can be set up to represent fate, karma, mercy, and grace. These can be considered 'forces' in consciousness which widen or narrow the quantum possibilities.
If Quantum Mechanics is a theory of everything, it should describe the limitations and choices we
have in life.
The Gauge Theory of Quantum Measurement might apply to life circumstances. Consider John,
a physics major just out of college and looking for a job. He is trained in astrophysics and has
some lab experience with infrared detectors. This qualifies him to work as a technician
developing infrared equipment for observing astronomical objects. However, to get a job, he
must look into a wider range of possibilities. He sets a gauge by choosing to contact a company
working in the broader field of experimental physics. Another gauge, that of his 'fortune', lands
him seven interviews. In one of these, he finds he isn't really qualified for the job. Another
employer doesn't like the birth mark on his ear. Several others don't have positions available. In
the end, he winds up with two job offers: neither of them is in astrophysics. This is a finer gauge
of his fortune. He then has a decision to make between the two. He can work for a laser
manufacturing company as a design assistant or test solar heating devices for an energy firm. He
makes the final choice for the solar energy work, because he likes the idea of promoting clean air.
This is a final choice of gauge.
The above train of events doesn't involve any single microscopic quantum measurements.
However, statistical laws might be involved in some of the changes. We also don't know for sure
whether John and his environment can be represented by quantum wave functions. These unknowns
await determination by clever experiments and observations.
Healing Schrödinger's Cat
There are circumstances in which consciousness might collapse the wave function. Consider a variant on the famous quantum 'paradox', Schrödinger's Cat. Erwin Schrödinger formulated the first quantum wave equation. In the usual version of the 'paradox', Schrödinger's very own cat is placed in a closed box. Inside, is a radioactive source with a 50% probability of emitting a detectable ray in a given time. (8) Should a detection occur, the detector triggers a hammer that bursts a vial of poison gas. The cat expires. The box is opened when the time is up. The cat is found either alive or dead with a 50% probability.
Before the box is opened, the wave function contains both the alive and dead states for the cat. These two quantum possibilities have equal probability at confinement's end. Thus, Quantum Theory says the cat is simultaneously alive and dead. (Lao Tzu might agree.) This is incongruent with reality as we normally understand it. However, it is the way the currently-accepted quantum interpretation views the situation.
This is level confusion. Above, we have proposed a three-level picture of existence: physical, conscious, and superconscious. The conscious level is where the wave function is half 'alive cat' and half 'dead cat'. It is different from the physical level where only one is possible.
What happens if the radioactive source goes off and the vial is broken, yet by some miracle the cat lives on in a very sick state. One can see why physicist Evan Walker says in Physics Today, "being a cat lover, I want to object to the entire experiment!" (9)
If Schrödinger's cat is sick, it is then in need of healing. We can put him through the experiment again. This time a fast-acting antidote replaces the poison gas. In this second experiment the cat is sick and well with equal probability. This is a little more humane. We would probably give him the antidote after the experiment anyway. However, what if the cat's karma, God's mercy, or the group soul of cats decides to give the cat the antidote? Could the quantum chances of healing be altered? Evan Walker thinks so.
Then why is it that experiments follow the statistical laws of Quantum Theory? They have
well-defined probabilities for different possible outcomes. It could be that karma and metaphysics
aren't a factor in the experiments so far performed. Where only microscopic particles are concerned,
a macroscopic karma doesn't pertain. However, when we mix microscopic objects with macroscopic
objects or subjects, it is possible that it does. The gauge could embody this. As A. J. Leggett writes
in a tribute to David Bohm's retirement in 1987,
"the assumption that the laws of quantum mechanics apply to macroscopic, complex, and possibly highly-organized systems of matter, in the same way they do to microscopic objects such as electrons and atoms, is just that: an assumption, for which at the time of writing there is no direct and little circumstantial evidence." (10)
To investigate the applicability of quantum mechanics to macroscopic systems, Leggett recommends SQUID experiments. SQUID stands for Superconducting Quantum Interference Device. This is a superconducting wire (no resistance) bent into a circle with a small gap in it. Quantum theory says that electrons in the wire could 'tunnel' through the gap. This happens because of quantum uncertainty in position. However, some electrons would bounce back, creating currents in both directions.
The many electrons in these two currents each make up a 'macroscopic' system. If Quantum Mechanics holds for this macro pair of systems, the probability waves of the wave function for the two opposing currents should interfere in a specific way. As Claudia Tesche from IBM has pointed out, this should produce measurable irregularities in the currents over time. (11)
The quest to understand the difference between macro and microscopic systems should not end with SQUID experiments. These experiments involve quantum possibilities that may elude obvious influences of karma. A search should be made for the influence of karma and free will on macroscopic quantum events. This would specifically involve highly-organized and evolved life systems like humans or animals.
There is plenty of room in a Gauge Theory for such possibilities. Even single microscopic events may be 'caused' by conscious or superconscious decisions. However, it would take many single events to demonstrate a violation of quantum statistics.
An experiment has been performed which lends some credence to the possibility of a karmic gauge. It involves a cat again: 'Schmidt's cat'. Physicist Helmut Schmidt of Duke University connected a heat lamp to a random number generator. He placed one apparatus in a shed without a cat, and one with a cat. The random number generator was supposed to assure the heat lamp was on half the time. For the shed had no cat in it, this was close to true. However, with the cat in the shed, the lamp stayed on much longer than half the time. This happened to an extremely high degree of statistical significance.
The random number generator was triggered by a radioactive source. Schmidt's conclusion was that quantum interconnectedness linked the cat's will with the radioactive decay--a kind of telekinesis. An equally likely possibility is that it was the cat's karma or cosmic mercy that she should be warm. This ascribes the effect to something beyond the cat. Perhaps causal laws working through the karmic gauge could accomplish the result.
This means there is some hope that Schrödinger's cat (distinct from Schmidt's cat) could be saved from a cruel death. God or psychic powers 'bending' quantum statistics might intervene.
Thus, it is possible that God does not always play dice with the universe. Perhaps God plays fair--is a just God. If so, existentialism is in for a jolt. It does matter what we do.
Consider the following thought experiment to test karmic wave function collapse. This is one which to a degree excludes the possibility of willing the result. This could be called 'quantum execution'. It is only suggested as a thought experiment to stimulate more practical research. It does not intend to offend those who oppose capital punishment.
Suppose a law were passed that all murderers sentenced to the death penalty be compelled to submit to the same trial as Schrödinger's cat. This includes the radioactive source, the hammer, the poison gas, and the supposed 50% chance of survival. Most of them would have murder karma for which the retribution could be death. The survival percentage might be significantly less than 50%, if the sample were large enough. Murder is a likely crime for which God or the universe might seek to balance. Thus, we are dealing with a powerful karmic force. The results might reveal karmic influence on quantum statistics. At least this thought experiment might lead to a more realizable study of other human conditions with more positive ramifications.
Perhaps metaphysical laws can be tested and given mathematical treatment in the quantum gauge. After all, the gauge can be set up to collapse the wave function. In 1970, physicist Evan Harris Walker first suggested that consciousness could collapse the wave function. (13) However, he did not recognize the quantum gauge as the means to do so.
The Gauge is a Hidden Variable
The mathematical form of these metaphysical laws must also play an important role in a hidden variable interpretation of quantum mechanics. Hidden variable theories postulate that because of its statistical nature, Quantum Theory is incomplete. What do we mean by incomplete? Consider the theory of gases, which describes collections of particles with statistical laws. The molecules of gas have well-defined locations and velocities. However, theory doesn't tell us what they are. Thus, these individual positions and speeds are 'hidden variables' to the statistical theory. The theory says nothing about them. So the statistical theory is incomplete without specifying single particle trajectories. It doesn't describe particles as we understand them.
Quantum Theory is also incomplete. We only have a statistical prediction of the state of an individual particle, when we measure it. Thus, the usual interpretations deny particles have definite positions and speeds.
In contrast, individual quantum particles can have positions and momenta in hidden variable theories. The first was proposed in the '20s by prince Louis deBroglie. It was later elaborated upon in 1953 by David Bohm, a former grad student of Einstein. This theory is sometimes called the 'pilot wave' theory. The wave function 'pilots' particles with classical variables. To be considered like normal classical particles, they must move under the influence of very unusual forces. These allow instantaneous 'communication' of the particle with the rest of the universe.
These forces are the result of a new 'quantum potential' in Bohm's theory. Learning about the rest
of the universe instantly, particles violate Einstein's postulate that no signal can go faster than the
speed of light. Bohm's theory illustrates what is today known as the quantum interconnectedness of
the universe. One could call this instant knowledge of the entire universe, present everywhere, a
manifestation of the omniscience and omnipresence of God. It is implemented through the quantum
Not only particles exhibit these God-like qualities. Consider a teenager in catechism class, struggling with the meaning of 'omniscience' and 'omnipresence'. When they are clearly explained to him, he lights up and says, "'omniscience'--that's
like my Dad, and 'omnipresence'--that reminds me of my baby brother!"
In Bohm's theory the electromagnetic field is also a hidden variable. It changes the momentum of a particle. However, our previous chapter told us this field has an arbitrary piece related to the gauge. Thus in hidden variable interpretations of this type, the gauge should be interpreted as a free hidden variable. You might say it is the hidden variable of consciousness. Consciousness may choose it to alter the quantum wave function. It is 'hidden' because the quantum equations do not allow it to be determined. This is the free choice of the consciousness of God or man. This type of hidden variable is like an invisible person on an Easter Egg Hunt. The results are affected without being describable by normal 'reality'.
In Quantum Theory, the hidden becomes revealed, if we understand the 'invisible' consciousness. Consciousness sets up how the gauge rotates the wave function (quantum Tai Chi) to provide a perspective which determines the measurement. Bohm would say that it is the quantum interconnectedness of the system and the environment which causes the collapse of the wave function to one possibility. It's like each particle having a computer in an instantly signaling network. It can give it a picture of what all the other particles are doing. Particles have instant computer mail!
However, the particle must not only consider the physical universe. The 'environment' includes consciousness working through the gauge. It is associated with additional forces within the mind or 'spirit' which collapse or modify the wave function. In the Bohm theory a quantum 'force' behaves similarly. The view presented here, however, leaves behind ordinary interpretations of Quantum Mechanics. It postulates the influence of free will of conscious beings on the quantum process. This freedom is implicit in the Quantum Theory. It is the gauge freedom of the wave function.
Thus gauge freedom gives 'God' the option to set the quantum boundaries for man. It gives man the free will to measure the universe as he wishes within these boundaries. Dr. Bertlmann was free to choose his non-conformist ways of selecting socks. Quantum Theory allows the cosmic consciousness behind the universe to have its way (Tao).
5. THE YANG-MILLS PARADIGM
"The theoretical scientist is compelled to an increasing degree to be guided by purely mathematical, formal considerations...
The theorist who undertakes such a labor should not be carped at as 'fanciful'; on the contrary, he should be granted the right to give free rein to his fancy, for there is no other way to the goal."
Albert Einstein (My World Picture)
"He who is aware of the Male
But keeps to the Female
Becomes the ravine of the world.
Being the ravine of the world,
He has the original character which is not cut up,
And returns again to the innocence of the babe."
To understand the impact of gauge freedom on physical law, we need additional mathematical insight from a woman's point of view. Remarkably, it came in 1918, the same year that Weyl published his Gauge Theory of Relativity. Even more remarkably: this was shortly after Einstein revealed his General Theory of Relativity. These events coincided with the end of World War I. The quantum gauge of history must have been working overtime.
Emmy Noether has been called by Einstein, "the most significant creative mathematical genius thus far produced since the higher education of women began". (17) She was a nearsighted and apparently unexceptional child with an interest in languages. At the University of Gottingen, she could not register for courses because she was female. However, she could take examinations if the professor agreed. It is not surprising that after one semester she transferred to Erlangen. There, she registered alongside male students. At Erlangen, she met the mathematicians Minkowski, Klein, and Hilbert. There, she developed an interest in their 'art'.
Her first professorial position at the University of Gottingen was without pay. Again, this was because she was a woman. She would not have obtained that post had it not been for her friendship with Hilbert. Somewhat later, in the early 1930's, she had to leave Germany because of Hitler's threat to those of Jewish descent. She took a post at Bryn Mawr College near Philadelphia.
Much earlier, in 1918, however, she published her work on the theorem known by physicists as 'Noether's Theorem'. It had a two-fold impact. First, she derived the relationship between symmetries and conservation laws. This principle took about forty years to perculate into elementary particle physics. It now holds a cornerstone position. Second, she showed that global gauge invariance implied that a current (like an electric current) was conserved. This became a major factor in the development of Quantum Field Theory. We will discuss these two important advances one at a time.
It is not too difficult to understand why symmetries or invariances imply conservation laws. Consider simple circumstances. Let us examine the case in which all other bodies in the universe do not effectively interact with an object. Since we can build bodies out of particles, consider one of them: a test particle.
