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Spin, the origin of the natural laws, and the binary universe.

Abstract

The goal of classical physics was to identify "Physical Reality," sought for many centuries. The natural philosophers believed that there is a physical reality of nature, which when found will tell us the origin of the natural laws and the connections between microphysics and cosmology. Richard Feynman wrote of this, in connection with the Conservation of Energy. He said, "Nature has a hidden accountant who keeps honest books of energy input and output, but we don't know how she does it."

The great philosophers of physics--Clifford, Mach, Einstein, Wyle, Dirac, Schroedinger, and others--have pointed out that only a wave structure of matter (particles) can conform to experimental data and fulfill the logic of reality and physics. Such a Quantum Wave Structure of Matter (WSM) has been found in the last decade and is described here. Since the WSM provides a quantitative origin of the fundamental natural laws, it becomes the basis of everything in science. It is Physical Reality.

Only three basic principles of Nature underlie the Wave Structure of Matter. For the electron, the simple structure is a pair of spherical outward and inward quantum waves, convergent to a center, existing in ordinary space and termed a space resonance. This wave pair is also the physical origin of the previously unknown electron quantum spin, which is described here. Spin occurs when the inward quantum wave undergoes spherical rotation to become the outward wave. These two waves are a Dirac spinor satisfying the Dirac Equation. Thus, the space resonance has a binary basis like computer hardware.

Each space resonance shares its wave structure in an infinite space with all others, creating an inter-connected binary universe. The significance of the WSM on communication, our life, and our place in the binary universe is discussed.

Part I--Introduction

Historically, science has attempted to explain all phenomena in the physical universe by means of a small number of universal laws, which describe the behavior of particles. These are the laws governing the forces of gravity, electromagnetism, and the principles of conservation of energy/momentum, relativity, and quantum mechanics. However, the origin of these laws themselves has remained unknown. This article proposes that the WSM can explain quantitatively the origin of the known laws of physics, and moreover suggests how these laws may be extended to apply to phenomena of life and consciousness.

Finding the WSM was very simple. You simply replace the ancient Greek notion of a point particle with a spherical wave structure, which had already been predicted by Einstein and Irwin Schroedinger, 70 years ago. Nothing complex, but it is different because it reveals a universe of real quantum wave structures that we live in but seldom see.

Why had this not been found before? Because no one had looked! Unfortunately, the Democritus particle, 1600 B.C., agreed with human emotional experience (but not logic) so most people were satisfied with it. Engrained habits are hard to displace.

Nature has made the true structure of particles like the electron, proton, and neutron very simple, typically a pair of spherical waves whose center is the location of the particle. The proof of this natural truth is that all the natural laws can be obtained mathematically from only three basic principles describing the wave space medium.

Human perspective has another bias. We tend to see space as three rectangular dimensions, one of which is the vertical gravity vector of Earth, plus two other vectors perpendicular to it, shaped like the Earthly houses we live in. On the other hand, the true shape of the space medium is spherical whose dimensions are inward and outward, the direction of waves in space. In the vast expanse of the real universe, gravity occurs so rarely, that its direction is inconsequential in the large cosmos, despite its local importance to us.

The main advantage of the WSM viewpoint to be emphasized in this paper is that it explains the physical origin of electron spin, a phenomenon that undoubtedly exists, but which is not explained adequately by previous theories. In contrast, conventional physics required dozens of assumptions plus many more arbitrary constants to explain the operation of some of the laws. Even then, some laws, like spin, were a puzzle and no origin was known. The comparison of the old physics with its new wave structure can be compared to the theory of epicycles of the planets around the Earth before Newton found that the planets traveled around the Sun.

History of the New Wave Structure of Matter

A wave structure of matter was proposed 120 years ago by the famous English geometer, William Clifford, (1) who wrote in 1876, "All matter is simply undulations in the fabric of space."

