Milo Wolff, Mass. Inst. Tech. (retired)
1124 Third Street. Manhattan Beach, CA 90266
Nornalup, West Australia
Einstein was queried about the huge numbers of short-lived heavy particles found using
high-energy accelerators. Those physicists were seeking basic matter and wanted to know
Einstein’s thoughts. Einstein was a careful thinker not given to theatrics and was very
serious when he replied, I would just like to know what an electron is. Why did he say
this? His answer implied that the pedestrian electron, was more important to science than
billions of dollars spent on accelerators. Little attention was paid to his remark.
But Einstein saw the electron as the leading player in the universe, as could any
careful scientist because most activity of the Universe is e-m wave energy transfers
involving the electron. At the time, neither Einstein nor others understood the wavemechanisms
of the electron. Although the force between ‘electrons’ can be calculated
using rules of Physics I, the rules did not always match Nature. The electron did not
appear to be a discrete particle. Something was wrong and Einstein knew it.
Answering Einstein. This article shows that the electron is indeed the leading player
in the universe, deeply involved with the laws of nature. The method is to simply follow a
suggestion by Clifford and Schroedinger to reject the discrete material electron and
replace it with a wave-structured electron. The math is easy because scalar waves in
space are the only choice; Only a space wave medium and two principles are needed.
Amazingly, it is found that the wave structure has all the experimental properties of the
electron and is the origin of all the natural laws fulfilling Einstein’s intuition.
The value of philosophy. Einstein was greatly concerned about the electron because he
felt that the answer to his question might have a world-wide impact on industry,
medicine, our lives, and human affairs, as well as science and the universe. His reason
was due to his philosophical understanding of the roots of modern industrial society. In
his mind the electron appeared to be a intimation of Nature itself revealing the origins of
the natural laws that are the basis of the industry and technology of the modern world.
Thus knowing the electron would open an enormous window on the world of human
affairs. This article will reveal that his intuition was right, as well as that of many
pioneer scientists of the electron who have yet to be printed in the textbooks of today. As
often happens in basic science you, the reader, will find that many of the treasured
concepts that you learned and believed to be true, are not true. You must like an ancient
philosopher, carefully re-evaluate the evidence for the truth of Nature.
B. The Problem of the Discrete Electron Seen by Einstein
The structure of the electron had always been a puzzle but in hindsight the obstacle was
the erroneous belief that it is a discrete material particle. Einstein had already deduced
this was impossible since Nature’s forces and properties do not match the discrete
particle. Einstein realized that matter is inseparable from the space it occupies. In
retrospect only a simple correction was needed: replace the material point electron with a
spherical quantum-wave electron. Then, its wave structure is easily found as a solution of
the scalar wave equation to get a quantum-wave electron based upon only two
fundamental principles of Nature. This is a new electron in current main-stream thinking,
but fulfills early proposals by William Clifford and Schroedinger. Surprisingly, all the
natural laws are found embedded in the wave structure of the electron – as suspected by
Einstein, Clifford and Schroedinger. Unfortunately research on this path was not as
exciting as the funded military and industrial technologies begun during WWII. ‘Truth is
no match for emotions.’
C. Historical Proposals for a Wave Structure of Matter (WSM)
William Clifford (1845-1879) a brilliant mathematician whose legacy includes modern
Clifford Algebras, lectured before the Cambridge Philosophical Society  on The
postulates of the Science of Space. He discussed our ability to deduce the geometry of
space at astronomical distances and in space too small (i.e. particles) to be observed,
stating: I hold:
1) That small portions of space are in fact analogous to little hills on a surface
which is on the average flat, namely that the ordinary laws of geometry are not
valid in them.
2) That this property of being curved or distorted is continually being passed on
from one portion of space to another after the manner of a wave.
3) That this variation of the curvature of space is what really happens in that
phenomenon which we call the motion of matter, whether ponderable or ethereal.
4) That in this physical world nothing else takes place but this variation subject to
the law of continuity.
Note that he was bold enough to conclude that the entire physical world ( motion of all
matter) therefore all of science and the Universe, was a result of this property of space.
This implied that all matter and motion was contained in ONE entity – space. In
hindsight, this paper shows that his analysis of the geometric properties of space, more
than a century ago, before quantum waves were discovered, were correct. Clifford’s
deductions about space were revolutionary at the time because space was not yet a
concept that many scientists recognized.