Imagine no forces on the test particle. It is as if the rest of the universe doesn't exist. This is realized by conducting experiments in space, far from the gravitational influence of planets and stars. Even on earth, we can imagine a place where the influence of gravity and other forces is insignificant. For example, the motion of high energy particles in a particle accelerator is not appreciably affected by gravity.
Consider a speeding electron. It is shielded from electrical devices in the lab to prevent the electromagnetic force from changing its path. Look at it in a region where it is not being accelerated. There, it does not feel the rest of the universe. It is like a lone electron in empty space.
The location of this lone electron in empty space doesn't matter. Empty space is no different when we change our position in it. This is called 'translational invariance' or symmetry. There are many experiments which are effectively free of external forces. It doesn't matter whether we perform them in Atlanta, Georgia or Daharan, Saudi Arabia.
With no force pulling in any particular direction, the particle has no preferred direction in which to change its velocity. Thus, its velocity remains constant. Momentum is mass times velocity. So the particle's momentum is also constant or 'conserved'. The particle continues in the same direction at the same speed. This is the essence of Newton's first law. Thus, this law can be derived from translational invariance.
There is a second symmetry for the lone electron. The particle in empty space is in an environment which doesn't change with time. This is time translational invariance. It is the indifference of an object in empty space to the passage of time. If the environment were to transfer energy to the particle, it would imply that it changes with time. This contradicts our original observation. Therefore, the energy of the particle is conserved. Again, a symmetry implies a conservation law. Time translation symmetry results in conservation of energy.
This sounds rather like saying, 'each car on the train looks the same, therefore cars all have the same number of passengers.' However, the mathematics is clear: each of the three symmetries has an associated conservation law.
The third symmetry for the lone electron relates to rotation. I could rotate the laboratory, and the empty universe would look the same. This is called rotational invariance. After such a rotation, there could be no change in particle spin. There would be no pull in a particular direction to change it. Thus angular momentum or spin is conserved.
These three conservation laws come from empty space-time. The corresponding conservation laws of momentum, energy, and angular momentum apply to any isolated group or system of particles. From these three laws, we can describe motion. This is so, if we experimentally know the nature of the forces involved.
Newtonian 'kinematics' is a classical study of motion without forces. It is the result of the flat or
'Euclidean' space-time geometry. We would like to see if the forces like gravity, electricity, and
nuclear forces are also the result of geometry. If they are, motion could be described by geometry
alone. Einstein, in his General Theory of Relativity, showed the force of gravity could be described
by bent geometry. This is curved space-time. To Einstein, God was a geometer.
To represent this force geometrically was a challenge for the one who called himself, "an artist
in science. The true artist will let his wife starve, his children go barefoot, his mother drudge for
his living at seventy, sooner than work at anything but his art." (P. 172) To go beyond Einstein,
and accomplish geometrization for electricity and the weak force took a similar dedication. It
took a Weyl, a Yang, a Weinberg, and a Salaam.
To describe forces other than gravity in geometrical terms, we must extend space-time to 'internal' gauge dimensions. These are similar to those which extend the clothesline by adding clothespins. This is allowed in Quantum Theory. However, describing the strong nuclear force in the Yang-Mills formalism requires three dimensions beyond space and time.
To discuss the geometrization of forces, we need to examine what they have in common. Both gravitational and electrical forces are proportional to a quantity. In gravity it is a mass. In electricity it is a charge.
Emmy Noether made two additional related assertions, 'corollaries' of her famous theorem:
(1) Gauge symmetry requires all forces to be due to a 'conserved' quantity like mass or charge. (Mass can be converted into energy via E=mc2. However, even energy has a gravitational effect.) (2) All forces also have an associated conserved current. This is much like an electric current. The 'stuff' that causes the force can move. It's rate of transport must be maintained. Consider a gravitational current. There is a mass current in the asteroid belt, for example. Even if this current were diverted, the total flow would remain the same. Global gauge invariance says that currents are conserved.
Global gauge symmetry for the electric force allows all the quantum Tai Chi's to be at the same arbitrary angle. This amounts to choosing a quantum gauge the same everywhere in space and time. (The quantum gauge just rotates the wave function.) For gauge invariance, such a choice may not change the energy of a system. To require that, Noether showed, is equivalent to demonstrating that electric currents and charges are conserved. Without this conservation we would not have a basis for the mathematical formulation of forces. This basis determines their magnitude.
The Electromagnetic Field is the connection for the gauge. We may couple conservation of current
and charge with the form of the Electromagnetic Field. Then the laws which govern forces and
motion become the result of a freedom of 'choice'. This is a 'choice' beyond our physical world in
the realm of 'consciousness'. Without freedom to measure space and time as we wish, there would
be no electrical force.
World politics is transforming itself into a thrust for personal and national freedom. Without freedom, there can be no personal or national 'force' or power. The 'force' is characterized by
the nature of the freedom, as in Gauge Theory.
There is a simple example of Noether's conservation of current. In a superconducting circuit, forces external to charged electrons (e.g., resistance to their flow) are almost eliminated. Thus, the current of electrons is not diminished in time.
In Noether's mathematics, electric charge is also conserved. It is neither created or destroyed. Benjamin Franklin was the first to suggest this. It has been verified to high precision in this century. Conserved currents are made up of moving 'charges' that can experience forces. Thus, currents of particles can interact with fields manifesting these forces, i.e., forcefields. Put a magnet on the side of a coffee cup and stir in iron filings. The forcefield of the magnet attracts the fillings which move in a 'current'. The current of iron filings interacts with the forcefield of the magnet.
Once we know the form of the quantum gauge, Noether's Theorem supplies the form of the
current. The field of the force is taken to be the connection for the gauge. This is the way of relating
differences in measurement throughout space-time. The product of the current and the field expresses
the energy of interaction between the particle and field.
This is like the expression for power output in a simple circuit, P = IV. I is the current and V is
the voltage across the circuit. Physicists call the product of current and field 'minimal coupling'.
This is the simplest possible mathematical description of the interaction of a particle and a field.
This minimal coupling, as well as the form of the field and the current, falls out of quantum gauge invariance. It comes from the equations of Quantum Field Theory. Thus, quantum gauge invariance gives a prescription for the behavior of forces and their interaction with particles.
For example, an electron in the presence of an electric field can be represented. Its quantum
behavior can be predicted. Without Noether's Theorem in one form or another, Gauge Theory would
not have had a launching platform.
The Foundation: the Electromagnetic Gauge
Before discussing the Yang-Mills Theory of the strong nuclear force, a brief review is in order. Weyl's Gauge Theory of the electromagnetic force is the only full-blown Gauge Theory we have examined. The gauge is like the angle to which a clothespin is twisted. This quantum gauge can be arbitrarily chosen at any position in space-time.
The electromagnetic potential is the connection for relating the quantum angle at different
positions in space and time. We are free to choose this gauge (Tai Chi angle) in any way we want
anywhere in space-time. This led Hermann Weyl to include an extra mathematical term in the
quantum energy equation. Its purpose was to cancel the term created by the quantum gauge. Thus,
choosing a different set of angles for the 'quantum Tai Chis' doesn't change the equation.
Adding this extra term is like putting in a precise 'fudge factor'. Consider developing an equation to determine safe driving speed, for example. The fact that eyesight worsens with age would have to be taken into account. A term could be added to the equation to compensate for that. Similarly, a term must be added to the energy to compensate for the term resulting from a changing gauge. This term is of the form 'IV' or current times the field. It represents minimal coupling.
The Nucleus As An Equal Opportunity Employer
Employers are not supposed to discriminate on the basis of sex. Thus, in the work market, it
would make more sense to call men and women 'persons'. Similarly, inside the nucleus, the strong
force does not discriminate between an uncharged neutron and a charged proton. The nuclear
force is so strong that it overpowers any electromagnetic effects caused by charge. Thus, inside
the nucleus we call neutrons and protons 'nucleons'. They both effectively experience the same
These 'nucleons' also have about the same mass. It is that of a hydrogen atom. In the Yang-Mills theory, both the proton and neutron meet the same strong nuclear force. If we replace a proton by a neutron, it doesn't change the energy which binds the nucleus together. This is the observed character of the strong nuclear interaction.
Replacement of a neutron by a proton with no effect is an example of a simple symmetry. The replacement changes nothing (inside the nucleus). We can make this a local symmetry. We can say that in one position on the space-time 'clothesline', a given particle could be a proton. In another, it could be a neutron.
Let's try to picture this freedom in our clothespin model. We could allow ourselves the liberty to paint every clothespin blue or yellow.
However, such a tentative description of proton-neutron symmetry does not follow one of our rules for a local Gauge Theory (Chapter 2). Gauge changes have to be smooth. In our painting spree, however, it is possible to have a discontinuous jump from a blue clothespin to an adjacent yellow. Thus, the continuous mathematics of the Gauge Theory would be violated. There is no room for all the shades between blue and yellow. Gauge Theory requires that a nucleon should be allowed to be part neutron and part proton. So we have to invent a theory in which the changes between neighboring 'clothespins' are continuous.
There is a theory like this for the electron. There are two types: one with spin up, and one with spin down. The electromagnetic force doesn't discriminate between them. It interacts with a spin up electron the same as it interacts with a spin down--at least in magnitude. The electron doesn't spin exactly like a top. However, an analogy can be made between the two types of electrons and two identical tops. We can spin a top clockwise or counterclockwise. Call the clockwise spin, 'spin up', and the counterclockwise spin, 'spin down'. 'Up' and 'down' form an axis around which the top spins.
Actually the orientation 'up' is arbitrary too. Empty space doesn't care. So this axis could be oriented in any direction at a given point in space-time. This is local gauge invariance.
To specify the direction of the axis of spin at a point in space-time, three coordinates must be used.
Similarly, three variables must be assigned to specify a point in three dimensional space, e.g., x, y, and z.
Three angles can serve as the three coordinates. Say we have three perpendicular axes to describe three dimensional space (see figure). Then one convenient system of angles is as follows. Rotate in sequence: 1) an angle A about the z axis, 2) an angle B around the new x axis, and 3) an angle C around the new z axis. The final x axis is the one about which the top rotates. These three angles are called the 'Euler Angles'. They were first suggested by the 18th century mathematician, Leonard Euler, to describe tops. They are a prescription for describing any random direction in three-dimensional space.
Now we take the big leap. Instead of real space, protons and neutrons have their identity in an imaginary three dimensional space. It's called 'isotopic spin space'. This is like the space a 'real' top spins in. However, it is imaginary. It's part of the way our imagination may interpret the nuclear observations. The term 'isotopic' has nothing to do with radioactive isotopes. Probably 'nucleonic' space would be a better term.
In this 'internal' isotopic or nucleonic space, we can have the isotopic spin axis oriented in any arbitrary direction. There is no physical reason for a particle to select a particular isotopic direction inside the nucleus. That would be like discriminating between a proton and a neutron. The National Organization for Neutrons would be up in arms.
Picture the 3-dimensional isotopic space on the clothesline. Imagine clothespins that are capable of interpenetrating one another. Each can point in any direction in three dimensions (see Figure). However, these dimensions can be thought of as existing in an 'internal' space. There is one imaginary space for each 'real' point in space-time. However, we represent them in regular space in the clothespin model.
Thus, we describe the nucleus by treating neutrons and protons the same. To do so, we must
postulate a Gauge Theory with a 3-dimensional space beyond each space-time point. In it, a neutron
'spins' clockwise, a proton counterclockwise. This mathematical 'machinery' is needed for a local
Fiber Bundles: Natural and Real
Describing the gauge invariance of isotopic spin mathematically was a big challenge for Yang and Mills. Chen Ning Yang worked on this problem for five years before finding a solution. The key was that the strong interaction is invariant under rotations in isotopic space. We expressed this as setting up our spin axis in any direction we want. Up along the z axis is a proton. Opposite to that is a neutron. This is like a traffic policeman's signals for stop and go. 'Hand up' and 'hand down' have different meanings.
As a nucleon moves from place to place, it is free to be any combination of a proton and a neutron.
It doesn't matter to the strong force. The strong force swamps the electromagnetic force inside the
nucleus. Thus, the approximate symmetry between neutrons and protons is promising. Only when it
is far away from other nucleons does a nucleon start acting as if it has a proton or neutron identity.
When men and women aren't being considered as 'persons' in a fair hiring law, men are men and
women are women. Perhaps someone could develop a sociological theory of employment based
on personhood gauge invariance.
These rotations in three-dimensional isotopic space involve two quantum states, the proton and the neutron. Since quantum states are described by complex fields, we need new mathematical objects which can transform one complex number into another. The number '1' is the basis of real numbers (i.e., multiples of it yield all real numbers). The number 'i = /-1' is the basis of complex numbers. There are three objects which are the basis we need. They are the 'quaternions'.