In Clifford's thoughts, the mass and charge substances we assume do not exist but are properties of a wave structure in space. In short, space waves were real, while mass and charge points are mere appearances of the wave structure, "Schaumkommen" in the words of Schroedinger. (2) Their proposals were consistent with quantum theory, since quantum mathematics does not depend on a belief in particle substance or charge substance. An interpretation of quantum waves believed to be real was written by Cramer. (3)

Ernst Mach (4) observed the mechanism of cosmological energy transfers in 1883. He noticed the inertia of a body depended on the presence of visible stars. He asserted: "Every local inertial frame is determined by the composite matter of the universe," and "When the subway jerks, it is the fixed stars that throw you down." His deduction arose from two different methods of measuring rotation. First, without looking at the sky one can measure the centrifugal force on a rotating mass m and use the inertia law f=ma to find circumferential speed and position, as in a gyroscopic compass. The second method is to compare the object's angular position with the fixed (distant) stars. Both methods give exactly the same result!

Mach's Principle was criticized because it appeared to predict instantaneous action-at-a-distance across empty space. How can information travel from here to the stars and back again in an instant? The answer lies in the energy exchange mechanism of the space resonance particle whose oscillating waves extend throughout space. Space is not empty because it is a quantum medium created by waves from every particle in the universe (Principle II below). Then, inertia is a local interaction with the space medium. There is no need to travel across the universe.

Mach's friend Albert Einstein was greatly influenced by this when he deduced the General Theory of Relativity (GTR). Now, Mach's Principle in a more exacting form has become Principle II of the Wave Structure of Matter (WSM) and the GTR can be obtained from the WSM.

General Relativity has been succinctly described: "All the matter of the universe tells space what it is. Then space tells the matter of the universe how it must behave." This reciprocity in the universe is the heart of the WSM. You will see this when they are reviewed below.

Einstein reasoned that particles must be "spherically spatially extended in space." He wrote, "... Hence the material particle has no place as a fundamental concept in a field theory."

Paul Dirac was never satisfied with the point particle because the Coulomb force law had to be corrected by "renormalization." He wrote: (5) "This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity because it turns out to be small, not neglecting it because it is infinitely large and you do not want it!"

Wheeler and Feynman (6) (1945) modeled the electron as spherical inward and outward electromagnetic waves, seeking to explain radiation forces. Unhappily they failed because there are no spherical solutions of vector electromagnetic wave equations. Nevertheless, their work pioneered the concept that every particle sends quantum waves outward, and receives an inward response from the universe.

After 1945, the next step in research on wave structure was taken in 1985 when the present author, (7,8) proposed a scalar wave equation with spherical quantum wave solutions, as a basis for the Wave Structure of Matter. It successfully predicted the natural laws and all of the properties of the electron, except one--its spin. Below, this paper reviews the WSM and provides a new physical origin of spin that accords with quantum theory and the Dirac Equation.

Part II--Review of the Wave Structure of Matter

The wave-structured particle, Figure 1, is termed a space resonance (SR). The medium of the waves, and the leading player in the new scenario, is space, that supposed void of which we formerly knew little. The properties of space resonances and the laws that they produce are derived from properties of space. Thus, this single entity, space, described by two principles, underlies everything.

[FIGURE 1 OMITTED]

Principle I--A Wave Equation

This Principle, an equation, describes how quantum waves are formed and travel in a space medium. If the medium is uniform, typical nearly everywhere, only spherical waves occur. The wave amplitudes are scalar numbers. If observed in relative motion, Doppler modulation and elliptical waves appear. If the medium is locally dense, as in the central region of a proton, waves circulate like sound waves in a drum or sphere. Principle I is:
 Quantum matter waves exist in space and are solutions
 of a scalar wave equation.