When J. J. Thompson discovered the electron in 1904 using cathode-ray tubes that
enabled him to calculated the charge to mass ratio, everyone was convinced that
electrons were discrete material particles. This discrete particle belief began to be
questioned about 1930, because the ‘wave functions’ of the Schroedinger Equation need
not be attached to individual electrons unless you assume that electrons are discrete. But
the Equation allows one to assume that discrete material electrons exist, or do not exist. It
is up to you to choose an interpretation. The math of quantum mechanics is neutral and
takes no position. The wave functions provide exact values of energy transfers but only
hint at how transfer happens. But knowing how was what Einstein wanted. We will see
below that it is not possible to know unless you abandon the notion of a discrete particle
and instead accept that the electron is a quantum wave structure. Then waves can transfer
In 1937, Irwin Schroedinger, the father of quantum theory, proposed  to eliminate
point particles by using a quantum wave structure. He wrote: What we observe as
material bodies and forces are nothing but shapes and variations in the structure of
space. Particles are just schaumkommen (appearances). That is, quantum waves
structures are real and discrete material particles are not. He was adding one element to
the work of Clifford – that the structure of the waves of space lead to the appearances we
observe of discrete particles These appearances underlie the rules we create to describe
the macro world of present day science but only indirectly do we see the real quantum
world of Nature itself. Again, by including all material bodies and forces, he was
concurring with Clifford and the ancient philosophers, that the space medium is the one
substance of everything.
A partial wave structure was found by Wheeler and Feynman  in a 1945 pioneer
attempt to find the energy-transfer mechanism of the electron. He sought a response of
the universe to the acceleration of an electron, by calculating waves traveling inward and
outward from the location of the electron center. This is reviewed in Section E below.
In 1950, Einstein  thought about the mechanism of the transmission of force from one
particle to another and concluded that space must possess a property that extends
throughout space to connect particles. In this sense, he agreed with Schroedinger and
Clifford. His knowledge of Nature told him that discrete particles cannot exist because
their borders would be an abrupt discontinuity. Particles and space must be continuous.
Further, assuming the Bohr concept were true, he asserted the notion of a discrete particle
being everywhere at once is impossible to imagine. He pointed out that the Bohr ideas are
never found in Nature. He rejected the point particle and Maxwell’s field Equations that
had become the bible of electrical engineering, writing: The combination of the idea of a
continuous field with that of material points discontinuous in space appears inconsistent.
Hence the material particle has no place as a fundamental concept in a field theory. Thus
even apart from the fact that gravitation is not included, Maxwell’s electrodynamics
cannot be considered a complete theory.
Research of Wave Structure. After 1945, particle physicists chose to work on post
WWII weapons. Research on wave structure stopped until 1985 when Milo Wolff 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 the properties of
the electron, except its spin. Below this article derives a physical origin of spin that
accords with quantum theory, the Dirac Equation, and adds new results.
The new electron in Quantum-electrodynamics. Akira Tonomura of the Hitachi Corp
published in 1998, “The Quantum World unveiled by Electron Waves” (World Scientific
Press) a beautifully illustrated book describing quantization of flux in closed current
loops of real electron waves at low temperature. Quantization occurs because the
circulating electron calculate the electro-magnetics of transistor circuits, MIT awarded
him a $500,000 prize.
Ancient Greek philosophers, Aristotle, Parmenides, etc, and recent mathematicians such
as Leibnitz, Descartes, Spinoza, and Kant asserted, using the logic of philosophy, that all
matter and motion, (the entire universe) was derived from ONE substance. We will see
below that ordinary space fulfills this role as the wave medium of the Universe.
Eric Storri a science historian at Bradley University carefully studied  the accuracy of
the periodic table of the elements, a foundation stone of chemistry. He find the rules of
counting electrons in orbits do not always work. He questioned the assumption that
electrons exist inside the wave functions, writing, According to quantum mechanics the
very notion of individual electrons in stationary states was shown to be invalid. He
concluded, like Einstein, that a full understanding of the Atomic Table requires a better
knowledge of the electron.
These leading scientists above had concluded that the logical structure of matter is
quantum waves in space. Recent this has been mathematically worked out by Wolff
[6,7], and Mead  and are summarized in section H below.