What are quaternions? The three basic quaternions are the Pauli spin matrices. These are named
after Wolfgang Pauli, who worked with Carl Jung to develop 'synchronicity'. This we will discuss
later. The three Pauli matrices can be considered distinct square roots of the two dimensional unit
I = 1 0
0 1 .
This is like a two-dimensional number '1'. When it multiplies a two dimensional number, like the
ordered pair (1, 2), it gives it back again. What are the rules of multiplication? Do the multiplication
one row at a time. 1x1 + 0x2 = 1 for row 1, and 0x1 + 1x2 = 2 for row 2. The results are in the same
order as the ordered pair. When we take the square root of I, we get three possible answers (aside
from I itself). One can check by multiplying the following Pauli matrices by themselves:
0 1 0 -i 1 0
1 0 i 0 1 -1 .
The rule for multiplying 2-D matrices is to multiply the row of the 1st times the column of the 2nd.
This intersects in a given position of the final result.
To describe the employment of men and women we could use a two dimensional matrix too. Say a company interviews 12 men and 10 women. From these, they can select 4 for one type of job and 6 for another. If the number of men and women has to be equal for
each job, the 'hiring matrix' is:
1/4 3/10 .
This converts the ordered pair, (12, 10) into the ordered pair (4, 6). It also obeys the constraint that an equal number of men and women have to be hired for the same job. To solve for this matrix requires the solution of 4 equations with 4 unknowns. Two-dimensional matrices are a convenient way of doing this. Each Pauli matrix rotates the two-dimensional quantum state through a unique angle in isotopic space. There are three angles, and three Pauli spin matrices. Thus, the Pauli matrices are 'generators' in Gauge Theory. Generators effect rotations in 'internal' spaces beyond each point in space and time. Each yields a unit rotation around an independent axis. This is a basis for the quaternion number system.
In the Yang-Mill's theory the quantum phase factor containing the gauge rotates the nucleon wave function. It uses the three Pauli matrices and three angles. The three angles can be arbitrarily but smoothly chosen from space-time point to space-time point, and specify the gauge.
The Pauli Matrices (and generators in many gauge theories) have properties unlike real numbers. We all know that 2 times 3 = 3 times 2. For two Pauli matrices, A and B, though, AB is not equal to BA. Real numbers are 'Abelian'. Pauli matrices are 'non-Abelian'. They do not 'commute'. Their order in multiplication cannot be reversed. Electromagnetism can be described by Abelian generators. However, the Yang-Mills strong force requires non-Abelian generators. Thus, in this picture, the character of the strong force is different from electromagnetism. The electromagnetic gauge is represented by ordinary real numbers.
Yang-Mills theory is different in other ways. Although one charge in a field obeys a law analogous to Coulomb's Law for electrical force, two charges do not. Thus two electric fields do not obey the principle of superposition. The effect of two forcefields isn't always the sum of each forcefield. However, the mathematics is sometimes not prohibitive.
Other differences can be found. In electromagnetic theory, the force is 'mediated' by the photon. The photon is a massless object with spin = 1 unit. Like charges repel because the charges throw photons back and forth. Like a catcher and pitcher, the force of the impacts pushes them apart.
In the Yang-Mills theory of the strong nuclear force, there are four unique massless particles that are exchanged. All of them have spin of unit one like the photon. Two of the four also carry a charge. The photon has no charge. All of this information comes out of the nature of the gauge freedom involved. There is symmetry for rotations in gauge space.
Yang and Mills had a big disappointment. They needed four massless 'baseballs' to mediate the strong force. However, it was already known to be mediated by three particles with mass called pions. Nevertheless, they hoped their beautiful theory, which seemed wrong, was right from another perspective. It did turn out to be right for the unification of two entirely different forces: the weak nuclear force and the electromagnetic force. However, to reach this understanding, physics had to take a long, difficult journey from the groundwork laid by Yang and Mills. The steps in this 'expedition' are retraced in the last half of this chapter.
The theory of Yang and Mills was a leap of faith in a fascination with beauty itself. The beautiful idea was that symmetry in an imaginary set of dimensions was the reason for the existence of forces. It was as if God conceived of allowing certain freedoms to man. Freedom means forces must move our world. This is like an artist painting a symmetric picture which symbolizes the real world. Bounds of limitation are set for man. Thus, forces acting in his world must have a certain character.
Such musings may give some physicists consolation. However, this is not usually sufficient
when the theory is incorrect. Rarely in the history of science has a theory which was so wrong turned
out to be so right from another perspective.
The mathematics of Gauge Theory had been outlined by mathematicians many years previous to this step. This was the theory of fiber bundles. Chen Ning Yang recounts a visit to his former professor, Shen Chern, a mathematician whose work helped expand this theory. Yang told Chern that it is "amazing that gauge fields are exactly the connections on fiber bundles, which the mathematicians developed without reference to the physical world. This is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere."
With the incisive brevity of a Zen master or a Star Wars Yoda, Chern replied, "No, no.
These concepts were not dreamed up. They were natural and real."
5. THE YANG-MILLS PARADIGM
The Electroweak Miracle
For the Yang-Mills Gauge Theory to prove useful, two obstacles had to be surmounted. In the last section, one of the difficulties was that it predicted massless intermediary particles for its forces. The other problem was that it was not known to be renormalizable. 'Mean, nasty' infinities crept into the equations, and no one knew how to deal with them.
The basic facts of life for quantum field theories were codified in the late 40's. This was when the theory of Quantum Electrodynamics was developed. In Quantum Electrodynamics (QED), the interactions of electron-like particles called leptons are accurately described. QED says forces between leptons are thought to be contributed by light particles passed back and forth.
Electron energy can be thought of as composed of numbers of photons which are self-emitted and self-absorbed (see figure ). These energies that contribute to the electron energy can be added up over all wavelengths. Physicists found there was an infinite amount of energy donated by short- wavelength photons. Ultraviolet wavelengths are shorter than those of visible light. Thus, this infinity was nicknamed 'the ultraviolet catastrophe'.
Physicists learned that they could throw away the infinite part of the energy caused by photons below a certain wavelength. Then the values for the electron energy and interactions came out right. The answer was so right that Quantum Electrodynamics (QED) is now considered the most precise physical theory in existence. It is on the button to 15 decimal places!
Feynman and Schwinger called this subtraction of infinite energy 'renormalization'. Physicists found other theories didn't work when this process could not be used. For many years, however, it was thought 'renormalization was like a cleaning woman sweeping dirt under the rug (see figure ).
The precision of QED and its many usages changed physicists' minds about renormalization. It was an odd proceedure, but it worked well. Yang and Mills presented their theory of the strong force in 1953. They could not prove it renormalizable. Thus, it gathered little attention.
The requirement of massive intermediating particles was met before renormalizability was resolved. In between, the Yang-Mills theory of the strong nuclear force was replaced by Murray Gell-Mann's elegant quark theory. However, the Yang-Mills formalism revived. This happened when Weinberg and Salam tackled the unification of the weak nuclear force with electromagnetism.
To provide massive particles for exchange in the nuclear force reguired a new concept: 'symmetry breaking'. What if a Yang-Mills type of symmetry with its massless exhange particles held only for an epoch in which the universe was young, compact, and hot?
Rotational symmetry, for example, holds for a Heisenberg ferromagnet only above a certain temperature. Above the Curie Temperature a ferromagnetic domain exhibits no magnetism. The magnetic atoms are jostled around in random directions. Below the Curie Temperature, however, the atomic magnets line up. An overall magnetism is achieved in a domain much larger than atomic.
In about 1965, Peter Higgs, a British physicist, showed thatYang-Mills fields undergo a symmetry breaking similar to that for magnetic atoms. They can make a phase transition from a state in which the intermediary particles are massless to a symmetry-broken phase where they are massive. To do this, an extra field called the 'Higgs field' had to be introduced. The intermediary particle in the Higgs field is the massive 'Higgs particle'. This is a particle so heavy it is beyond the reach of present particle accelerators.
The Higgs field, then, 'breaks' the Yang-Mills symmetry. (For a ferromagnet, the
magnetic field breaks rotational symmetry.) This forces the associated Yang-Mills particles
to take on mass. In 1968, Weinberg and Salam showed this proceedure could make one force
out of two. The electromagnetic and the weak force were thus 'welded' into the 'electroweak
force'. The massive particles making up the related field were three-fold: the W and two Z's.
These particles were discovered much later (1983) at Europe's CERN accelerator. This
breakthrough qualified Weinberg, Salam, and Rubbio (who discovered the particles) for
Guadalajara, Mexico, is famous for its Mexican Hat Dance.
Hombres and senoritas dance gingerly around a wide-brimmed
'sombrero'. This large head-covering is tailor-made for
picturing symmetry breaking. Put a Mexican jumping bean at
the top of the hat. To it, any direction looks the same ).
This is rotational symmetry (randomly oriented Quantum Tai Chis).
However, once the wayward bean has jumped down onto the brim, a
direction has been chosen. The symmetry is broken. In the
particle case, a specific phase for the quantum Tai Chi has
A typical mathematical function in symmetry breaking has the shape of a sombrero. This is the 'sombrero potential'. It describes the energy change going from a symmetric matter phase (the peak) to one with the symmetry broken (the brim).
With symmetry breaking, Weinberg-Salam theory had the massive particles it needed for its field. However, it still was not complete. Its Yang-Mills field was still unrenormalized. For this reason, Weinberg's paper was nearly ignored in the literature for several years. A gloom hung over hopes for the proposed unification.
The dawn broke in 1971. With a lengthy calculation, a Dutch graduate student named
T'Hooft proved that the infinities in Yang-Mills theories cancelled. This was similar to the
renormalization for Quantum Electrodynamics. The search was on for the massive
intermediary W and Z particles. It concluded in 1983, when Rubio and his collegues found
them at the Cern accelerator.
The Color Force and Grand Unification
As a result of the electroweak 'miracle', the Yang-Mills field gained even more adherents. It was next used to represent properly the strong nuclear force. Yang and Mills contributed the basic idea. However, they were unaware of the 'existence' of quarks when they wrote their original paper. They had no experimental evidence for the complexity of this force.
The complexity is that quarks compose neutrons and protons and yet are never seen alone. They are in a proverbial 'sack'. They come in three 'colors', analogous to primaries like red, blue, and yellow. Three primaries are necessary to make a nucleon, as if it required a 'white' hue. The Yang-Mills mathematics of a three color force (SU(3) symmetry) requires eight field particles called gluons. The gluons are the 'glue' that holds the nucleus together.
In honor of Quantum Electrodynamics, the new theory of strong interactions was dubbed 'Quantum Chromodynamics' (QCD). Quantum Chromodynamics along with the Electroweak Theory compose what is called the 'Standard Model'. This describes all physical particles and their forces--all forces except gravity. The Standard Model is a triumph for Yang-Mills Gauge Theory. It does, however, require 19 parameters which must be arbitrarily set. These are needed to give the model proper force strengths and the masses for the intermediating particles.
When constructing a Theory of Everything, the features of the Standard Model must be confirmed. These are the features of the known particles. What are these particles? There are only two types: quarks and leptons. Quarks make up the nucleus by composing neutrons and protons. When quarks interact, they exhange one of eight 'gluons'. This is required by color symmetry, the symmetry of Quantum Chromodynamics. Gluons themselves are combinations of two quarks each.
Leptons (electron-like particles and their attendant neutrinos) exchange photons when they interact. This is mandated by the electromagnetic version of symmetry called U(2).
Leptons and quarks interact with each other by Z and W exchange. This is a manifestation of 'electroweak symmetry'. Their interaction allows heavier particles to transform to lighter particles. This is done without leaving the lepton or quark family. This is evident in 'beta decay', a major decay mode of radioactive nuclei. In it, a neutron decays into a proton, an electron, and an antineutrino.
From here, the next step in the simplification of the Standard Model is Yang-Mills unification of the electroweak force with the strong force. This is the leap taken by Grand Unified Theories (GUTs). GUTs allow quarks to change into leptons. They enlarge the collection of exhangable particles to 24. There are 8 gluons responsible for the strong force. 1 photon is responsible for the electromagnetic force. 3 'weakons' (Ws and Z) mediate the weak force. 12 other particles intervene in quark-lepton transformations.
The earlier the stage of the universe, the higher the particle energies. In early epochs the
strengths of the weak force, strong force, and electromagnetic force transform. Physicists
have determined that their interaction strengths equalize at a certain epoch. At that epoch,
GUT symmetry between quarks and leptons may be broken. The values of the interaction
strengths separate. One remnant of such a time is the prediction that a proton should be able
to decay--with a small probability. However, early GUT estimates of this probability indicate
that proton decay should have been seen. It hasn't. GUTs are a good idea, however. New
versions of the theory are being worked on which provide a smaller proton decay probability.
Supersymmetry: Super 'Wu Hua'
GUT is still an incomplete representation of nature. It leaves out the force of gravity. What kind of magical transformation might have to be considered to include gravity? Consider the particle by which that force is considered to be mediated (in the lowest approximation). The particle interchanged in the gravitational interaction is called the 'graviton'. It has a unique characteristic. It has a spin of two.
