The Quantum Tai Chi

(Gauge Theory: The Dance Of Mind Over Matter)

by

P. Stephen Petersen, PhD. (Philip Petersen)

Empyrean Quest Publishers

Concord CA

©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

ISBN 1-890711-00-4

1. Quantum Theory (Physics) 2. Physics--Philosophy. 3. Quantum Interpretation (Physics)

First Empyrean Quest Edition 1996

Printed in the United States of America

CONTENTS

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)

Synchronicity

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'?

ACKNOWLEDGMENTS

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,

Resolves tangles;

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 physicists),

"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."

(12)

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

combinations.

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

force.

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

PART A

"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 down." (3)

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 expansion.

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 formalism." (8)

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 definition.

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 Little'.

"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

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." (18)

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 little." (19)

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 measurement.

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)

Lao Tzu

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 20^th 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 physically important.

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 s