D. Understanding Energy Exchange
We cannot measure anything in Nature without an energy exchange that tells us
something has happened. 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. Thus, finding
the energy transfer mechanism between particles is part and parcel of understanding the
electron and the natural laws. Thus we must probe energy deeply. We cannot accept any
statement about the measurement of a natural event unless we verify the energy exchange
that allowed it. This is the test that distinguishes true from false. Skepticism is good for
To understand the mechanism of energy exchange, we first need to understand it. Most
people assume that they understand energy exchange because they buy and use it every
day; Accordingly no further thought is needed. This is a logical trap because our human
scale experiences are not a guide for the real energy exchanges that take place on the
quantum level of electron and atoms.
The mechanism of energy transfer had often been sought using Maxwell’s Equations
(ME) and electromagnetic waves but the method has problems: The electron has
spherical symmetry but MEs have no wave solutions in spherical coordinates. Another
problem was the infinite fields (singularities) at the center of the discrete point electron.
Singularity avoidance was attempted using mathematical “renormalization” wherein
infinity was subtracted from infinity to obtain the desired result. In 1937, Paul Dirac
commented : This is just not sensible mathematics. Sensible mathematics involves
neglecting a quantity when it turns out to be small – not neglecting it just because it is
infinitely great and you do not want it.
Feynman commented on the renormalization problem: But no matter how clever the
word, it is what I call a dippy process! Having to resort to such hocus pocus has
prevented us from proving that the theory of quantum electrodynamics is mathematically
self consistent. I suspect that renormalization is not mathematically legitimate.
E. Wheeler and Feynman’s Calculation to Find Energy Transfer
In 1945 Wheeler and Feynman (W&F) sought  the mechanism of energy transfer by
calculating electro-magnetic radiation from an accelerated electron. Their electron
generated outward and inward spherical waves and evoked a response of the universe
from absorber charges. W&F calculated the electron mainly to find a fundamental
understanding of the universe so they looked at many ideas. They discussed this with
Einstein who suggested a proposal by Tetrode  that light was two-way
communication exchange between source and receiver utilizing in- and out-waves.
Tetrode wrote, An atom that emits light from a star one hundred light years away, knew
then, one hundred years ago, that it would enter my eye today, before I was even born.
They considered this proposal realizing it was controversial because in-waves appear to
violate the causality principle: Actions should not appear before their causes. W&F
wished to use the in-waves but avoid violation. Their mathematical goal was to verify a
formula for radiation force found by Dirac using in/out scalar quantum waves.
Their accelerated electron generated both in- and out-waves. The out-waves then
stimulated absorber charges elsewhere in the universe whose waves returned to the initial
charge, a response of the Universe. Upon arrival, those waves became in-waves of the
initial charge. Remarkably (but as they intended) causality was not violated because they
cancelled in-waves from the absorbers upon arrival at the initial charge by opposite inwaves
from the charge! Force on the electron was assumed to be the product of charge
times half the difference of total in- and out-wave amplitudes. Dirac’s formula was
verified, independent of absorber properties provided that absorption was complete.
W&F described the wave behavior: Absorber charges at a large distance produce
spherical waves headed towards the source. At the moment the source is accelerated
these waves just touch the source. Thus all the waves from the absorber charges form an
array of approximately plane waves marching towards the source. The Huygens envelope
of these plane waves is a spherical in-going wave. The sphere collapses on the source,
and then pours out again as a divergent outward wave.
This description above of in-and out-waves is almost identical to the quantum waves of
the electron that can be obtained rigorously using a scalar wave equation in Section H
below. In hindsight, the partial success of W&F’s method was due to changing the vector
e-m waves to scalar waves, during their calculation so that in effect they were calculating
scalar quantum waves, even though they assumed the final sum of waves had vector
properties. This was not proper math, but nevertheless pointed to quantum waves as the
real structure of the electron. They were also forced to assume an illogical behavior of the
absorber – the absorber out-waves began before the initial acceleration – in order to arrive
at the electron at the moment of acceleration. This switching from vector e-m waves to
scalar quantum waves was needed in order to reach their goal.