Particles come with only two types of spin. They are 'fermions' with half integer spin 1/2 , 1 1/2, 2 1/2, etc..., and 'bosons' with integer spin 1, 2, 3, etc... Leptons and quarks are fermions. Gravitons, gluons, and photons are bosons. In Supersymmetry theories, the two are allowed to transform one into the other. Fermions may become bosons. Bosons may become fermions.
This magical transformation ('wu hua'), is hypothesized for a time only shortly after the Big Bang. This is before 'supersymmetry' is broken. It is an earlier epoch than that in which GUT symmetry is broken. We can allow gravitons to transform into quarks and leptons in the early universe. This unifies the force of gravity with the other forces.
Simple supersymmetry theories were pioneered by physicists Wess and Zumino. They imply fermions and bosons have the same mass. To get the differing masses necessary for a viable theory, however, the symmetry must be broken. Thus, a new mirror image of the spectrum of particles must exist. There must be a gravitino for a graviton, leptino for a lepton, a photino for a photon, etc... The energies to create these 'superparticles' are yet unknown.
Superstring Theory, however, incorporates supersymmetry with a gravitational string. The
latest version of 'strings' are closed loops of warped space-time which have collapsed from
higher dimensional objects. Different vibrational modes of the strings produce the variety of
particles we observe. Certain versions of string theory have supersymmetry built in. They have
the standard model and its particles implicit in the structure of the symmetry group. The
problem is that these theories involve such complex equations physicists cannot make
predictions from them. They do know, however, that the four forces are represented.
Lao Tzu and the Tzupercollider
Physicists hope the Theory Of Everything will be elegant and simple. They expect one force, one symmetry, one perspective. To check out the candidate theories, however, we need a new line of particle accelerators. The latest version would have been the supercollider. It never got funded. Fortunately, new less expensive possibilities for high energy accelerators have recently been discovered. For example, electrons have been accelerated to high energies by taking a ride on a plasma wave. (A plasma is an ionized gas.)
The goal is to find particles whose production takes energies that are beyond the range of our present accelerators. The main means of attaining such energies has been to collide beams of particles with antiparticles. Antiparticles have charge opposite in sign to particles. Colliding the two allows the transformation of energetic matter into energy. The energy then produces new particles.
The Higgs particle breaks the electroweak Yang-Mills field. Finding it in a collider would be a great advance. The creation of '-ino' particles like the leptino and photino would also confirm supersymmetric theories and string theories. This would provide values for their masses. In addition, there are particles for 'technicolor' theory, an extended color theory. There are 'axions' and 'wimps', particles invented to explain dark matter in the universe.
The search for a Theory Of Everything could be called a 'Taoist' pursuit. The word 'Tao'
itself denotes 'the whole of reality'. In another school, it is 'the way the universe works'.
Chuang Tzu expresses a philosophy which sounds like supersymmetry itself:
"All the various species of things transform into one another by
a process of variation in form. Their beginning and ending is
like an unbroken ring (string?), of which it is impossible to
discover the principle."
It may not be 'impossible', after all.
6. INTERPRETING THE QUANTUM TAI CHI
Chuangtse concerning himself:
"The foundation of his thought is big and wide deep and
unconfined. The core of his teaching encompasses all
phenomena and reaches up to the divine order. However, in
its adjustment to the changing life and understanding of
physical things, its principle is inexhaustible, traceless, dark
and formless, and it is difficult to get hold of."
Up to this point, we have focussed on the Gauge Theory of physics and its application, looked at symmetries for forces generated by elementary particles. In the last chapter, we saw how the four forces can be unified by symmetry. In this description, broken symmetries result in the apparent separation of forces. Broken symmetry also gives us individual particles with unique properties. However, symmetry is the hidden order of the universe. From unity, comes diversity.
In time, the universe unfolds its secrets. It changes from a state with many possibilities to a state
in which there is one. In Grand Unified symmetry breaking, a mixture of quarks and leptons emerges
out of the uncertain past.
This is strangely reminiscent of the collapse of the wave function in Quantum Theory.
Various quantum possibilities exist before observation. However, only one possible state of
a particle manifests. This is also 'wu hua', a magical transformation. It is like a man dreaming
about a butterfly becoming a butterfly. Could we apply the notions of Gauge Theory and
symmetry breaking to interpret this 'magical' change?
Perhaps 'God does not play dice with the universe,' as Einstein said. Is it possible the brain brings about a single observed quantum state from the alternatives? If so, what are the rules for its 'dice game'? Are the dice ever loaded? Are rules other than statistical Quantum Theory ever needed to explain the world? These are pertinent questions when considering macroscopic objects. We are not sure whether microscopic quantum rules strictly apply to them.
Prominent scientists have now been led to understand that the brain is intimately involved in the
quantum process. It is not clear how this is implemented. However, we can see the steps which led
to this realization.
Apparatus Tai Chi In Italian
Atomic physicist Neils Bohr used the Tai Chi as his coat of arms. It was also a symbol for what he called 'complimentarity' in quantum theory. However, he had a different meaning for the yin and yang than we suggest in this book. For him, the Tai Chi symbol embodied the uncertainty principle of Heisenberg.
In an experiment to measure the momentum of a particle, its location is uncertain. If we measure
its location, its momentum is uncertain. This is a mutual exclusivity. It has nothing to do with the free
angle of the wave function. That is identified in this book with the phase of the Quantum Tai Chi, and
its yin-yang polarity. Bohr is the chief architect of the 'Copenhagen' interpretation of Quantum
Theory. However, his interpretation leaves wave function collapse a non-causal process.
"...we have been forced step by step to forego a causal description of the behavior of
individual atoms in space and time, and to reckon with a free choice on the part of nature
between various possibilities to which only probability considerations may be applied." ( )
Three Italians wrote the first research paper to explore the relationship of the quantum phase to the collapse of the wave function. A. Danieri, A. Loinger, and G. M. Prosperi proposed that the observation introduces random phases in the quantum state of the macroscopic measurement apparatus. The observing apparatus (with its random phases) and the system interact. This collapses the wave function by phase interference.
Consider a physical example. In a geiger counter, electrons react to charged particles coming through the tube containing the detecting gas. They are in well-defined states when a particle is detected (see figure ). If it were not so, they would not hit the electrode with a quantifiable energy. To be in a definite quantum state, these electrons must have specific phases in their wave functions or quantum Tai Chis.
These well defined phases imply the wave function for the apparatus plus system must have
them too. Thus, the 'observed' particle must have a definite phase. In Hilbert Space, this is equivalent
to a definite state. This is our first glimpse of what we will call Hilbert space 'phase magnetization'.
It's like putting a single iron filing on a magnet. It will line up in a direction along the magnetic field. Without the magnet, the filing could be in any random direction. Thus,
Quantum Tai Chis in an apparatus 'magnetize' Quantum Tai Chi's in the observed
quantum system. As Lao Tzu says, "the heavy is the foundation for the light."
Another analogy for this process is the way in which a seed crystal tends to crystalize the
solution around it. It is a version of macroscopic definiteness, aligning microscopic molecules in a
A Watched Pot Never Boils
There is another property of quantum observations which has a parallel in psychology. This is the 'quantum Zeno effect'. Zeno, the Greek philospher, proposed that a runner could never cross the finish line. If he runs half the distance to the finish, half the distance again, ad infinitum, he will never reach his destination. Similarly, a quantum system will never change state if continually observed. This was first demonstrated theoretically by Anthony Sudbery at the University of York.
Psychologically, time gets stretched out when we are waiting and watching. If we wait
and watch anxiously for a pot of water to boil, the wait seems interminable.
For this reason, the quantum Zeno effect is like the 'watched pot' that never boils. This was demonstrated in 1989 by Wayne Itano and his colleagues at the National Institute of Standards and Technology. 5,000 atoms of Beryllium were bombarded by radio waves to raise certain of their electrons to an excited state. A pulse of laser light then stimulated all of the electrons that hadn't made it to the higher energy state. A portion of that light was re-emitted immediately. This informed Itano of the portion of electrons still in unexcited states.
Assume we make no intermediate observations with the laser pulse. Then most of the atoms make it to the excited state in, say, 1/4 of a second after the radio bombardment is turned on. We make we make another 1/4 second run with a laser observation 1/8 of a second into the bombardment. In this case, only half the atoms are observed to be excited after the full 1/4 second. More observations between mean less excitations observed at the end of the 1/4 second interval. If 64 intermediate pulses are employed, almost no atoms make the transition. A watched pot never boils.
Classically, this behavior does not make sense. It is exactly as if time is stretched in proportion
to the number of 'glances'. This adds something very important to the quantum perspective.
Somehow the mind is intimately linked with the process of quantum observation. Were it not so, the
act of observation would not change anything. Observation becomes 'Quantum Metaphysics', as
Tony Sudbery says. It is as if the world has no existence independent of the mind.
"All things in the world are born of being,
being is born of non-being."
Lao Tzu--Tao Te Ching
Pearle Dives Into the Unknown
The mystery deepens when one realizes that the angle of the Quantum Tai Chi may not be 'free' after all. In 1976, Philip Pearle of Hamilton College, New York, proposed that wave function phases select the outcome of a quantum experiment.
He suggested that Quantum Theory be extended by adding an extra energy term. This term uses the quantum Tai Chis of the possibilities as initial conditions. They 'drive' the quantum equations to select a single observed quantum state. These initial quantum gauge angles are chosen randomly. This says (although he did not) that 'someone' might be 'playing dice' with the Quantum Tai Chis.
Pearle's theory harmonizes with all the known facts. It is a wonder that it hasn't been given
more attention. However, is there a way in which this random choice of Quantum Tai Chis is made?
Could this choice lose its statistical character where macroscopic objects and events are concerned?
A Phase Transition In the Brain?
A glimpse of what might be going on has been given by Roger Penrose, black hole and 'twistor' theorist. In The Emperor's New Mind, he suggests we may grow neuronal networks in the brain in a way analogous to wave function collapse. Consciousness may examine the alternative networks and chooses the best for the purpose. Penrose was searching for a solution to the dillemma presented by the behavior of quasicrystals. However, it is important that the brain may be pivotal in understanding quantum behavior of macroscopic objects. This may not always be a probabilistic choice. In this picture, the mind is constantly programming the brain hardware. It uses principles comparable to Quantum Theory, but with additional constraints. It may be capable of finding the best dendritic network, not just one of many possible.
This is true for the process of learning. Might it also be true for the collapse of the wave function, particularly for macroscopic objects? Physicist Amit Goswami, physics professor at the University of Oregon, considers this possibility. In his ground-breaking book, The Self-Aware Universe, he comes to the inescapable conclusion that consciousness creates the material world by collapsing the quantum wave function. If so, could this be expressed in neuronal patterning in the brain?
We do not directly perceive quantum events. Perhaps conventional probabilistic rules always apply when we observe them. However, in the macroscopic world a choice of phases for possible wave functions matters. Our decisions and dendritic patterns matter. This is particularly true if we believe in a fusion of the ideas of Pearle and Penrose. Pearle's explanation for the collapse of the wave function may apply to dendritic connections. Consciousness may be working with quantum Tai Chi's to select neuronal patterns.
In such a picture, wave function phases are symmetric before collapse. The symmetry is broken in the process of microscopic observation. In a ferromagnet above the Curie Temperature, atomic 'magnets' are randomly oriented. No overall magnetism is observed, because these random vectors cancel. However, when the material is lowered below the Curie Temperature, the atomic magnetic vectors align. Macroscopic magnetism is observed.
Danah Zohar, in her book, The Quantum Self, proposes a quantum mechanical model of consciousness which she claims analogous to a magnetic phase change. She postulates that Bose-Einstein condensation is the phase change responsible for the unbroken awareness we call consciousness. Bose-Einstein condensation occurs in a superconducting medium. It is signaled by all the wave functions of a large group of particles randomly choosing a given phase. From then on, they 'wave together'. This phase is physically manifest in the velocity of a group of particles. Observation of the superconducting phase is an example of a macroscopic 'object' exhibiting quantum properties.
Choosing a phase angle for the overall superconducting wave function is analogous to
magnetization. The same equations apply for magnets alowed to align only in 2 dimensions. Ms.
Zohar notes that in choosing to adopt the same phase, the particles are exhibiting 'unbroken
wholeness'. This is a vital characteristic of consciousness. She concludes:
"I think that... Bose-Einstein condensation among neuron constituents is what distinguishes the conscious from the unconscious. I think that it is the physical basis of consciousness."
This model for brain functioning has been suggested by several reputable scientists (Marshall, Orlov, and Frohlich). However, it does not provide the solution to the quantum interpretation dilemma. It does leave us two clues: (1) the key may be a phase change, (2) consciousness itself may be described by a phase change involving interactive elements.
