MILO WOLFF
Technotran Press
1124 Third Street, Manhattan Beach, CA 90266
Abstract: The
great philosophers of cosmology, Clifford, Mach, Einstein, Wyle, Dirac,
Schroedinger, have pointed out that only a wave structure of matter
(particles) can conform to experimental data and fulfill the logic of
reality and cosmology. This Quantum Wave Structure of Matter (WSM) has
been found and is the origin of the natural laws. Since the WSM
provides a quantitative origin of the fundamental natural laws, it
becomes the basis of physical sciences.
Only three basic Principles of Nature determine the wave medium and
enable quantitative calculation of the WSM and the origin of the natural
laws. The medium of the waves is space. The properties of particles and
the laws embedded in them are derived from the properties of space.
This single entity, described by three principles, underlies everything.
For the electron, the structure is a pair of spherical outward and
inward quantum waves, convergent to a center, existing in ordinary space
and termed a space resonance. Every space resonance shares its binary
wave structure pair with all others in our universe. Thus we exist in an
inter-connected binary universe.
The predictive power of the WSM shows how the electron's wave pair is
the physical origin of the previously unknown quantum spin. These two
waves are a Dirac spinor satisfying the theoretical Dirac Equation. Spin
occurs because the inward quantum wave continually undergoes spherical
rotation at the center transforming to the outward wave.� The
significance of the WSM on �communication, life, and our connection with
the binary universe is discussed.
Part I - Introduction
Our knowledge of science is based on the natural laws
that describe the behavior of particles. These laws are the rules for
calculating electricity, gravity, relativity, quantum mechanics, and
conservation of energy and momentum. The origins have been unknown.
Now for the first time the origin of the natural laws is found to be a
quantitative result of the WSM.
The origins of the laws had been sought for
centuries. Finding all of them at the same time and place is a
philosopher’s dream come true. It is of great importance to science
because the natural laws and quantum spin determine the structure of the
Atomic Table, which dictates the varied forms of matter: metals,
crystals, semi-conductors, and the molecules of life. The deep
understanding of basic physics that is revealed opens a door to broad
fields of applied technology such as integrated circuits, photonics, and
commercial energy. It reveals a universe of real quantum wave
structures that we live in but seldom see.
Finding these origins was very simple. The ancient Greek notion of a point particle was replaced with a spherical wave structure, which had already been predicted by Clifford, Einstein and
Irwin Schroedinger, a century ago. After World War II enthusiasm for
wave structure waned for 40 years. It was not complex or difficult but
it was different because it disagreed with human emotional
experience of point particles that most people were satisfied with.
Emotions play a powerful, often hidden role in the motivation for
research.
We don't easily see the space medium because our
survival as an animal species depends mostly on our ability to fight
with other animals seeking food, and to compete for mates that produce
children, not closely related to the quantum space medium. In our
self-focused human perspective few of us are even aware of the wave
medium in which we exist. For survival, it doesn't matter what space
is, or whether we can observe it - it exists nevertheless. This
situation is much like the life of a fish who cannot comprehend the
existence of water because he is too deeply immersed in it.
Like the fish, traditional science has tended to
comprehend the universe in terms of our own local experiences. It was
assumed that matter particles are like tiny grains of sand - an idea
proposed by the Greek philosopher Democritus many centuries ago. As
microscopy improved, models were created subdividing grains into other
‘grains’ - ad infinitum. But only a few people like Einstein saw that
grains were impossible or ever asked how the grains communicate forces -
unexplained by the old science. Formerly, forces were accepted as faith
in Nature.
Human perspective has many biases. 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 houses we live in. But in the cosmos, the shape of the
enormous universe is spherical whose important 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 larger scheme of things, despite its local
importance to us.
The proof of the WSM is that all the natural laws can
be obtained mathematically from the three basic principles describing
the wave space medium. This wave structure of matter is simple and
matches experimental measurements. In contrast, conventional physics
required dozens of assumptions plus many more arbitrary constants to
explain the operation of the laws. Even then some laws, like spin, were a
puzzle with no origin known. On the atomic scale electromagnetism is
inaccurate. 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 Copernicus and Galileo found that the planets
traveled around the Sun.
1. A New Science Odyssey
The discovery of the wave
structure of the electron and other matter is a beautiful adventure in
which you find the origin of the natural laws, a new powerful tool of
technology, and an exciting window on science, cosmology, and ourselves.