F. Philosophical Importance
W&F’s work goes beyond explaining radiation forces because energy transfer and the
motion of matter are important fundamental processes of nature. Further their concept,
that the absorbers in the whole universe contributes to each electron, implies an interconnection,
i.e., Every charged particle is part of the universe and the universe is part of
each charged particle. This implies that each of us, including you and me, are connected
together as part of the observable universe! This fundamental but revolutionary concept is
still not recognized by mainstream physics. It caused much speculation and others, such
as Hoyle & Narlikar , and Cramer  used W&F’s work to examine the universe.
G. The Answer to Einstein’s Question
Einstein wished to resolve the disparity between the experimental properties of the
electron and the common discrete electron model. He also wanted to know why it appears
that “God plays dice” according to the uncertainty interpretation of quantum mechanics,
that he did not believe.
Wolff [6,7], Mead , and Haselhurst  explored the Scalar Wave Equation and found
that its solutions form a quantum-wave structure, possessing all the electron’s
experimental properties, eliminating the paradoxes of quantum mechanics and
cosmology. This wave structure completely replaces the material particle. This is what
Einstein wanted to know. Finding that the discrete particle electron does not exist,
removes the Bohr interpretation of the wave functions and assures us that God does not
play dice as well as removing the infamous wave-particle paradoxes. The mathematical
approach below describes the electron, its origin and role in the universe.
H. Solutions of the Scalar Wave Equation
Waves without Mathematics. You need not be a mathematician to understand the wave
structure of the Universe, so I have written the description below in ordinary prose. At
the same time, I have also written the related equations. Why both? So you can ask
your mathematician friends to verify that indeed both descriptions agree. You can read
either or both as you like.
Principle I – The scalar wave equation in Space. The universe abounds with things that
oscillate, such as; the ocean surface, a violin string, a drum head, a child on a swing, and
the structure of electrons and atomic matter. All have a property in common: Energy of
motion is exchanging back and forth with energy of position. It is precisely this
energy exchanging property that is the heart of a wave equation. There is always a
wave medium involved such as: water, a string, a membrane, a rope, and, for microatomic
matter, basic to all oscillators, the medium is space. Mathematicians use the
equation to calculate position and speed of the moving thing but you can understand it
just knowing about the energy exchange.
To understand the electron we need to find and solve a wave equation in space. Since the
universe is three-dimensional, the logical choice is the well-known scalar 3D wave
equation. It is not fruitful to consider the vector wave equation – so familiar in
electromagnetic wave guides – because it has no solutions in 3-D space. Thus this step
was easy – only one choice.
I won’t write the scalar wave equation because your math friend already knows it.
Sufficient to say there are only two possible spherical wave solutions. Again an easy step:
The outward wave = Øout = (1/r) Øo exp(iwt – kr) (1a)
The inward wave = Øin = (1/r) Øo exp(iwt + kr) (1b)
Where Øo is a scalar wave amplitude, frequency w = 2″mc 2/h, k= wave number. The
physical dimension is the radius r of the spherical waves, from a wave center.
You can picture the waves as continually expanding and converging bubbles of energy
as drawn in figure 1. From our human scale perspective we imagine the location of the
‘particles’ as the wave centers. But better yet – a trip to your computer will show you
moving animated waves of the electron – the four best web sites are:
1. http://www.QuantumMatter.com/see – It shows the electron – made by Winston Wolff in
Berkeley, California. 2. daugerresearch.com/orbitals/index.html It shows the H atom –
by Dean Dauger at UCLA, Los Angeles. 3. http://www.SpaceAndMotion.com/Physics
providing philosophy by Geoff Haselhurst in Nornalup, Australia.
4. http://www.geocities.com/glafreniere00/matter.htm by Gabriele Freniere in Canada.
These animations show you how the two oppositely moving waves form a resonance in
space around a center. You can exchange ideas at a Yahoo discussion group:
Waves of the electron-positron. These two waves can be combined in only two forms
which are the structures of the electron-positron. These are combinations of the in- and
out- spherical waves:
electron = Øin – Øout + CW spin (2a)
positron = Øout – Øin + CCW spin (2b)
The in-waves reverse direction at the center to become out-waves. This reversal is
expressed mathematically by CW and CCW rotation (spin) operators on the waves .