The wave equation is: [(grad).sup.2](AMP) - (1/[c.sup.2]) [d.sup.2](AMP)/d[t.sup.2] = 0

Where AMP is a scalar amplitude, c is the velocity of light, and t is the time. Its solutions are a pair of spherical in/out waves, which form the simple structure of the electron or positron. The waves extend from center to infinity and decrease in intensity with increasing radius, like the forces of charge and gravity. The mathematical and physical properties of a space resonance display the laws of mechanics, quantum mechanics, special relativity, and electromagnetism. All properties of the waves depend on the medium, space. This dependence on media is not unexpected since it is a well-known characteristic of oscillators of all kinds, from violins to Christmas bells.

Two combinations of the basic waves form electrons and positrons, which have opposite phase and spin rotation. Thus, matter is constituted of two binary elements, like computer hardware. Although the variety of molecules and materials populating the universe is enormous, the basic building bricks are just two. Is there a profound meaning to this?

Origin of the Natural Laws

The two combinations contain all electron-positron properties. Charge depends on whether there is a + or - amplitude of the IN-wave at the center. If a resonance is superimposed upon an anti-resonance, they annihilate. The amplitude at the center is finite as observed, not infinite as in the Coulomb rule. They obey Feynman's Rule, "A positron is an Electron going Backward in Time." See this in the Math Appendix.

The properties of quantum mechanics (QM) and special relativity (SRT) are the result of the motion of one SR relative to another, which produces a Doppler shift in both the IN- and OUT-waves. All parameters of QM and SRT for a moving particle; that is, the deBroglie wavelength of QM and the relativistic mass and momentum changes appear as algebraic factors in the Doppler-shifted waves exactly as experimentally measured. Details are in the Math Appendix.

Energy Transfer and the Action-at-a-Distance Paradox

The energy exchange of forces implies deeper meanings than are provided in the classical force laws. Experience tells us that communication or acquisition of knowledge of any kind occurs only with an energy transfer. Storage of information, whether in a computer disk or in our brain, always requires an energy transfer. Energy is required to move a needle, to magnetize a tape, to stimulate a neuron. This rule of nature is embedded in biology and our instruments. Thus, a major deficiency of the classical force laws is that they have no physical mechanism for energy transfer. The formulas contain only constants, "mass" and "charge,"--no mechanism. This is the fault of the static point particle model. We conclude that finding the energy transfer mechanism between particles is essential to understanding the natural laws.

Principle II--Space Density Principle (SDP)

This principle defines the quantum wave medium--space. It is fundamentally important because properties of waves depend on properties of the medium. But, since the natural laws depend on the waves we deduce that the natural laws depend on the medium. Thus, space--the medium--is the wellspring of everything.

Principle II is:
 At each point in space, waves from all particles in the universe
 combine their intensities to form the wave medium of space.


The medium = space density ~ m[c.sup.2] = hf = k'[SUM OF:{[([AMP.sub.n]).sup.2] x (1/[r.sub.n.sup.2])}]

In other words, at every point in space, the frequency of the mass m of a particle depends on the sum of squares of all wave amplitudes, [AMP.sub.n], from the N particles in the Hubble universe, which decrease inversely with range [r.sub.n] squared. This universe exists inside a radius R = c/H, where H is the Hubble constant.

This principle contains a quantitative version of Mach's Principle because the space medium itself is the inertial frame of the law F=ma. When mass or charge is accelerated, energy exchange takes place in it and the surrounding space medium. Incidentally, this is the mechanism of charge radiation, unsuccessfully sought by Wheeler and Feynman (6) (1945). They focused e-m waves instead of quantum waves.

Because there are a large number of particles, N = [10.sup.80], in the Hubble universe, the medium is nearly constant everywhere and we observe a nearly constant speed of light. But, near a large astronomical body like the Sun, the larger space density produces a measurable curvature of the paths of the inward and outward waves and, thus, of matter and light. We observe these as the effect of gravity described by Newton. This effect is also found in Einstein's general relativity.