But some classic concepts must be discarded. For instance, a quantum
physicist may expect that all quantum phenomena must derive from
Schroedinger's Equation. Instead, it is the other way around;
Schroedinger's Equation is derived from the quantum wave structure of
the universe.
Some concepts must be changed such as the meaning of
charge and mass, formerly assumed to be inherent properties of each
independent particle. Instead of this assumption we find, as
Schroedinger deduced, that location, charge and mass are properties of the wave structure and ultimately of the wave medium - space. This can now be proved.
Understanding our misconceptions comes from
anthropology, which teaches that the quantum wave universe is not as
helpful to survival of our personal genes as recognizing apples we can
eat and avoiding tigers who want to eat us. We need to recognize those
quickly. But it was not necessary that nature equip us to observe
quantum waves quickly. Lacking personal experience of simple quantum
waves, people chose to imagine that the electron is a "particle," like a
bullet. Laboratory evidence does not support this human-oriented idea.
Accordingly, belief must change from discrete particles to wave
structure. But emotional rejection can occur if the new truth conflicts
with established belief. Max Planck once said, "New scientific truth
does not triumph by convincing its opponents, but because the opponents
die and a new generation grows up unopposed to the new idea."
2. History of the New Wave Structure of Matter
A wave structure of matter was proposed 130 years ago by the famous English geometer, William Clifford1,
who spoke before the Cambridge Philosophical Society in 1870, "All
matter is simply undulations in the fabric of space." He developed this
concept2 as three-dimensional dynamics that reduces to
four-dimensional kinematics describing matter, electromagnetism and
kinetic energy as curvature of a dynamic Riemannian space. His work, the
progenitor of the WSM and General Relativity was neglected.
In Clifford's thoughts, the mass and charge
substances that 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 Schroedinger3. Their proposals were
consistent with present day quantum theory, since quantum mathematics
does not depend on a belief in particle substance or charge substance.
Ernst Mach and Bishop Berkeley had proposed about
1890, that the law of inertia depended on all the matter of the
universe. This was known as Mach's Principle. It was the first
recognition that a natural law depends on cosmology. Albert Einstein was
greatly influenced by it 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 (below) from which
all the laws derive.
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 remarkable reciprocity in the universe is the heart of the WSM. You will see this when they are reviewed below.
The failure of the point particle concept began to
appear. Einstein and Ernst Mach reasoned that space and thus matter
cannot be discontinuous so that particles must be "spherically spatially
extended in space." Einstein wrote, "…Hence the material particle has no place as a fundamental concept in a field theory."
Paul Dirac was never
satisfied with the discrete point particle because the infinity of the
Coulomb force law had to be corrected by ‘renormalization’. He wrote4, ﾒ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! Of course the
inference is that the basic equations are wrong and radical changes need
to be made." Dirac seemed to foresee the WSM.
Wheeler and Feynman5 (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. In hindsight, if they had used scalar
quantum waves instead, this paper would have appeared 55 years ago! So
close and yet so far! "A hair’s breadth separates the false and true."
After 1945, research on wave structure stopped until 1985 when Milo Wolff 6,7, using a scalar
wave equation with spherical quantum wave solutions, found the Wave
Structure of Matter described here. 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 physical origin
of spin that accords with quantum theory and the Dirac Equation.
Figure 1. The Dynamic Waves of a Space Resonance
The resonance is composed of
a spherical IN wave, which converges to the center, rotates to become
an OUT wave, and diverges from the center. These two waves combine to
form a standing wave whose peaks and nodes are like layers of an onion.
The wave amplitude is a scalar number, not an electromagnetic vector. At the center, the wave amplitude is finite, not infinite, in agreement with observation.
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
three principles, underlies everything.
3. Principle I - A Wave Equation
This Principle, an equation,
describes how quantum waves are formed and travel in a space medium. The
wave amplitudes are scalar numbers. If the medium is uniform, typical
nearly everywhere, only spherical waves occur. 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 a sphere. Principle I is:
Quantum matter waves exist in space and are solutions of a scalar wave equation.
The wave equation is: (grad)2(AMP) - (1/c2) d2(AMP)/dt2 = 0
Where AMP is a scalar amplitude, c is the velocity of light, and t is the time. Its solutions, Figure 1, are a pair
of spherical in/out waves that form the simple structure of the
electron or positron — an oscillator. The waves decrease in intensity
with increasing radius, like the forces of charge and gravity.