The operators cause either ‘3D clockwise’ or ‘3D counter-clockwise’ allowed motions
that do not tangle up the coordinates of space. The inward wave rotates twice in a 3D
fashion, that converts it to an outward wave as is Figure 1. The rotation fulfills a
geometric requirement of wave continuity and produces the formerly mysterious quantum
spin of value h/4″. Both the amplitude of the waves and the direction of spin are opposite
to each other in the electron and positron. This is the reason that electron-positron
superposition experimentally produces annihilation. Notice how simple Nature makes the
electron by choosing the simplest and only means of oscillating in free space!
Look above in Section E above, where W&F approximately described the behavior of
the actual waves of the electron or positron, even though the waves were not known at
that time. Their description of the in-waves as a Huygens superposition of out-waves
from other particles (absorbers) in the universe, shown in Figure 2, accords with other
calculations. Missing from the W&F description was the 720o rotation of the in-wave that
changes it to an out-wave. This basis of electron spin was not known before the work of
Wolff  and Batty-Pratt .
The second Principle II of the WSM is used to calculate the density of the quantum
wave medium – the space all around us. The role of the medium was foreseen in 1883
by Ernst Mach  who noticed that the inertia of a body depended on the presence of
the visible stars. His deduction of the familiar law F=ma, 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. He asserted: “Every local inertial frame is determined by the composite
Figure 2. Formation of the in-wave. The spherical
out-waves of an initial electron encounter other
electron wave-centers. At each encounter, a signature
of the initial electron is transferred to the out-waves
of the other electrons. The out-waves generated
become a Huygens combination, the in-wave of the
initial electron. This intermingled exchange of waves
makes each particle like a 3D hologram of all others
in the universe, Wolff .
Figure 1. The spherical waves of the electron or positron.
Each is a pair of waves, one converging, one diverging, that
form a continuous resonant structure in space. The wave
amplitudes of the electron are exactly opposite to those of
the positron. Rotations of 720o at the center that transform
in-waves to out-waves, are also opposite. The resulting spin
= ± h/4″. Thus, superposition of an electron and a positron
causes annihilation since Eqn. 2a = – Eqn. 2b.
matter of the fixed stars (the universe)” and jokingly, “When the subway jerks, it is the
fixed stars that throw you down.”
At first, 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? It cannot. The answer is that the inertial energy
exchange mechanism, formerly unknown, is the interaction of waves from accelerated
matter with the universal space medium around it. Space is not empty because it is a
quantum wave medium created by waves from every particle in the universe. Inertia,
charge, and other forces are seen by us as effects of the wave interaction with the
surrounding space medium. There is no need to travel across the universe.
There is only one way to rationalize Mach’s principle of inertia and our experience: That
is, the matter of the universe creates the wave medium in all space of the Universe. Thus
the inertia of an accelerated object is an energy exchange to the waves in the space
around it. We observe space as coincident with the framework of the fixed stars. The
laser gyro used in commercial aircraft is an important application of Principle II. You can
experience rotational inertia yourself by spinning on a piano stool.
How is Principle II obtained mathematically? Wolff  extended Mach’s Principle by
calculating the density of the wave medium as the sum of the squares of the waves from
every particle in the universe, each diminished by the inverse square of the distance.
Knowing the density you can calculate the velocity c of the waves, their amplitude and
the motion of the wave centers. The velocity c is almost constant everywhere because
there are so many (1080) particles contributing waves. Nevertheless, c varies somewhat
near large masses like the Sun.
It is important to realize that inertia is an interaction between an accelerated object and its
surrounding space. You should not try to imagine that the object is interacting with the
distant stars. Instead the density of the surrounding space is already created by the waves
from the distant stars. This agrees with laboratory experience using gyroscopes,
accelerometers, and the laser gyros that navigate aircraft. Before knowledge of the space
medium, inertia was a paradox stated by Newton as: action-at-a-distance.
If you think Principle II over carefully, you will see a strange feedback loop in Nature, as
follows: The matter of the universe combines to tell the space medium what it is and in
turn the medium tells all matter how to behave. In other words: The matter of the
universe determines the particles and the particles determine the matter.
The reader may be inclined to disbelieve this strange result. But there are several
confirmations, one of which is Einstein’s General Relativity (GTR) which contains the
same feedback loop: Reduced to basics GTR calculates the density of space-time at each
point in space using the density of matter and energy everywhere in the universe. A
varying density is referred to as curvature of space. This space density is then used to
determine the paths of moving matter and of light which follows the curvature. Archibald
Wheeler expressed this: All the matter of the universe tells space what it is and in turn
space tells matter how it must move. The feed back loop is the same. This is not
surprising because we have already found that all physical laws are a result of the WSM
and its space medium. If GTR were not included in the WSM this would be unexpected
indeed. Nevertheless, this feedback in Nature is puzzling and perhaps the reader can
assess its further meaning.