The Energy Exchange Mechanism and Charge

Note that the self-waves of a resonance are counted, too. Thus, space becomes dense near the resonance centers due to their own large wave amplitude. Space becomes non-linear at the central region, which produces the coupling between two resonances that allows energy transfer. We observe this process and call it "charge." Can this mechanism be tested? Yes. If a resonance's self-waves dominate space density at the center, then the intensity of self-waves at some radius, ro, must equal the total intensity of waves from the other N particles in the Universe. Evaluating this equality yields

[ro.sup.2] = [R.sup.2]/3N

This is called the Equation of the Cosmos, a relation between the size ro of the electron and the size R of the Hubble Universe. Astonishingly, it describes how all the N particles of the Hubble Universe create the space medium and the "charge" of each electron as a property of space.

The best astronomical measurements, R = [10.sup.26] meters, N = [10.sup.80] particles, yield ro = 6 x [10.sup.-15] meters. This should be near the classical radius, [e.sup.2]/m[c.sup.2], of an electron, which is 2.8 x 10-15 meters. The test is satisfied.

The Conservation of Energy

The transfer mechanism between combinations of resonances is a result of the non-linear (dense) space at resonance centers that permits coupling or exchanges of waves. When the waves of a possible source pass through a possible receiver, the minimum amplitude principle (MAP) finds a way to minimize amplitudes. In the source, an electron's frequency (energy) shifts downward. In the receiver, there is an equal shift upward. Only oscillators with similar frequencies "tuned" to each other can couple and shift frequency. Accordingly, the frequency (energy) changes must be equal and opposite. This is exactly the content of the Conservation of Energy law. The origin of this universal law is reduced to the matching of waves of two particles--not too different from tuning up an orchestra matched to the "A" played by the first violin!

Principle III--Minimum Amplitude Principle (MAP)

This third principle can be obtained from Principle II, but because it is a powerful law of the universe, which determines how interactions take place and how wave structures will move, we write it out separately:

The total amplitude of all particle waves in space everywhere always seeks a minimum.

This principle is the disciplinarian of the universe. That is, energy transfers take place and wave-centers move in order to minimize total wave amplitude. Amplitudes are additive, so if two opposite resonances move together, the motion will minimize total amplitude. For example, "Like charges repel and unlike charges attract" because those rules minimize total amplitude. The MAP produces the Heisenberg Exclusion Principle, which prevents two identical resonances (fermions) from occupying the same state. This is not allowed because total amplitude would be a maximum, not a minimum.

The operation of MAP is seen in ordinary situations like the water of a lake, which always levels itself and is also seen in the flow of heat that always moves from a hot source to a cold sink.

The Origin of the IN-Waves and the Response of the Universe

At first thought, it is puzzling where the IN-waves come from. The puzzle is a result of studying the waves of only one particle, and ignoring the waves of all other particles in space. That is oversimplified. To find reality, we must deal with the real wave-filled universe. When we accept this reality (9) we find a rational origin of the inward waves:

Two hundred years ago Christian Huygens, a Dutch mathematician, found that if a surface containing many separate wave sources was examined at a distance, the combined wavelets appeared as a single wave front having the shape of the surface. This wave front is termed a "Huygens Combination" of the separate wavelets (Figure 2). This mechanism is the origin of the IN-waves, as follows:

[FIGURE 2 OMITTED]

When an outgoing wave encounters other particles, their OUT-waves are joined with part of the initial OUT-wave. These waves arrive in phase at the initial center. Then OUT-waves from all other particles can form a Huygens Combination wave front that is the IN-wave of the initial particle. This occurs throughout the universe so that each particle depends on all others to create its IN-wave.

We see it is wrong to imagine each particle as one pair of IN- and OUT-waves, because one pair cannot exist alone. We have to think of each particle as inextricably joined with other matter of the universe. Although particles are widely separated, they are one unified structure. Thus, we are part of a unified universe and the universe is part of us.

Part III--The origin of the electron's spin

The Dirac Equation

The physical nature and cause of electron spin was unknown before the WSM. However, a successful theoretical theory of spin had been developed by Nobel laureate Paul Dirac in 1926, which is nicely described by Eisele. (10) It theoretically predicted the positron, found in cosmic rays five years later by C. D. Anderson, with a spin of h/4pi angular momentum units.