There are two combinations of the two basic in/out waves that form electrons and positrons, with 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?
As is true for all oscillators in Nature the
properties of the waves, such as speed and amplitude, derive from
properties of their medium. Formation of the space medium is given by Principle II below.
4. Origin of the Natural Laws.
The two combinations contain
all experimental 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."
The properties of quantum mechanics (QM) and special
relativity (SRT) are the result of the motion of one space resonance
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 de Broglie 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.
5. Energy Transfer and the Action-at-a-Distance Paradox
A necessary new concept
is the mechanism of energy exchange. 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. There are no exceptions.
This rule of nature is embedded in biology and our instruments. Finding
the energy transfer mechanism between particles is essential to
understanding the natural laws. It is found naturally in Principle II
of the WSM.
A major deficiency of the classical force laws is that they have no theoretical or physical mechanism
for energy transfer. The formulas contain only constants, "mass" and
"charge," - no mechanism. This was an inherent defect of the static point particle model. Einstein, Wheeler and Feynman5
knew this, recognizing that there must exist a continual dynamic means
for forces to transfer energy and sought it in electromagnetic waves.
Unfortunately there are no spherical solutions of the vector e-m wave equation. Hence the mechanism had to await the scalar waves of the WSM. We will see that wave communication is the means.
Ernst Mach’s9 observation in 1883 was the
first hint of the mechanism of cosmological energy transfer. He noticed
that the inertia of a body depended on the presence of the visible
stars. He asserted: "Every local inertial frame is determined by the composite matter of the universe" and jokingly, "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 gyroscope. 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? Again the answer had to await the WSM
where Nature’s energy exchange mechanism, formerly unknown, is now seen
as the interaction of waves in an ever-present universal medium. Space
is not empty because it is a quantum wave medium created by oscillating
waves from every particle in the universe (Principle II below).
Inertia, charge, and other forces are mediated by the pervasive space
medium. There is no need to travel across the universe.
6. Principle II - Space Density Principle (SDP)
This principle defines the quantum wave medium -
space. It is fundamentally important because the properties of waves
depend on properties of their medium. But, since the natural laws
depend on the waves we deduce that the natural laws in turn 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 ~ mc2 = hf = k’[SUM OF:{(AMPn) 2 x (1/rn2)}]
In other words, at every point in space, the frequency f or the mass m of a particle depends on the sum of squares of all wave amplitudes AMPn from the N particles inside the "Hubble universe", whose distance decreases inversely with their range rn squared. The "Hubble Universe" is of radius R = c/H, where H is the Hubble constant.
This principle is a quantitative version of Mach’s
Principle because the space medium is the inertial frame of the law F =
ma. When mass or charge is accelerated, energy exchange takes place
between it and the surrounding space medium. In hindsight, this is the
mechanism of charge radiation, unsuccessfully sought by Wheeler and
Feynman4 (1945), attempting to use e-m waves instead of quantum waves.
Because there are a large number of particles, N ~ 1080,
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 light and the motion of matter. We observe these as the effect
of gravity described by Newton and also by the space curvature of Einstein's general relativity.
7. 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. Dense space at the central region
propagates waves non-linearly, which allows energy transfer or coupling
between two resonances. We observe this process and call it ‘charge.’
But there is no ‘charge substance’ involved. It is a property of the
wave structure at the center.
Can this mechanism be tested? Yes. If a resonance’s self-waves can be dominate in its space, then at some radius, ro from the center, self-wave density must equal the total density of waves from the other N particles in the Universe. Evaluating this equality6,7,8 yields
ro 2 = R2/3N
The best astronomical measurements, R = 1026 meters, N = 1080 particles, yield ro = 6 x 10-15 meters. This should be near the classical radius, e2/mc2 of an electron, which is 2.8 x 10-15 meters. The test is satisfied.
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’ and ‘mass’ of each electron as a property of space.
8. 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, I 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. This explains
empirical rules like, "Like charges repel and unlike charges attract"
because those rules minimize total amplitude. The origins of many rules
are now understood. For example, MAP produces the Heisenberg Exclusion Principle,
which prevents two identical resonances (two 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 levels itself, and in the
flow of heat that always moves from a hot source to a cold sink.