In this chapter we have laid a foundation for the search for a workable interpretation of
Quantum Theory. However, we desire more insight into the nature of consciousness. In the next
chapter, we get it in the Quantum Phase Ensemble Phase Transition (QPEPT) model for wave
7. MIND OVER QUANTUM MATTER
"In the State of Lu there was a man named Wang T'ai, who had one of his legs cut off. His disciples were as numerous as those of Confucius. Ch'ang Chi asked Confucius, 'The man has been mutilated, and yet people call him 'Master'. He must be very different from the ordinary men. If so, how does he train his mind?' 'Life and death are indeed changes of great moment,' answered Confucius, 'but they cannot affect his mind... It can control the transformation of things, while preserving its source intact.'
We have reached a strange impasse in physics. The very small is more completely understood than the very large. Quantum Theory is the best and most universal physics paradigm of all time. It has described the humble electron with precision beyond what we had ever dreamed possible. The electric coupling constant has been determined to at least 15 decimal places, a success unheard of in other theories.
It is suspected that Quantum Theory in some form applies to macroscopic objects like chair and
humans. We have a straightforward idea of how we could apply it. However, we have no way of
testing our supposition. To do this we would have to add up the wave functions of quadrillions of
atoms. Will Quantum Theory with no additions apply to the behavior of large objects, or will we need
The Tai Chi of Superconductivity
The strange behavior of superconducting material may be the best clue we have to unravel this mystery. Ginzburg and Landau, two Soviet physicists, developed a theory to explain superconductivity which identifies its large-scale order as macroscopic quantum order. They suggested that superconducting electrons form a macroscopic quantum state.
A change in matter phase can be described by an 'order parameter'. It describes how much of the object is ordered in a certain way. In going from a non-magnetic to a magnetic state in a magnetic material, the order parameter is the magnetization. In a liquid crystal, the order parameter is molecular bond orientation.
Ginzburg and Landau shocked the physics world. They indicated that the superconducting order parameter looks exactly like a wave function for a single quantum state. This is a quantum state involving billions of electrons. Can that many electrons choose to 'dance' the 'Quantum Tai Chi' together?
Like the Quantum Tai Chi, the superconducting 'wave function' has an amplitude and an associated phase. The energy associated with the group of electrons depends in a special way on this wave function. The energy is a minimum for a change in state. It turns out that this energy is minimum when each pair of electrons ('Cooper pair') has the same phase. A system comes to equilibrium in the state with the least energy. Thus, the quantum wave function is a superposition or addition of the single pair wave functions. It has the same phase as each pair
to minimize the energy.
It is as if each electron pairs moves in step. It is as if each is aware of the others, or
coordinated by command. Similarly, a group of students can do a Tai Chi routine in
synchronous motion. However, training and coordination are required.
The form of the superconducting energy is the same mathematically as for two-dimensional magnets with non-local interactions. Such magnets are constrained to align only in a plane. 2-D magnets with non-local interactions are like beings in 'flatland' equipped with telephones. They have a massive 'conference call' in which they are all requested to orient themselves to the northeast, for example. A minimum in energy is achieved when they are all aligned at the same angle, so they do so. In the same way, superconducting phases 'magnetize' to the same phase angle. It is as if there were a force between them.
Normal 2-D magnets only interact with their nearest neighbors. They develop no long-range order. They have no non-local interactions. However, Cooper pairs of electrons in superconductors do.
Thus, in superconductivity there is an energy associated with quantum phase alignment of the constituent particles. One could ask whether this is true for the wave function possibilities in a quantum measurement as well.
In the Ginzburg-Landau Theory, the 'wave function' plays the role of a 'magnetization' which
aligns the Cooper pair phases in the same direction. Random alignment of phases is gauge symmetry.
This is broken when the phases line up. The phases are 'out of alignment' when the temperature is
high. This is a 'buffeting' process. It is similar to what occurs for atomic 'magnets' in a magnetic
material above the Curie temperature. We can transfer this 'buffeting' process to a phase change in
the brain. It is the neuronal noise background caused by random firing of brain cells.
Wave Function Reduction as a Change of Mind
Stephen Weinberg received the Nobel prize for his part in the gauge unification of the weak
force and electromagnetism. He gives us a prescription for the next step in the evolution of the
quantum theory of measurement. This is quoted from his 1993 work, Dreams of a Final Theory:
"What one needs is a quantum mechanical model with a wave function that describes not only
various systems under study but also something representing a conscious observer. With such
a model, one would try to show that as a result of repeated interactions of the observer with
individual systems, the wave function evolves with certainty to a final wave function, in which
the observer has become convinced that the probabilities the individual measurements are what
is prescribed in the Cophenhagen interpretation."
We wish to represent the observer in the process of quantum collapse. We have repeatedly suggested that the quantum gauge be used to describe the functioning of the brain or consciousness. Consider a microscopic quantum measurement. Is it possible that consciousness changes state in a way analogous to the superconducting transition? This is tantalizing suggestion. After all, each possible state's wave function has an infinity of equally probable possibilities for its phase.
The choice of a single phase for each state could be accomplished by phase 'magnetization'. Though this would require a complex arrangement, the number of neurons in the brain is staggering. Within each neuron are microtubules which may record information like components of a minicomputer. With trillions of neurons, we may have trillions of microcomputers at our command.
It is also known that the process of memory storage is redundant in a multitude of locations in
the brain. Even when brain cells die with age, our memories live. As Naval brain researcher Leon
"... a distributed memory... possesses in a very natural way the property of relative
invulnerability to the loss of storage units: individual memory sites hold superimposed
information concerning many events. In order to obtain a single event, information must be
gathered from many sites. Loss of individual units decreases signal-to-noise ratios, but does
not lose items of information."
Cooper further reasons there is 'parallel processing' going on in the brain. If so, why not processing in which each parallel computation involves a 'micro magnet' in gauge space? The processing 'magnetically' selects gauge angles and brings about wave function collapse. Before collapse, the possible states exist in the unconscious. After collapse, the 'magnetic' alignment of phases selects one of them repeated in redundant portions of the brain. This redundancy then 'creates' the real world of observation, as Dr. Goswami has suggested.
Thus, a set of phases is randomly chosen for the possible states in a quantum observation. Pearle's theory can then be used to pick a unique state from among the possibilities. The wave function collapses as the result of a phase change in the brain or consciousness.
All this may be accomplished mathematically without changing Quantum Theory. We just add an energy term for the phase interactions in the brain or consciousness. This term would be identical to the energy term suggested by Ginzburg and Landau for superconductivity. Such a choice solves one of the problems presented by Pearle's theory. Using the Ginzburg-Landau form for the energy, a necessary sign change occurs at the transition in state. This sign change is obtained by changing Quantum Theory in Pearle's version.
The Temperature of Consciousness
One can set an upper limit on the average energy of a 'particle' of consciousness or the brain in this process. A large disk-shaped object should have uncertainty in its angle of orientation in this model. This is caused by the 'buffeting' of consciousness which 'creates' the observation. We can observe to what precision a macroscopic disk lies still. Thus, we can have an idea what fluctuations of energy a 'unit' of consciousness might be limited to.
If the 'particle' of consciousness is a neuron, we could compare this with the neuronal background
firing rate and energy. Microtubule 'noise' is still an unknown. Finding it may eventually determine
a transition 'temperature' for consciousness. This consciousness makes the 'real' world from the
world of possibilities..
Quantum Gravity's Simplest of all Possible Worlds
The merger of Quantum Theory with Gravity has been the most challenging pursuit in the history of physics. The search for a useful Quantum Gravity goes on. As Stephen Hawking has pointed out, the uncertainty principle is in conflict with the unique bending of space-time in Einstein's General Theory of Relativity. If the position of a particle is uncertain, how can it follow a precise path in space-time as Einstein suggests? Superstring Theory purports to be a solution to this dilemma. However, its equations are still too complex to allow predictions to be made.
The simplest imaginable solution is called Semiclassical Quantum Gravity. In it, the possible states of matter are 'averaged' (a quantum 'expectation value' is taken). That average state's energy configuration is used to determine the curvature of space-time.
However, in the 'phase magnetization' theory we have been discussing, we don't need to take an expectation value to have Semiclassical Quantum Gravity. A given curvature of space is magnetized when the brain phase transition precipitates 'physical reality'.
At its essence, Quantum Phase Ensemble Phase Transition Theory (QPEPT) eliminates quantum uncertainty in the curvature of space. Such uncertainty is only existent in the redundant circuits of the brain or consciousness before magnetization 'creates' the world. For a given set of phases, or Quantum Tai Chis, only one location of a particle is possible after quantum collapse. This is the difference between conscious awareness and pre-collapse unconscious awareness. Pre-collapse awareness is multiple and not redundantly amplified.
Thus, it is a phase transition in the brain or consciousness that precipitates a given position for a
particle. It determines the curvature of space itself. This picture is a deterministic one. The playing
of 'dice' obeys deterministic rules in a real dice game. In the phase transition of consciousness, the
laws of deterministic physics also determine the outcome.
"There is a virtue, a power that issues from the Way (Tao) like a magnetic field around a magnet.
As the magnet controls the shape of the field, so the Way controls its virtue or power."
Paraphrase by R. B. Blakney
Tao Te Ching by Lao Tzu
8. TOWARD A GAUGE THEORY OF CONSCIOUSNESS
"...the mind is at every stage a theatre of
simultaneous possibilities. Consciousness
consists in the comparison of these with each
other, the selection of some, and the
supression of others, of the rest by the
reinforcing and inhibiting agency of attention...
The mind, in short, works on the
data it received much as a sculptor works on
a block of stone."
William James, The Principles of Psychology
Wave Functions (Tai Chis) For Life Decisions
An off-Broadway play often has 200 or 300 actors trying out for a leading role. The director chooses a scene from the play and watches each actor perform. He chooses only one of the actors for the part.
People believe that various factors write the script for their lives. Cosmos, karma, God, or destiny are blamed for their life circumstances. However, most believe we have some form of free will (at least the appearance of choice) in how we interpret that script. We choose from a panorama of selves, which will read each line. This decision is like 'fixing the gauge'. In the QPEPT picture this realizes one world from the many possible. As Danah Zohar, iné The Quantum Selfü, points out, "A choice is... nothing but an act of concentration that collapses the wave function of possible thought."
Perhaps Quantum Theory does apply to our life decisions. It must if it is a Theory Of Everything. If it does, there is a wave function representing, as William James describes it, the 'theatre of simultaneous possibilities'. We ignore the possibility Quantum Theory may not apply to macroscopic objects. This is supported by preliminary data (particularly in SQUID experiments).
Postulate that we could construct 'life choice' wave function. This function represents a separate universe for each choice. This is similar to the universal wave function in the Everett-Wheeler-Graham 'many worlds' interpretation of Quantum Theory. In that picture, there is a universe described for every outcome of a quantum experiment. The difference is that a decision is under the control of an individual. However, the rules governing a microscopic quantum experiment cannot be controlled. They follow the laws of probability.
Thus, the overall wave function for a life decision is enormously complicated. It involves sums of universal wave functions. The collapse of the wave function in Quantum Theory is normally limited by the probabilities associated with each possible observation. In the Gauge Theory of Consciousness we espouse, the result is more definite. A choice of gauge 'makes the decision'. It is the prerogative of the consciousness perceiving the possibilities.
The sense data, the memory, divinity, or the human ego presents the possibilities. However, the 'person' must choose. This is 'free will'. It is the domain of Gauge Freedom. In an unhewn block of stone, a sculptor can see many creative possibilities. He or she will bring only one to completion. To understand this process, we might ask what role the brain plays in the decision-making. Where in the brain does the mysterious 'consciousness' live? Does it reside in the brain at all? Studying the brain and the mind, we may better understand the gauge choice involved in decision making. The purpose is to provide a mathematical basis for the psychology of consciousness. With the Math in hand, we can then make models of consciousness at human and metaphysical levels. We can test these models by observations and experiment. Thus, we may know the scientific 'truth' about realms beyond our ordinary consciousness.
The brain itself, not to mention the mind and consciousness, is an elusive 'butterfly'. If consciousness is 'the ghost in the machine', what is the nature of the machine?
In 1848 a construction worker named Phineas Gage (a coincidence?) was tamping gunpowder into a rock with a 1 1/2 inch steel rod. The powder exploded. The rod was driven into his brain just above one eye. It emerged at the top of the head, destroying large portions of his thinking 'mechanism'.
After the incident he sported a hole in his head which could have been used as a telescope tube. However, he continued working and functioning as a 'normal' human being. 100 years later, psychologists used his remarkable case to justify lobotomies for very depressed patients. In this proceedure, they inserted a metal 'icepick' through the eye socket. They severed a portion of the forebrain.