Dirac was seeking the connection between the conservation of energy given by

[E.sup.2] = [p.sup.2][c.sup.2] + [m.sub.0.sup.2][c.sup.4] (1)

and Schroedinger's quantum theory. The procedure that had been found to work is to use an energy relation for a particle, like (1) and change it to a wave equation. Then, the solutions will describe the amplitude of waves of the particle. No one knew why this worked but the results for the H atom are amazingly accurate, so it is trusted. The usual way to change the terms for energy E and momentum p into two wave equation operators using,

E = (h/i) [d AMP/dt] p = h[d AMP/dx] (2)

where AMP is the amplitude of the Schroedinger wave function sought.

Unfortunately for Dirac, Eqn (1) uses squared terms whereas Eqns (2) cannot be squared. He had a new idea, "Try replacing Eqn (1) with a matrix equation."

[Identity]E = [alpha]pc + [beta][m.sub.0][c.sup.2] (3)

This avoided squares of E and p but placed severe restrictions on the new factors [Identity], [alpha], and [beta], which are matrix operators.

Dirac saw that Eqn (1) is similar to Pythagoras' Theorem that the square of a triangle's hypotenuse equals the sum of its sides. Therefore in Eqn (3) the equivalent of squaring has to become part of the matrix algebra. Dirac felt that this was possible. He found that solutions existed if E and p had fixed values. These values matched experiments and his Equation (3) became famous.

Dirac also noticed that only two functions were found in the electron's solution. So Dirac simplified the algebra by introducing number pairs, termed spinors, and 2x2 matrices called spin operators, creating a two-dimensional algebra, instead of a four-dimensional algebra or the one-dimensional algebra of real numbers. His theoretical spinor algebra produced correct values of the electron's energy and spin but gave no hint of the physical structure of the electron. Now we shall see below that the IN- and OUT-wave pairs of the WSM are real physical spinors, the counterpart of Dirac's theoretical spinors.

The Mechanism of Spin

Spin occurs when the IN-wave arrives at the center and rotates continuously in order to become the OUT-wave. However, there are strict requirements on the amplitudes and polarity of the IN- and OUT-waves. Rotation cannot be allowed to twist up space without limit. The spherical waves must continually and smoothly change amplitude and direction of motion. It turns out there is one way to do this with either clockwise or counterclockwise rotation.

Batty-Pratt & Racey (11) (1980) analyzed a known (12) property of 3D space called spherical rotation in which space returns to its initial state after two turns. They showed that any exponential oscillator, [e.sup.iwt], was a spinor. Wolff (13) realized in 1988 that the exponential IN- and OUT-waves of the WSM were the real physical spinors satisfying the Dirac Equation.

In spherical rotation there is no fixed axis like cylindrical rotation of a wheel. Spherical symmetry is preserved because the center of rotation is a point. "Rotation" is probably a poor word choice to describe it. It is significant that this type of spherical rotation is possible only in three-dimensional space. (12)

The continuous rotation and reversal of the inward wave amplitude at the center is expressible in Dirac's spinor algebra. One direction of rotation produces the electron; the other, the positron. This is why every charged particle has an antiparticle. It is easy to calculate that rotating an IN-wave two turns each cycle produces an angular momentum of [+ or -] h/4pi thus obtaining Dirac's result very simply.

The Equivalence of the WSM and the Dirac Equation Procedures.

The results of the WSM and Dirac methods are the same: namely, electron spin = [+ or -] h/4pi and energy = m[c.sup.2].

However, the energy given by Dirac's method is actually [+ or -] m[c.sup.2], and Dirac was forced to interpret the puzzling negative energy as an unseen "sea of positron particles." These have never been observed. This strange concept has since been abandoned but the reason was unknown until the WSM. Now we see that if the sign of the product of energy and time is negative, -wt = -Et/h, this is the same as exchanging the IN-wave with the OUT-wave of a space resonance. This changes the electron into a positron with a positive energy.