9. The Conservation of Energy
The transfer mechanism between combinations of
resonances is a result of the dense (non-linear) space at resonance
centers, which permits coupling or exchanges of wave frequency. When the
waves of a potential source and a potential receiver, pass through both
centers in an allowed transition, MAP minimizes the total of both
amplitudes. In the source, the frequency (energy) of a wave state shifts
downward. In the receiver, there is an equal shift upward. Only wave
states (oscillators) with equal 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!
10. The Origin of the IN Waves and the Response of the Universe 
Figure 2. Formation of in-waves.
The out-wave of every particle interacts with other matter in the
universe. The response to the outgoing wave is Huygens wavelets from
other matter that converge back to the center of the initial out-wave.
When the wavelets approach the center, their combined amplitude becomes
larger, forming the IN wave. Thus every particle depends on all other
particles for its existence. We are part of the universe and the universe is part of us.
At first thought, it is
puzzling where the IN waves come from. This puzzle is our own fault - a
result of looking at the waves of only one particle, and ignoring the waves of all other particles in space — over simplification! To find reality, we must deal with the real wave-filled universe. When we study this question13 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 the in-waves, as follows: When an outgoing wave
encounters other particles, their out-waves are joined with part of the
initial out-wave. Then out-waves from all other particles can form a
Huygens Combination wave front that is the in-wave of the initial
particle. These waves arrive in phase at the initial center. This occurs
throughout the universe so that every 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 particle centers are widely separated, all
particles together 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
As an example of the depth
of understanding and universality of the Wave Structure of Matter, I
will describe for the first time the origin of the spin of the electron.
The physical nature and cause of electron spin has been sought for 75
years ever since a theoretical theory of spin had been developed by Nobel laureate Paul Dirac10 in 1926. He theoretically predicted the positron, found in cosmic rays five years later by C. D. Anderson.
11. Dirac’s Theory
Dirac was probably not
interested in spin but in the philosophical differences between
relativity and quantum theories. Dirac studied the connection between
the conservation of relativistic energy given by
E2 = p2c2 + mo2c4 (1)
and Schroedinger’s quantum theory. E is energy and p
is momentum of a particle of mass m. Schroedinger’s procedure was to
use an energy relation for a particle, like (1) and change it to a wave
equation. His usual way was to change the terms for E and 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. Then the solutions should 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.
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)moc2 (3)
Where the new factors (Identity), (alpha), and (beta) are matrix operators. This avoided squares of E and p but placed severe restrictions on the new operators and their solutions.
Dirac saw that Eqn (1) is similar to squaring the
sides of a triangle. He deduced that in Eqn (3) the equivalent of
squaring had to become part of the matrix algebra. He found that
solutions existed if E and p had fixed values. This theoretical matrix algebra produced correct values of the electron's energy mc2,
and spin h/4pi angular momentum units, but gave no hint of the physical
structure of the electron. But Equation (3) became famous.
Dirac also noticed that only two functions were needed 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-number algebra instead of a four-algebra or our common one-number
algebra. A detailed reader-friendly review of Dirac’s Equation is given
by Eisele10.
12. The Physical Mechanism of Spin
Spin occurs when the in-wave arrives at the center and rotates
continuously in order to transform into the out-wave. To accomplish
rotation there are strict (boundary) conditions on the amplitudes and
polarity of the IN and OUT waves. Rotation cannot be allowed to twist up
space without limit. The spherical wave amplitudes must continually and
smoothly change while changing direction of motion. The in-wave
amplitude at the center must be equal and opposite to the out-wave (one
half cycle different).
It turns out this happens using a known12 property of 3D space called spherical rotation in which space rotates continually around a point and returns to its initial state after two turns. 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.
One direction of rotation produces the electron, the other the
positron. This is why every charged particle has an anti-particle.
Batty-Pratt & Racey11 (1980) analyzed spherical rotation and showed that an exponential oscillator, eiwt, was a spinor. Wolff8 realized in 1989 that the exponential in-out oscillator waves of the WSM were the real physical spinors satisfying the Dirac Equation. It is significant that only 3D space12
has this remarkable property. If this real property of 3D space did not
exist, particles and matter could not exist. Life and the universe as
we know it could not exist.
13. The Equivalence of the WSM and the Dirac Equation Procedure
It is easy to calculate the rotation of an in-wave of frequency (energy) = mc2/h
and wavelength = h/mc. The rotation rate is two turns each cycle. This
produces an angular momentum of ± h/4pi obtaining Dirac's result
simply.
The results are almost the same for both WSM and the
Dirac Equation but not quite the same. The energy given by the Dirac
Equation is + or -mc2 while the WSM says the electron and positron energy are both a real mc2.