In spite of this gruesome history, several things were learned from Gage's post-accident behavior. First, the brain can function in spite of severe damage. Thus, certain of its systems are non-local in nature. Second, Gage's moral sense was impaired. He changed from a straight-laced gentleman to a shiftless, seducing drunkard. His case was the first to implicate the forebrain as the seat for 'moral' control. Did the mind program moral control into the forebrain? Alternately, was the forebrain the location of the thinking, deciding mind? Is the mind a separate source of energy from the brain, as Descartes suggested?
In 1952, Dr. Wilder Penfield, a brain surgeon from the Montreal Neurological Institute, found that he could disconnect the decision-making capability of human subjects. He stimulated a deep region of the temporal lobe of the brain with an electrical probe. The temporal lobe is an area on the side of the brain which activates memory. Under stimulation, the subject acts like a confused robot. He is not able to initiate any actions not already begun. However, he completes his 'program' without decision-making ability.
Such behavior is identical to the symptoms of a 'petit mal' epileptic seizure. This area of the temporal lobe, when disturbed by a probe, spreads its disturbance to grey matter in the center of the higher brainstem. Also, in cases of physical damage to the brainstem, loss of consciousness often occurs. Considering these facts, Penfield concluded: "The indispensable substratum of consciousness lies outside the cerebral cortex, probably in the diencephalon (the higher brain stem)."
Roger Penrose, black hole investigator, has also suggested that consciousness is separate from the brain. To represent a learned function, some form of consciousness may select a particular neuronal network. In QPEPT theory, the higher brain stem might be the center for the dissemination of the information from a phase transition in consciousness. This transition is due to a kind of 'magnetization'. It selects one macro or micro quantum 'world' from among the many possibilities.
This brain pattern creates the world of perceptions to match its character. Perhaps the world constantly changes because of our decisions (or the consciousness behind us). On the other hand, the appearance of the world may be a delusion, a 'maya', a 'shadow play'. Is is like that seen by Plato's allegorical inhabitants of 'the cave'.
Does our choice of worlds have restrictions? If so, what might restrict it? We know the sun's
cycle about the earth influences our choice to get up in the morning. Could it be that many different
cycles regulate our lives? Do they mirror those in deeper layers of consciousness?
The Gauge Theory of Cycles
"The fatal order of destiny is an eternal chain, forever looping
itself in cycles consistent with its own order." Nostradamus
A cyclic occurrence reveals a symmetry in time. A periodic change in nature repeats itself after a certain length of time. The time between repetitions, we call the 'period'.
It is trivial to construct a periodic wave function. Make the gauge linear in time, i.e., equal to wt, a constant times time. It then mimics the phase in the Tai Chi of ancient Chinese lore. The 'two fishes' rotate at a constant rate through mixtures of yin and yang.
However, this time dependence defines a 'stationary state' in Quantum Theory. Stationary states do not evolve with time. Quantum objects with unvarying potential energy are 'stationary'. Thus, we cannot represent a physical cycle this way. We need to make something physical (not the wave function) periodic.
It is easy to make the potential energy periodic and calculate what form the related gauge will take. This calculation requires a gauge that is sinusoidal. A sinusoidal gauge is reminiscent of the 'two fish' which make up the Taoist Tai Chi. The central portion looks like a sine function turned on its side. Was this similarity intended originally? Whether it was or not, a sinusoidal quantum gauge has a unique effect on the forces which such a 'gauge' symmetry implies.
The force is repulsive at the beginning of a cycle, and attractive in the middle. Say that quantum wave functions represent human beings. Also, suppose that the resultant force of the corresponding Gauge Theory is between persons and the world. Then the beginning of a cycle finds the individual acting on the universe. The middle of the cycle finds them attracting what they have put out. With many cycle gauges in action, the result becomes more complex. It may look periodic, depending on the focus.
In another sense, 'cycle time' is time transformed. It is the 'sine function' of time. It represents sowing and reaping of deeds. The New Testament (Jesus) says, "whatsoever ye shall sow, that also shall ye reap." The action of the force is the same at t = 0, t = T, t = 2T, etc. It ignores linear time. The hands of a mechanical clock move with a similar symmetry. The hour hand moves past the twelve digits. It also returns to its original position. In completely cyclic interactions, the future and the past are one at the same position in the cycle. This is 'recycled time'. With no future and no past, time and space 'disappear'.
The right brain could easily accomodate such 'timekeeping'. It functions to process similarity in perceptions and thoughts. On the other hand, the left brain perceives events in the normal serial, linear, or causal time. To it, one event causes another at a later time. The process never begins again.
The Gauge Theory of Consciousness, then, suggests there is another form of time. It is a multiple
time--cycle time--in which archetypal experiences are outpictured as a fabric for perceiving the world.
Children often think in a right-brained way. In a process called 'syncretism' in psychology, a child
will relate one similar event or object to another. We have all heard a child calls a woman who
is not her mother, 'mommy', a cat a 'doggie', or a school a 'house'. The mode is to name sense
objects by their similarity. Perhaps this all happens on cue, as manifestations of different cycle flow
phases. These phases are particular mixtures of 'yin' and 'yang', and have archetypal significance.
Is 'cycle time' an escape from causality? The answer is 'yes' if we think of causality in the ordinary sense. It is, if we think physical objects always cause events later in time. However, in the 'cycle time' picture, we relate perceptions to a causal physical phenomenon in the brain or the consciousness which rules it. This does not always mean the perceptions are causal. They are on another level from the phase transition producing them.
This transcendant causal phenomenon is like the spinning of a wheel. Only one portion of it at a
time rises above the murky waters of the unconscious. In this picture, the causality described does
not exist in the outer world. However, the outer world is produced by a causal phenomenon in the
brain or consciousness.
The Memory Tai Chi
Memories could be recorded in cyclic or archetypal fashion, analogous to the way sound is recorded on a compact disc. The winding of the recorded memory coil occurs at a rate of one turn per cycle period. All information at a given phase of the cycle is given a similar coded character. Accessing memory in this model is like shooting a laser towards the center of the disk. This accesses all records at the same cycle phase. The perceptions then reflect the records of all experiences in that phase of the cycle.
Scientists have found the right brain can analyze perceptions frozen in a moment. It can break down that moment or 'gestalt' into categories of information. The right brain could sort all the information from an instant's experience according to the qualities represented by the individual cycles.
The recording angle for each impression is important. This is because all the information stored
on the same radial line in the disk is accessed so consciousness can produce the world. This represents
the 'sowing and reaping' of our actions implied by the gauge force. At that point, the possibilities for
choice become apparent. The wave function collapses to produce a single world.
Once the perceived world is 'chosen', the left brain linearizes our perceptions and creates the impression that 'time marches on'. Thus, we perceive that events 'cause' one another. In contrast, at times we catch a glimpse of the right-brain 'acausal' process Carl Jung called 'synchronicity'. We will disscuss this concept in the next chapter. From the perspective of synchronous events, linear time does not exist.
Let us examine an example of how one cycle might play a part in this process. This example,
though speculative, may show how an outer cycle might relate to an 'inner' one.
The circuit of Jupiter about the Sun takes a little less than 12 years. The sun's magnetic
field reverse in about the same time. There have been theories connecting the two cycles. The
reversal of the sun's magnetic field relates to the 11-12 year periodic increase of sunspots.
The increased sunspots are connected with increased solar wind. This is the stream of charged
particles which comes from the sun and bombards the earth. It affects fluctuations of the
earth's magnetic field. The major cycle of fluctuation is about 10 Hertz (cycles per second).
This cycle is mirrored by the alpha state of brain waves (also 10 Hertz).
We then have a chain of causality. Jupiter causes the sunspot cycle, sunspots cause the solar wind, and the solar wind causes fluctuations in the earth's magnetic field. This information is placed on a 10 Hertz carrier wave. It resonantly feeds energy into the alpha state of the human brain. Such a manifestation is a combination of two cycles recorded by human beings. These are the 12 year sunspot cycle and the 10 Hertz cycle of the earth's magnetic field. The larger is information on the carrier wave of the smaller.
Every twelve years, a landmark in time is reached. It is a kind of rebirth in solar, Jupiter energy. The child becomes the adolescent at age 12. The adolescent the becomes the young adult at age 24, the young adult middle-aged at 36. The middle-aged is senior at 48, the senior elderly at 60, and the elderly on the average passes on at 72. Each of these ages is a benchmark in the life of a human being. It is a rebirth of direction and emphasis. One might almost think that Jupiter, the king of the Roman gods, is directing their lives.
The above digression is not intended to give credence to astrology as it stands. Rather it shows
that certain cycles relate to the unfolding of our lives in an impelling 'causal' fashion. We see the
cause within the brain or consciousness.
9. FOREVER JUNG (AND YANG)
"No man should know where his dreams
come from. It spoils the mystery!"
Data's father, Star Trek,
The Next Generation
"There is something formless yet complete
That existed before heaven and earth.
How still! How empty!
Dependent on nothing, unchanging,
All pervading, unfailing.
One may think of it as the mother of
all things under heaven.
I do not know its name,
But call it "Meaning. (Tao)"
Lao Tzu, Tao Teh Ching
Adapted from Arthur Waley by Carl Jung
Carl Jung was a psychotherapist and a student of alchemy, mythology, and Eastern philosophy. He once had a close friendship with Sigmund Freud, the inventor of the psychology of repression. In 1906, Jung wrote a paper defending Freud's theory of obsessional neuroses. Freud invited him to visit. At the time, Freud was the laughing stock of the psychological world.
Jung's sympathy with Freud's ideas created a bond that was intense but short-lived. From the
beginning, Jung disagreed with Freud's theory concerning the sexual basis of all neurosis. However,
he soon saw that sexuality for Freud had become a 'numinosum'. This is a compulsive dominating
complex in one's psychology. It became obvious when he told him,
"My dear Jung, promise me never to abandon the sexual theory. That is the most essential thing of all. You see, we must make a dogma of it, an unshakable bulwark."
(Memories, Dreams, Reflections, Jung)
This statement alarmed Jung. It suggested Freud's theory was founded on a 'personal power drive', rather than strict scientific evidence. As Jung states, it "struck to the heart of our friendship." Furthermore, the 'bulwark' Freud desired was actually a defense against religion, philosophy, occultism, and parapsychology. He considered them a "black tide of mud."
Jung was shocked. Freud was at war with a whole segment of life. He recognized the "eruption of unconscious religious factors." Freud hoped the barrier of his sexual obsession would withstand the onslaught. His 'God' had become sexuality.
A dream, which he shared with Freud, illuminated differences in Jung's understanding of the psyche. Jung describes the setting of the dream as "my house." The upper floor was a salon, decorated with 'precious old paintings'. The dreamer explored the salon, then descended the stairs to the ground floor. The tone was ancient, 'medieval', and dark. In one of the rooms, a heavy door led to the cellar. The cellar had a vaulted, Romanesque stone block construction. Encountering a ring-fitted stone slab on the floor, he opened it. He stepped down a stairway into a low cave. Dust, broken pottery, and bones lay about, "like remains of a primitive culture." Two disintegrating human skulls startled him awake.
Freud interpreted the skulls in Jung's dream as an embodiment of a death wish. He later claimed it was directed at himself. Jung, on the other hand, began to understand the house as an image of the structure of the psyche. The salon was the conscious level. The ground floor was the first level of the unconscious. Jung later called this the 'personal unconscious'. It is where unwanted impressions, thoughts, and perceptions are stored by the ego. It was the level Freud himself had penetrated. However, he claimed it under the control of sexuality alone.
Jung saw the deeper levels as the more primitive parts of himself. The cave bordered on the "life of the animal soul." These lower levels he later considered common to all men. He called them the 'collective unconscious'.
Jung's differences with Freud, who espoused no such 'collective unconscious', came to a head. At the time, Jung was working on a chapter called 'The Sacrifice' in his book, Symbols of Transformation. In it, his discussion of incest questioned Freud's emphasis on the sexual significance of early childhood. He went ahead with publication, sensing it would destroy their friendship. Freud was miffed, and abandoned contact.
As a result, Jung endured a period in which he doubted himself and his work. He was ostracized from the psychological community. Even now, the academic establishment does not fully recognize the scope and importance of his work.
How does Jung's picture of the levels of human consciousness correspond to the Gauge Theory of Consciousness described in the last chapter?
The conscious level is intrepreted as the world chosen by extensive collective magnetism of quantum Tai Chi phases. It involves redundant replication of a 'world' possibility. Thus, the conscious state exhibits unbroken wholeness and single-minded awareness. It harmonizes with micro quantum observations. It also represents the locking-in of a conscious 'decision' involving macroscopic entities. This occurs through a Quantum Tai Chi, or wave function.
Repression of experiences and thoughts accomplished by the ego are a lowering of the impression amplitude below the background neuronal noise level. After subsidence, there may be only a weak record in memory. The imprint exists, but at a much lower intensity. Sometimes, portions of complexes beneath the surface of the personal unconscious appear in a process of spontaneous 'magnetization'. If this happens during sleep, dreams may occur. This is because the attention is not focussed enough to magnify the alignment.