Batty-Pratt (11) showed that rotation of the In- and OUT-waves of a resonance (see Appendix), when written as spinors, produce the Dirac Equation. The Dirac Equation does not describe the WSM, only rotation at the center.

The relativistic energy equation (1) used by Dirac is obtained from the WSM. See Egns (e-h) in the Appendix.

Spherical Rotation at the Wave Center

What are the geometric requirements on the wave motion that does not destroy the continuity of the space? The coordinates of the space must participate in the wave motion without discontinuity. This requirement is satisfied by stating that the motion must be represented by a compact, simply connected group. The most elementary such group for motion with spherical symmetry is named SU(2).

A Model of Spherical Rotation

SU(2) motion can be modeled12 by a ball held by threads inside a cubical frame. The threads represent the coordinates of the space and the rotating ball represents the space at the center of the converging and diverging quantum waves. The ball can be turned about any axis starting from any initial position. If the ball is rotated continuously it returns to its initial configuration after every two rotations.

Using the ball or its IN/OUT-wave equivalent, we can reverse the spin axis, by reversing time (t --> -t) or by reversing the angular velocity (w --> -w). Both are equivalent to exchanging the outgoing spherical wave of an electron with the incoming wave. In spinor notation, the change would be,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Dirac matrices also perform geometric operations. For example, inverting a spin state is produced by the inversion matrix operating on the spinor,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

NOTE: The rule of matrix algebra is to multiply and add the row elements of a spin operator by the column elements of the initial spinor. Each result is the new element of the final spinor.

In these two examples, note that inversion and spin reversal are not the same. They are different than our human view of rotating objects. The difference is characteristic of the quantum wave electron and is important to understand particle structure.

A rotation in the spherical mode can be represented by any operator that will transform one spinor into another position. It is usual to assign a unit radius to spinor amplitudes. Then, the rotations can be described by the mathematics of the SU(2) group. The notation of some spinors invented by Dirac are shown in TABLE I.

For example, a ball in laboratory space can be rotated 180[degrees] about the z-axis by the operator (spin-z). Such a z-axis is imagined by humans in human x-y-z coordinate systems. However, the spherical waves of a resonance travel in universal cosmic space that has spherical symmetry. No x-y-z axes exist. Thus only spherical rotation around the wave center is meaningful.

Nevertheless, if a laboratory magnetic force (field) or electric force (field) is applied to an electron, or if the observer is moving with respect to the electron, an axis is created. In this case, the IN/OUT-waves are changed into an elliptical form by the applied external effects -creating an axis along the ellipse. Then, spin effects can be measured with respect to that created axis.

Remember being puzzled in your college course on QM101? Why did the spin z-axis appear without geometric reason? The above clears up that confusion found in quantum physics textbooks, which, not knowing the cause, glibly provide an x-y-x axis.

Connecting Natural Laws and the Physical Electron Spin

Before the WSM, there had been no known physical reason for the theoretical mass increase of relativity. Likewise, there were no physical reasons for quantum theory or spin. Were these apparently separate laws connected or not? Indeed, many theorists proclaimed that these phenomena were irreconcilable! Others had not thought about a connection because most physicists were satisfied with the separate but accurate theoretical reasons for each.

Dirac's work might have been seen as a clue that they are connected because all three were joined in Dirac's work, albeit theoretically. The WSM now provides a simple physical connection due to the wave structure of matter.

Recall that the relative increase of mass (energy or frequency) of a space resonance is due to the Doppler increase of frequency seen by a relative observer. This immediately results (Wolff 7,8,13) in the conservation of energy equation used by Dirac.

[E.sup.2] = [p.sup.2][c.sup.2] + [m.sub.0.sup.2][c.sup.4] (1)

Likewise, the deBroglie wavelength L = h/p is also a Doppler change of wavelength seen by a relative observer, shown below, and it leads to the Schroedinger Equation.

The union of spin, mass increase, and quantum theory are found in the spherical rotation at the wave center.