Dirac was forced to interpret the puzzling negative energy as an
unseen "sea of negative energy particles". This strange concept has
never been observed and has been abandoned but the reason was unknown
until the WSM.
What is the correct
interpretation of the Dirac result? To find it look at the
electron/positron wave algebra in the Mathematical Appendix. In the
electron wave write the sign of the product of energy and time as
negative, that is: -Et/h = -wt. But this is the same as exchanging the
in-wave with the out-wave, which changes the electron into a real
positron! We see Dirac’s numerical result was right but the
interpretation was wrong. Wrong because he had no wave structure theory
to guide him. He assumed the electron was a discrete particle instead of
a wave structure! This mistaken assumption has plagued physics for
centuries.
Note that the Dirac Equation only describes rotations at the electron center, not the entire WSM. The work of Batty-Pratt12 (pp 453-455) analyzed only the rotation of local exponential waves, found that these spinors and their rotation produced the Dirac Equation.
14. A Model of Spherical Rotation
Spherical rotation in 3D space can be modeled by a
ball held by threads inside a cubical frame shown in Figure 3. 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 exponential wave equivalent, you 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
Dirac matrices perform geometric operations. For example, inverting a spin state is produced by the inversion matrix operating on the spinor.
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 examples, note that inversion and spin reversal are not
the same. This differs from our human view of cylindrical 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 a 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
For example, a ball in laboratory space can be rotated 180o
about the z-axis by the operator (spin-z). Humans in human coordinate
systems (like a lab) create rectangular axes. However the spherical
waves of an electron travel in cosmological space which 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 formed. In
this case, the in/out waves are changed into an elliptical shape by the
applied external effects - forming an axis along the ellipse. Then, spin
effects can be measured with respect to that axis.
16. Connecting Quantum Theory and Relativity
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! Few had thought
about a connection because most physicists were satisfied with the
separate and reasonably accurate theoretical reasons for each.
Dirac's work was a clue that they are connected
because spin, relativity, and QM were joined in Dirac's work, albeit
theoretically. The WSM now reveals their simple physical connection -
Doppler effects.
The Appendix (20) shows that the increase of mass (energy or frequency) m = mo[1 — v2/c2]-1/2
of a space resonance is due to the Doppler increase of frequency seen
by a moving observer. This immediately results in the conservation of
energy equation used by Dirac:
E2 = p2c2 + mo2c4 (1)
This energy equation is also found using the wave perspective because E and p
are super-imposed waves. In engineering the total intensity of two
waves is given by the sum of their squares. Likewise, the de Broglie
wavelength L = h/p is also a Doppler change of wavelength seen by a
moving observer (Appendix 19) and it leads to the Schrodinger Equation.
Thus the union of spin, mass increase and quantum theory occurs in the
spherical rotation at the wave center, and is part of the WSM in
general.
Part IV - Conclusions
We can have confidence that
the Wave Structure of Matter is the true physical reality of the
universe. The required 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 simple WSM rules than with conventional
rules. For example, an infinity of charge potential at r=0 in Coulomb's
law is not found 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 concerning the connectedness of the universe:
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 insight14
it provides. It allows scientists to deeply analyze quantum wave
structures, the cosmos, and the natural laws. In the R&D laboratory,
the new insight should 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 should improve communication and
the efficiency of energy transmission. For example, conduction of
electric energy along a wire is a quantum energy transfer process
between SRs. Knowing this, energy losses may be reduced, lowering cost
and increasing transmission distances.
17. Less Certain Conclusions
Is it possible the nature has made use of the
fact that each particle is connected with the waves of other particles?
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 processes15.
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 programs.
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 information
transfer. Since every life cell (each particle) contains the holographic
image of waves from other parts (other particles) of the body, each
cell is a memory device. So the apparatus of computers appears to be
there but whether or not nature has arranged our body cells into a
physiological computer we do not know. Indeed, the mechanisms of
ordinary sensory communication in the nerves of the body, and in the
brain are still poorly known. The new understanding of energy transfer
may clarify them but we won't know much about their quantum
communication without more lab research.
Interested readers should begin
the study of the quantum universe in references 7 and 8 and at the
"Quantum Science Corner" web site: http://members.tripod.com/mwolff. A future article Cosmology will describe the origin of the Hubble universe and the red shift.