Jung recognized "consciousness posesses a threshold intensity which its contents must have attained, so that all elements that are too weak remain in the unconscious." ('The Transcendent Function', P. 69 Bollingen Series XX)
The collective unconscious contains the past and future. This harmonizes with the QPEPT picture of the many possible worlds. Their subspaces represent archetypes or patterns of behavior. In this realm, none of the possibilities achieve enough alignment to surface as a conscious conglomerate. They do not, unless activated by conscious events. Conscious thoughts and perceptions act as a polarizing magnet. They magnetize possibilities relating to the history of mankind. The archetypes may appear in cycle time. They may be amplified selectively by the personal unconscious, with differing values or power. They attract complexes to themselves which are like aligned magnetic domains.
The whole process may happen in the opposite direction. The unconscious may influence conscious perceptions, thinking, and decisions. It does this by applying a magnetism in a direction toward certain possibilities exclusive of others. Thus, spontaneous magnetization will be chosen by unconscious forces, often without conscious thought. Sometimes our conscious mind has freedom to choose. At other times, we compulsively act or react without thought.
The degree of consciousness of a possibility is represented by the degree of magnetic alignment of redundant 'cells' in the brain or consciousness beyond. A spectrum of continuous levels is described.
When the magnetization is just at the level of 'neuronal' noise, the impression is one of the personal unconscious. This is because it has the character of a personal 'world' by the time it reaches that level. Levels in the collective unconscious have coalesced only in racial and human terms. They have values or magnetizations still below the level of noise.
One way in which the nature of the unconscious levels may be realized is by consciously lowering the noise level. This can be done by such isolating activities as prayer, meditation, and retreating from the outer stimulation of the world. Normal life and psychological processing 'disturbs the waters'. With a lowered noise level, magnetization is easier to achieve. This is especially true for formerly unconscious possibilities. In this way one begins to consciously understand the psyche and the self which unifies it. This is commonly called 'self realization'.
It is also why sleeping on a problem sometimes brings a solution. Sleep lowers the noise level.
It allows clarity and decision to 'snap in'. I have noticed that a snapping sensation occurs after I have
gone into a deep nap. This is a transformation which clears my mind and soul. At that time, I feel the
purpose of the nap has been accomplished. I wake up, lining up my 'magnets' in a new direction.
The emergent magnetization of a subconscious possibility or event can magnetize similar conscious events. It does this when the two have gauge dimensions in common. Carl Jung called this parallel connection 'synchronicity'. Such occurrences defy the laws of probability. They obey only a law of similarity.
The principle of synchronicity began to crystallize for Jung when he was studying the image of the fish and its impact on the collective unconscious. The fish was associated with Jesus Christ as a symbol of his mission. It was also a symbol of the prescession of the spring equinoctal point into the constellation Pisces.
Jung relates the following experience with a recalcitrantly 'mental' female patient as the archetypal
"She had had an impressive dream the night before, in which someone had given her a golden
scarab--a costly piece of jewelry. While she was telling me this dream, I heard something
behind me gently tapping on the window. I turned round and saw that it was a fairly large
flying insect that was knocking against the window pane from outside in the obvious effort
to get into the dark room. This seemed to me very strange. I opened the window immediately
and caught the insect in the air as it flew in. It was a scarabeid beetle, or common rose-chafer
(Cetonia aurata), whose gold-green colour most nearly resembles that of a golden scarab. I
handed the beetle to my patient with the words, 'Here is your scarab.'"
The patient, who had intellectual barriers to the progress of her analysis, experienced a breakthrough.
There are synchronisitic events other than those that take place simultaneously. Jung placed in that category psychic knowing at a distance and precognition (knowing events before they occur). J.D. Rhine, explored 'psychic' phenomena at Duke University. He found that symbol cards could be read with equal success at any distance. This occurred with any interval of time lapse between prediction and selection. The synchronistic 'power' was independent of space and time.
Magnetization of conscious 'worlds' by unconscious tendencies is plausible. However, what about events separated by large intervals of space or time that make signalling impossible?
Clairvoyance or clairaudience can be seen as a manifestation of the 'magnetized' world being cognized from within. This happens before it is aligned enough to manifest. The collapse of the wave function for an entire world happens instantaneously. Before it occurs, the process is partially aligned in the brain or consciousness. This is before it surfaces and fully aligns as a polarizing 'magnet'.
The workings of cycle time and the cyclic gauge can account for precognition. All similar phases
of a given cycle magnetize events similar throughout time. Several cycles may coincide to provide
more detail. Then the present may provide us a glimpse of the future as a seed within.
The Tibetan Wheel of Time
Similar ideas are encountered in the Tibetan Buddhist teaching on the Kalachakra, or 'Wheel of Time'. This teaching is said to have come from the legendary city, Shamballa. This is the suggested source of the Tai Chi itself. As Edwin Bernbaum has written in The Way To Shamballa, the Tibetan systems of Astronomy and Astrology as well as the Kalachakra came from this 'mythical' metropolis. Some say it once lay in the Gobi Desert.
Enlightment, in the Kalachakra discipline, involves letting go of the past and future. Then one must lose the sense of the present. The experience of time takes place only in the 'now'. The whole of time, past and future, exists as patterns in the unconscious. These are archetypes which surface cyclicly in a wheel-like fashion. They obey the rules of 'cycle time'. However, with meditation and practice, one becomes aware of the entire series of archetypes in the universal cycle. The surface of the unconscious is penetrated. All time becomes realized in the present. Time itself becomes a timeless, eternal wheel.
This process is the cycling of the archetypes of various phases of the Quantum Tai Chi. In a given cycle, it involves a surfacing of one at a time. This imitates a spinning archetypal wheel immersed in unconscious waters. Only a small part emerges into conscious awareness at one time. Many wheels with many cycle times are necessary for creating the 'illusion' of change and evolution. The greater awareness 'sees' all the cycles and their archetypes at once. When one has it, the 'gears' of unfolding events are comprehended.
The process is to realize outer events as the result of an inner flow. This flow magnetizes life circumstances to us. Time then becomes "a succession of mental images that have no existence of their own apart from the timeless moment of actual experience" (Bernbaum). The left brain (linear) and right brain (cyclic) times become unified as awareness extends beyond the conscious.
The Tibetan deities representing the cycling archetypes are realized to be one with the central tutelary deity of the Kalachakra. Similarly, in Jungian psychology all is under the rule of the
unconscious self. The mastery of these initiations is said to give the ability to travel in time and space. The initiate can go to the past, the future, or distant worlds.
This would be impossible without the 'many worlds' of Quantum Theory. In that theory, it is not contradictory to disturb the present world by visiting the past. To travel in time to the past, one must change 'leaves' to a parallel but 'adjacent' world. The future world is dependent on choice, however, and may not be predicted with certainty. We may only visit the possibilities as quantum parallel worlds.
Ezekiel and the Wheels
Ezekiel had a vision which corroborates the 'wheel' of archetypes, cycling into conscious manifestation. He describes the visitation of four four-winged creatures, each with four heads. These were the lion, the man, the calf, and the flying eagle. These beings had the body of a man. Each moved forward in the direction of one of the heads, without turning. Thus, they descended from heaven and touched the earth. With each of them came lightning flashes of great energy... and a wheel.
"I saw a wheel touching the ground beside each of the four-faced creatures. The
appearance and structure of the wheels were like glittering chrysolite (beryl or emerald)...
each wheel seemed to have another wheel inside it... Their circumference was of
awe-inspiring size, and the rims of all four sparkled all the way round... the wheels shared
the spirit of the animals... In my hearing, the wheels were called 'galgal' (something which
revolves or whirls). Each had four faces: the first was a winged creature's face, the second
a human face, the third a lion's face, and the fourth an eagle's face... When the winged
creatures moved, the wheels moved beside them... When the former halted, the latter halted
(on the earth)."
The wheels descend from heaven (the superconscious) as a part of the ritual of dispensing
retribution in a cycle. The wheels turn except when they are on the ground. They and the winged
creatures carry an energy to be used for the judgment of men:
"He (Yahweh) said to a man dressed in linen (an angel?), 'Go in between the wheels
below the winged creatures; take a handful of burning coal from between winged creatures
and scatter it over the city... " (New Jerusalem Bible)
Yahweh then showed Ezekiel the evil in the city of Jerusalem which was to be judged by the 'burning coal'.
The wheels, in the King James Version, are said to have "eyes about them four." This
description inspired Jung to comment,
"The identification of the All-Seeing with Time probably explains the eyes on the wheels
in Ezekiel's vision... We mention this identification because of its special importance: it
indicates the relation between the mundus archetypus of the unconscious and the
'phenomenon' of Time--in other words, it points to the synchronicity of archetypal
events... " ('On The Nature Of The Psyche', P. 198.)
Further, Jung suggests that synchronistic phenomena,
"are, so far as I can see at present, completely explicable on the assumption of a
psychically relative space-time continuum. As soon as a psychic content crosses the threshold
of consciousness (the wheel touches the earth), the synchronistic marginal phenomena
disappear, time and space resume their accustomed sway, and consciousness is once more
isolated in its subjectivity."
The vision of the 'wheels' is corroborated by the ancient Book Of Enoch, in which they are called 'Ophanin', or spinning disks. They accompany the cherubim, a term sometimes used for the winged four-faced 'men'.
Revelations 4:6-9 details a vision similar to that of Ezekiel, in which "four beasts were full of eyes, before and behind." Again the lion, the calf, the man, and the flying eagle are depicted. In Revelations, each is a separate beast with six wings, "full of eyes within." In addition, four and twenty elders bow down before the throne of Yahweh. These may be cyclical archetypes as well. They sit in circular formation on 24 seats around the throne. These elders relate in pairs to the twelve zodiacal constellations. They were symbolic archetypes in ancient religious lore.
The lion, the man, the calf, and the flying eagle have their significance as the four zodiacal beings of Leo, Aquarius, Taurus, and Scorpio. Each represents one of the four elements of creation: fire, air, earth, and water. Yahweh confers with the four and twenty elders about the visitations of the four winged creatures to earth.
The relevance of the heavenly schemata to the theory of Cycle Gauge Theory is clearly indicated. The turning of the 'wheels' of the cyclic form of the Quantum Tai Chi magnetizes events to recompense mankind for their deeds. Thus, the four forces manifesting through earth, air, fire, and water bring something to the conscious mind of man. It is the energy manifestation of the spinning archetypal wheels of time. In cyclic Gauge Theory, retribution for one's deeds is accounted for by a field and a force. This functioning of the cycle gauge sobers man's free will with a sense of responsibility. It narrows the dimensions of the quantum possibilities.
The freedom left after the narrowing corresponds to free will. It is a matter of personal choice. It is a freedom to choose which of the remaining worlds one will inhabit.
The 'wheels' of cyclic Tai Chi's work through unconscious 'magnetism'. This helps to precipitate
full-fledged magnetism of conscious possibilities or realities.
Healing Rivers: The Breath and the Blueprint of Life
The Yellow Emperor, in his 'Classic On Internal Medicine', describes channels of energy flow related to the human body. These 'healing rivers' or meridians, are cleared by acupuncture and acupressure. They assist the body's self healing and increase vital energy. The meridians could be considered channels for the flow of the 'life force'.
The flow of chi in these meridans could be likened to a force field which changes its location periodically. We have earlier compared 'chi' to a particle field. The paradigm of Gauge Theory, however, inspires a thought. It is that symmetry (expressed in the gauge) may be the reason for the character of the force. What is the reason for character of the life force?
What is the mathematical nature of the gauge symmetry which rules life? If we could understand this, the healing process could be better utilized. This is because the gauge relates intimately to the workings of the conscious and unconscious mind. We have seen this clearly in this chapter.
The meridians together form one continuous channel. There are 14 major meridians in the body. Two of them, the central flow (front center of body) and the governing flow (rear center), continually pulsate. The twelve others achieve maximum life force potential in succession. A pulse wave of potential passes through the body. It charges one portion of the continuous channel at a time. We may follow Yin and Yang flow in the meridians by picturing a person with raised hands ). Yang energy flows to the earth from above (the Sun). Yin flows from the earth upward (towards the sun).
This may relate to ionic flow in the earth's large electric field. This is a field sometimes reaching thousands of volts per meter of ascent into the atmosphere. Flow from the fingertips to the face or from the face to the feet (positive ions) is Yang. Flow from the feet to the torso and from the torso to the fingertips (negative ions) is Yin.
The overall flow of maximum potential through the twelve variable meridians takes 24 hours. This process pictured is analogous to the slow passage of a broad pulse of light through a long, curved light pipe or optical fiber. Every two hours the moveable pulse of the life field switches polarity from Yin to Yang or Yang to Yin. This happens as it changes from a meridian with an upward or downward flow to one going in the opposite direction. The Yang flows manifest an attractive force and concentrates energy. The Yin flows yield an repulsive, dispersive force.