Part IV--Conclusions

We can have confidence that the Wave Structure of Matter is the true physical reality of the universe. The logical proof of the WSM is that the experimental evidence, which empirically founded the natural laws, must necessarily agree with the laws predicted by the WSM. It does.

There is further confidence because empirical evidence agrees better with the WSM than with conventional laws (rules). For example, an infinity of charge potential at r=0 in Coulomb's law does not occur experimentally, in agreement with the WSM. There are more examples: Conventional physics has no explanation for the energy exchange mechanism of forces, or the Pauli Principle, or spin, or charge attraction and repulsion. These are now direct conclusions from the WSM.

The philosophical conclusions are fascinating, particularly the connectedness of the universe that asserts: Everything we are and observe here on Earth, matter-laws-life, necessarily depends on the existence of all the matter in the universe. We must conclude, if the stars and galaxies were not in the heavens, we could not exist!. Thus, we are part of the universe, and the universe is part of us.

But the practical value of the WSM theory is the insight it provides. It will allow scientists to deeply analyze quantum wave structures, the cosmos, and the natural laws. In the R&D laboratory, the new insight may advance electronic applications, especially IC and memory devices because their tiny transistor elements use quantum effects to control the flow of currents.

The new knowledge may improve communication and the efficiency of energy transmission. Conduction of electric energy along a wire is a quantum energy transfer process between SRs that was formerly unknown. Now, energy losses may be greatly reduced, perhaps at low temperatures, permitting the use of smaller conductors for longer distances.

Less Certain Conclusions

Is it possible the nature has made use of the fact that each particle contributes to the IN-waves of others? Researchers often find a new discovery, only to realize later that the discovery already existed in nature. "Nature did it first!" is a common occurrence. We can speculate that this inter-connectedness could affect human thinking, physiological, psychological, or genetic processes. That is, quantum energy transfers, as a requirement of the MAP, could create hidden communication links between parts of our bodies or with neighboring matter, like computer circuitry.

What is the mechanism of these matter wave connections? Each atom of our body structure arranges its waves to form minimum amplitudes that satisfy MAP. In the process, each of its neighbors makes a contribution to its in-wave structure. If one atom is disturbed, others must be affected. This is an elementary bit transfer. Since every body cell contains the holographic image of waves from other parts of the body, each cell is a memory device. So, the apparatus of computation appears to be there but whether or not nature has arranged our body cells into a physiological computer we do not know. Indeed, the mechanism of ordinary sensory communication in the nerves of the body, and in brain function is still poorly known. We won't know much about quantum communication without more laboratory work.

Interested readers may continue the study of the quantum universe in references (8, 9 and 13), and at the "Quantum Science Corner" web site: http://members.tripod.com/mwolff

V. Mathematical Appendix

Solutions of the Wave Equation (Principle I)

The wave equation must be written (following Wolff (7,8,13)) in spherical coordinates because universal space has spherical symmetry. Uniform density of the medium (space) is assumed that yields a constant speed of the waves and "light"). Then the only two solutions describe the charge waves of common charged particles including the electron, positron, proton, and anti-proton. They are:

IN-wave = (1/r){A-max} exp (iwt + ikr) (a)

OUT-wave = (1/r){A-max} exp (iwt - ikr) (b)

where A= wave amplitude, wave number k=mc/h , w=2[pi]f, r= radius from wave center, and energy is hf= mc2.

Joining these two as a standing wave produces the electron or the positron space resonances. The only two ways they can be joined is to rotate the In-wave at the center to become the OUT-wave. Rotation can be either CW or CCW. These rotation directions are shown as [R.sup.ccw] or [R.sup.cw]

The electron E(-) = {- IN-wave + OUT-wave} [R.sup.ccw] (c)

The positron E(+) = {+ IN-wave - OUT-wave} [R.sup.cw] (d)

You can experiment with particle inversions by changing the signs (+ or -) in the amplitude equations. To perform a Time inversion change t to -t, which converts the positron into an electron. To perform a mirror inversion (Parity), imagine that the waves are viewed in a mirror. You will see that a positron is a mirror image of the electron. To change a particle to an anti-particle (Charge inversion), switch the IN-waves and the OUT-waves, and the spin direction. Successive C, P, and T inversions returns to the initial state, which is a proof of the empirical-theoretical CPT rule, now seen to be a property of the wave structure.