Part V. Mathematical Appendix
18. Solutions of the Wave Equation (Principle I)
The wave equation must be
written (following Wolff 6,7,8) in spherical coordinates because
cosmological space has spherical symmetry. Uniform density of the
medium (space) is assumed which 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 amplitude = (1/r){Amax} exp (iwt + ikr) (a)
OUT-wave amplitude = (1/r){Amax} exp (iwt - ikr) (b)
A= wave amplitude, k = mc/h = wave number, w = 2¹f, r = radius from wave center, and energy = E = hf = mc2.
At the center, the in/out waves are joined by
rotating the in-wave to transform it to the out-wave. Superposition of
the two amplitudes to produce a standing wave can occur in two ways
depending on rotation, CW or CCW. One is the electron, the other the
positron, with opposite spins. Write the rotation operators as Rccw or Rcw . Then the two resonance amplitudes are:
The electron = E(-) = {- IN-wave + OUT-wave} Rccw (c)
The positron = E(+) = {+ IN-wave - OUT-wave} Rcw (d)
You can experiment with particle inversions by changing the (+ or -) signs 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 amplitude to the positron amplitude, the resulting amplitude is zero or annihilation.
19. Origin of Special Relativity (SRT) Mass Increase and the De Broglie Wavelength of QM Theory
Write the equation of a SR, as seen by an observer with relative velocity b = v/c, as shown in Wolff8. Then, insert relativistic Doppler factors, g = [1-v2/c2] -1/2. The amplitudes received by the observer 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. The origin of the de Broglie wavelength (QM) and the
relativistic energy and momentum ( mass increase of SRT) is as follows:
In the exponential factor:
Wavelength = h/mvg = de Broglie wavelength with relativistic momentum.
Frequency = kgc / 2¹ = gmc2 / h = mass frequency with relativistic energy.
And in the sine factor:
Wavelength = h/mcg = Compton wavelength with relativistic momentum.
Frequency = b gmc2/h = b x (mass frequency) = relativistic momentum frequency.
Thus the space resonance physically displays all properties of an electron, viz: QM, SRT, forces, annihilation, conversion to a positron, and CPT relations between Charge, Parity (mirror image) and Time; all of which were formerly empirical or theoretical properties. These properties depend on the spherical wave structure and ultimately on the wave medium - space.
20. References
1. Clifford, William (1870), "On the Space Theory of Matter", Cambridge Philosophical Society, 2, pp.157-158.
2. Clifford, William (1882), Mathematical Papers, Editor: Robert Tucker, Chelsea Publishing, N.Y. 1968.
3 Moore, Walter (1989), Schroedinger - Life and Thought, Cambridge U. Press, England, p. 327.
4. Dirac, Paul (1937), "Quantum Electrodynamics" Nature, London, 174, p. 321.
5. Wheeler, J. A. and Feynman, R. (1945), "Interaction with the Absorber...." Rev. Mod. Phys.,17, p.157.
6. Wolff, Milo (1991), "Microphysics, Fundamental Laws and Cosmology", Invited paper at 1st Sakharov Conf. Phys, Moscow, May 21-31, pp. 1131-1150. Proceedings by Nova Scientific Publ., NY.
7. Wolff, Milo (1993), "Fundamental Laws, Microphysics and Cosmology," Physics Essays, 6, pp. 181-203.
8. Wolff, Milo (1990), Exploring the Physics of the Unknown Universe, ISBN 0-9627787-0-2, Technotran Press, CA.
9. Mach, Ernst (1883 - in German), English edition: The Science of Mechanics, Open Court, London (1960).
10. Eisele, John A. (1960), Modern Quantum Mechanics with Elementary Particle Physics, John Wiley, NY.
11. Battey-Pratt, E. and Racey, T. (1980), "Geometric Model of Fundamental Particles", Intl. J. Theor. Phys., 19, pp. 437-475.
12. Misner, C. W., Thorne, K. and Wheeler, J.A. (1973), Gravitation, W.H. Freeman Co. San Francisco, p. 1149.
13. Wolff, Milo (1997), "Exploring the Universe", Temple University Frontier Perspectives, 6,
No 2, pp. 44-56. 14. Wolff, Milo (1995), "Beyond the Point Particle — A
Wave Structure for the Electron", Galilean Electrodynamics,
Sept-Oct, pp. 83-91.
- Wolff, Milo (1999), "Matter Waves and Human Consciousness", The Noetic Journal, 4, No 2, pp. 67-75.
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