Therefore, in cycle time, this flow requires two major cycles. They are one two hours in length, and one 24 hours. The two hour cycle reverses the polarity of the life force hourly. It is represented by a two hour cycle gauge. The 24 hour period is divided into day and night. This gives it an alternating Yang and Yin nature as well. This is a second cycle gauge symmetry. So in effect, there are two forces acting in the body. They are the alternating force of day and night and the alternating force of the hourly flow up and down the body. They are caused by the polarity of sun (or moon) and earth.
This movement of the life field could be termed, 'the breath of life'. There is another component of the life force, however. That has to do with the location of the flow. It also relates to the location and power of the 'pumping stations' along the way. These are the acupressure points. This component could be called, 'the blueprint of life'.
In Gauge Theory language, the 'blueprint of life' breaks the perfect translational symmetry of empty space. It creates a geometry for the life field. This relates to the force which moves the currents of field sources through the body. This matrix also may be programmed in the consciousness or brain through gauge angles (Tai Chis) relating to specific locations in the body.
Say we ignore the large pulse of field intensity that flows through the meridians. We also ignore an additional rapid pulse of energy at 70-74 beats minute (another cycle gauge not related to the heart rate). Then, a constant spatial matrix of field intensities exists in the meridians. It is superimposed over the temporal flows.
In short, the breath and the blueprint of life are recorded in consciousness as quantum Tai Chi's
with specific symmetries. They yield the character of the life force. Similar rythyms of life and spatial
patterns constitute the living forcefield of plants and animals.
Healing and the Quantum Tai Chi
Of all the possibilities for these patterns in space and time, only certain ones manifest. If this beautiful life pattern in space-time is somehow interrupted or changed, dis-ease occurs. The process is one in which the individual chooses to live outside the given or natural life pattern. There is the factor of free will. It is a certain freedom in Hilbert Space, or the quantum possibilities. This free will allows the pattern to be transformed by human will. It can either devolve or evolve. These choices are given to allow freedom for man to transform or recreate himself.
There are two ways assist the return to wholeness.
The first is to recognize the original space-time pattern and choose to live in the world in which it is in place. We can affirm wholeness, making the right choice from among the quantum possibilities.
A salamander with its tail cut off retains the blueprint and chi flow time-patterning for the tail, and grows it back. Human beings sense, dream, and often live as if a missing arm or leg were still there--the phantom limb. Kirlian photographs of a leaf from a tree show a complete pattern. This occurs even when a portion of the leaf is cut away. (A Kirlian photograph is created by high frequency electronic stimulation. Patterns of coronal discharge relating to the life field are created and recorded on a photographic plate.)
There is a second prescription for healing. It is to find out the lie or perpetration that caused the departure from the ideal space-time pattern. Some claim that this can be done by muscle testing or 'kinesiology' (as in the Kalos Process invented by Valerie Seeman Moreton). Others suggest meditation or prayer. Still others recommend self analysis or psychoanalysis.
The inner complex or archetype causing the perpetration must then be convinced of the truth.
Some resort to talking to the wounded inner child and reassuring it. Others transform negative images
in meditation, bathing them in a flaming violet light. They love and forgive those in their lives who
have caused the wound. All these processes recreate our world. Then change can happen
instantaneously. It takes no time to collapse the wave function, to choose a new world to experience.
We desire a healthier world selected from among the many possible. Metaphysics is Quantum Physics.
Mind over matter is gauge over the universe. We have choice (within any bounds of limitation). This
is because we are the masters of the gauge forces. They originate at the deepest levels of our
awareness. These are levels where gauge magnetization has not yet occurred. There, all possibilities
still exist in infinity.
Gauge Theory: A 'Proof' of the Existence of God
There is a puzzling question related to the QPEPT theory advocated in this book. Can the phase change which 'produces' the world be accomodated by the brain? Must it occur in some consciousness beyond it?
Robert J. Baron, in his book, The Cerebral Computer demonstrates that there are not enough neurons to handle stream of consciousness memory. This Wilder Penfield's recall experiments has shown to exist.
The argument is as follows. If we are awake for 11 hours each day and have a lifespan of 80 years, we are alive for 1 billion seconds. Consider the 100 billion neurons in the brain. This allows for only about 100 neurons per second of processing memory. Only one tenth of neurons are allocated for memory (a reasonable assumption). Thus, this allows only 10 neurons per second of memory.
The patterns which make up our experiences have about 300 dimensions. Thus, only one neuronal bit can be stored every thirty seconds. This contradicts experience. In 30 seconds someone could pick up the newspaper, read three headlines, walk in the house, greet his spouse, and pour himself a glass of water.
However, there are 100s of synaptic connections per neuron. Thus, the amount of informational space available becomes makes memory more plausible. However, this is not so for the redundancy necessary for the QPEPT phase transition.
Each parallel world, or at least the differences between them, must be held in storage in redundant areas in the brain. For one process, this requires at least a million times more memory than the numbers of synapses will allow. Many, many processes must be held in latency. Thus, this would require the storage of information far in excess of one bit per atomic particle in the universe.
Bryce Dewitt was one of the first to do a calculation of the information contained in the Many Worlds of Quantum Theory. One can estimate the information in one 'world' or one universe. This number far transcends the synaptic capability of one brain.
Thus, the phase transition described by QPEPT is in a consciousness which has an awesome capability for information storage and redundancy. It is far beyond any computer conceivable. To build a computer to hold the information for one world alone would require a computer more complex than the universe itself. To consider Many Worlds, or Many Worlds in redundancy is mind-boggling.
Say we believe in the impelling nature of QPEPT Theory. Then to contain the possibilities for human experience requires a consciousness many times more vast than the physical universe itself. The only word we could have for such a vast consciousness is 'infinite'. If we conceive of any set of possibilities, we can always conceive of more related to those conceived. These must all be in place.
Therefore, consciousness must be unlimited and everywhere manifest ('everywhere' could be considered a byword of the Many Worlds 'doctrine'). This conclusion was arrived at from Quantum Theory alone by Amrit Goswami (The Self-Aware Universe). We echo his conviction that this omnipresent consciousness creates the world from the possibilities. QPEPT, however, details a model for the working of this consciousness. The infinite possibilities are made finite by breaking the symmetry of the gauge which allows them.
What then is 'God' or the 'Divine Self' (depending on your conviction) in this picture? It is the infinite possibilities behind the apparent manifestation of our world. 'God', then projects out a limited portion of him/her self by fixing the gauge. This is the human self, 'Adam' in the garden. Adam, however, has free will, and chooses to limit himself further. The 'human dilemma' is born.
Some mystics see the process as 1x1x1x1x... = 1. The oneness multiplies itself to become limited.
However, it is still one with the infinite possibilities: redundant infinity. Like the multiplication of
cells, each new 'monad' or separate being retains the possibility of realizing the infinite possibilities.
EPILOGUE: THE UNIVERSE: HOLOGRAPHIC OR PHASE MAGNETIC?
"Every body placed in the luminous air
spreads out in circles and fills the
surrounding space with infinite likenesses
of itself and appears all in all and all
in every part."
Leonardo Da Vinci
I wanted to end this book with a comparison between David Bohm's Holographic Universe and my Phase Magnetic Universe of the Quantum Tai Chi. I wanted to discuss their advantages and disadvantages. In contemplating this goal, however, I found the two complimentary and mergable. This is in keeping with the philosophy of wholeness espoused by Bohm, and made necessary by Quantum Theory.
Both theories are wholistic, explain the redundant nature of memory and brain function, and represent the processes behind 'psychic phenomena'. However, the Quantum Tai Chi is 'internal' and the Holographic Universe 'external' in a way described below.
The vision of Leonardo he describes above is nearly identical with the vision of the Holographic Universe espoused by David Bohm and Karl Pribram. This vision is well described Michael Talbot in his book, The Holographic Universe:
"Our brains mathematically construct objective reality by interpreting frequencies that are ultimately projections from another dimension, a deeper order of existence that is beyond both space and time. The brain is a hologram enfolded in a holographic universe... the objective world does not exist, at least not in the way we are accustomed to believing. What is 'out there' is a vast ocean of waves and frequencies, and reality looks concrete to us only because our brains are able to take this holographic blur and convert it into the sticks and stones and other familiar objects that make up our world."
To 'catch the wave' of this revolutionary point of view, it is helpful to know how a holographic image is constructed. A laser beam is split into two parts. One part is scattered off a 3-dimensional object and recombined with the second. The interference patterns between the two beams are recorded on a photographic plate. Later, an image of the original object is reconstructed by shining a laser beam on the plate ). This last process is the analogue for the brain's construction of the world from the 'holographic blur' of interfering waves.
David Bohm suggests that there is an implicate and explicate order. The implicate order is that which brings forth the changing holographic 'plate', the mind, to be interpreted by the brain.
The explicate order includes the interference patterns generated and their interpretation as 'the world'. The movement from internal dimensions beyond space and time to create consciousness waves and their resultant 'physical world' Bohm calls 'holomovement'.
In the gauge magnetization picture of the Quantum Tai Chi, the implicate order is mathematical rather than inferred. It comprises the myriad of gauge spaces beyond space and time which characterize the many possible worlds. Such a picture is a filling out of Bohm's idea with a mathematical structure.
The explicate Quantum Tai Chi order is the interpretation of the magnetized gauge dimensions as a realizable, tangible world. The flow from internal dimensions to a transformable world could also be called a 'holomovement' of sorts. Local gauge symmetry is well adapted to the stream of consciousness 'flowing and unfolding' Bohm is seeking.
If the processes both have at least surface similarity, what is the need for a new theory? First, and foremost, the holographic universe is a classical theory. It is not clear how it harmonizes with Quantum Theory. The interfering waves are the wave functions representing possible realities. However, the process of holographic projection is classical. In addition, the holographic universe does not give a reason for the sudden collapse of the wave function. It is not yet the long-sought interpretation of Quantum Theory.
However, in 1966, Bohm and Bub proposed a hidden variable dynamical reduction theory for the wave function ( ). A 'hidden' or unmeasurable vector worked through an extension of Quantum Theory to collapse the wave function. Nevertheless, this hidden variable did not relate to any 'physical' circumstance or quantity. Their theory was meant to show that hidden variable theories could be constructed. It was not that this was the right one. This was a first attempt at showing that implicate orders could be found.
The Quantum Tai Chi magnetization picture is similar. A new term is added to the quantum equation. However, phase magnetization is based on the process going on in a superconductor, not just a mathematical guess. The process is also a possible representation of the functioning of the brain or consciousness. It is as physical as water freezing to ice. It is a phase transition theory, analogous to 2-d magnets.
Phase magnetization is a viable candidate for the Bohm's proposed implicate order. However, the holographic universe represents the explicate order. The two may fit together like pieces of a puzzle.
How could the fusion of these two ideas be accomplished? Waves analogous to magnetic waves may be the answer. It is possible that the information needed to create the world from the magnetized Quantum Tai Chi's may be converted into a pattern similar to that on a holographic plate. This could be manifested as a continual flow of interfering wave patterns in the many phase 'magnets' distributed throughout space. The brain could transform this into the sense perceptions we experience as 'the world out there'.
Such a fusion completes the holographic paradigm by providing an answer to the question
posed by Dana Zohar: "If 'the brain is a hologram perceiving and participating in a holographic
universe' who is looking at the hologram?" The awareness of infinite possibilities magnetized into a
coherent awareness localized in spacetime is at least the beginning of an answer. The magnitude of
consciousness is the magnitude of phase magnetization. A new kind of wholism which transcends the
divisible holographic plate becomes the Quantum Tai Chi. As Zohar concludes:
"...if holism is to have any real meaning it must be grounded in the actual physics of consciousness, in a physics that can underpin the unity of consciousness and relate it both to brain structure and to the common features of our everyday awareness. I think that to achieve that, we must turn to quantum mechanics."
My own inner experiences confirm the nature of The Holographic Universe and the redundant Quantum Tai Chi magnets. When I close my eyes, I see patterns of light and darkness flowing in waves and related to the physical objects in my awareness. Are these holographic interference patterns of the holomovement?
Through my practice of yoga meditation and breathing exercises I have also had the experience of seeing the essence of the world before my eyes transform into billions of points of light. Each point of light contained, not only the entire universe, but infinite universes of possibility. Later, these mini multi-universes condensed into an infinite light glowing and radiating all possibilities from the center of my head. I realized my oneness, not only with the universe, but also with all possibilities and all dimensions behind it. In reality, there is only one infinite Quantum Tai Chi, and Gauge Theory makes it mathematical.
Could we start our theoretical science with this 'law of the one', and work downward into the
dimensions of manifestation? We would then realize 'the Ridgepole of the Universe'. This is the
bipolar opposite of the fragmentation which science has given us. This fragmentation divides the
universe up into illusorily independent parts. The fragmentation also postulates that life evolved from
inanimate matter, a contradiction of the law of the one. In truth there is no 'inanimate matter'.