If you add the electron structure to the positron structure, the resulting amplitude is zero or annihilation.

Origin of Special Relativity (SRT) Mass Increase and the DeBroglie Wavelength of QM Theory

Write the equation of an SR, as seen by an observer, with relative velocity b = v/c, as shown in Wolff.13 Then, insert relativistic Doppler factors, g = [[1-[v.sup.2]/[c.sup.2]].sup.-1/2]. The final received amplitudes are,

Received amplitude = 1/r {(2 A-max) exp [ikg (ct + br)] x sin [kg (bct + r)]}.

This is an exponential oscillator modulated by a sine factor. This equation shows the origin of QM and SRT, as follows:

In the exponential factor:

Wavelength = h/mvg = deBroglie wavelength with relativistic momentum. (e)

Frequency = kgc / 2[pi] = gm[c.sup.2] / h = mass frequency with relativistic energy. (f)

And in the sine factor:

Wavelength = h/mcg = Compton wavelength with relativistic momentum. (g)

Frequency = b gm[c.sup.2]/h = b x (mass frequency) = relativistic momentum frequency. (h)

The results for mass in (e to h) can be written m = [m.sub.o]g = [m.sub.o][[1-[v.sup.2]/[c.sup.2]].sup.-1/2]= which can be changed to Eqn (1) used by Dirac.

Thus the space resonance physically displays all properties of an electron: QM, SRT, forces, annihilation, spin, conversion to a positron, and CPT relations between Charge, Parity (mirror image) and Time; all of which were formerly theoretical properties. These properties depend on the spherical wave structure and ultimately on the wave medium.

References

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(6.) Wheeler, J. A. and Feynman, R. (1945). Interaction with the absorber. Rev. Mod. Phys.,17, 157.

(7.) Wolff, M. (1991). Microphysics, fundamental laws and cosmology, Invited paper at 1st Sakharov Conf. Phys, Moscow, May 21-31, in reprint by Nova Scientific Publ., NY.

(8.) Wolff, M. (1993). Fundamental laws, microphysics and cosmology. Physics Essays, 6, 181-203.

(9.) Wolff, M. (1997). Exploring the universe. Frontier Perspectives, 6(2) 44-56.

(10.) Eisele, J. A. (1960). Modern quantum mechanics with elementary particle physics. New York, NY: John Wiley.

(11.) Batty-Pratt, E. and Racey, T. (1980). Geometric model of fundamental particles. Intl. J. Theor. Phys.,19, 437-475.

(12.) Misner, C. W., Thorne, K., and Wheeler, J. A. (1973). Gravitation. San Francisco, CA: W.H. Freeman Co.

(13.) Wolff, M. (1990). Exploring the physics of the unknown universe. Manhattan Beach, CA: Technotran Press.

Milo Wolff

Technotran Press

1124 Third Street, Manhattan Beach, CA 90266

Email: milo.wolff@worldnet.att.net
TABLE I: Properties of Spherical Rotation for
an Electron in the SU(2) Representation

 Matrix Initial Final
OPERATION Operator spinor spinor

Leaves space as it is. 1 0 1 1
[Identity operator] 0 1 0 0

Rotates space 180[degrees] 0 i 1 0
about the x-axis. i 0 0 i
[spin-x operator]

Rotates space 180[degrees] 0 -1 1 0
about the y-axis 1 0 0 1
[spin-y operator]

Rotates space 180[degrees] i 0 1 i
about the z-axis 0 -i 0 0
[spin-z operator]
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Date:Sep 22, 2001
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