Equation of the Cosmos. A simple calculation  using Principle II also yields an eyeopening
relationship between the effective radius r of the electron waves, the radius R of
the Hubble universe and the number N of particles in the universe, termed the Equation
of the Cosmos:
r2 = R2/! [3N]
This is remarkable! The smallest things of the universe, r, depend only on the largest, R
and N. This equation also expressed the connectivity of matter – each particle depends
upon all others in the universe. The computed value of r corresponds with the classical
electron radius, approximately 10-15 m. This is expected. It is the logical common thread
between Mach’s Principle, General Relativity, and the ancient philosopher’s concept of
ONE substance, which are brought together as consequences of the Wave Structure of
Why can’t we feel ‘space’? Feeling requires a sensor of an energy exchange. We don’t
easily sense 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. Observing the medium would not help our survival so Nature has not
equipped us to sense it. 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. As Sir Oliver Lodge quipped: A fish
cannot comprehend the existence of water. He is too deeply immersed in it.
I. Origin of the Natural Laws
The wave structure of the electron Eqns. (2a & 2b) contains the experimentally observed
natural laws. The mathematics are derived by Wolff [6,16] and summarized as follows:
a) Doppler. The most surprising consequence of the WSM is found from the Doppler
effect between two relatively moving wave centers. Say, one is an observer electron and
the other is a source (another electron). Using Doppler math, you will find the relativistic
mass increase, the Compton and deBroglie wavelengths, and consequently the
Schroedinger Equation. At first it seems astonishing that all these occur together but
upon reflection it is logical since each of them depends on relative velocity. They are
calculated by writing two waves, like Eqns. 2a or 2b, for the two relatively moving
electrons. The Doppler effect is then inserted into both the inward and outward waves.
Then you find that in each term of the resulting total Doppler shifted wave that contains
mass or frequency, there is a relativistic mass-increase factor. And the Doppler
wavelength becomes the deBroglie wavelength, and, the phase velocity contains the
Compton wavelength. Before the WSM there was no theoretical explanation of either
QM or SRT or their common origin. Now the reason is immediately clear from the wave
algebra: Both the in- and the out-waves have symmetrical roles in the Doppler. This
means there is no dependence on the direction of the relative velocity, as is
b) Annihilation of electron and positron waves occurs when super-imposed. This is
immediately obvious because Eqn. 2a = – Eqn.2b.
c) Spin of h/4″ occurs due to 3D rotation of the in-wave at the center to become an
out-wave. This rotation is. described by the SU2 group theory of Battey-Pratt .
The two opposite rotations produce matter and anti-matter that make up the binary
universe in which we live. This is especially interesting because group-math
theorists have shown that this type of rotation is a property of 3D space only, not
4D, or 10D or 11D etc. Thus matter and anti-matter can occur only in a 3D world.
d) Energy Conservation occurs because only identical wave states can resonate
with each other, producing equal and opposite frequency (energy) shifts.
e) Electric force interactions appear to occur (as proposed by Schroedinger) at the
high-density centers. The wave centers look like point charges, as in Figure 3.
f) Gravity is a property of the behavior of wave centers . It occurs because the
in-wave, on arrival at the center, establishes the position and motion of a particle.
Then matter nearby can modify the density of the surrounding medium, according
to Principle II. Finally, the changed medium density causes the in-wave to speed
up going towards the nearby matter. We observe this speed-up as gravity force.
Other forces are also produced by a similar change of medium density.
g) The CPT (charge, parity and time) transformation properties of an electron have
been observed in experimental QM for many years but the reasons have not been
known. CPT means that if you switch a particle to its opposite property in the
order C >P >T you will arrive back to the initial particle. Now you can easily
show with a little algebra that Eqns. 2a and 2b contain this property.
h) Inertia – The acceleration of matter changes its Doppler frequency relative to the
surrounding wave medium. Restoring frequency equilibrium produces energy
exchanges with the medium that appears as a local force F=ma that has been
known experimentally since Galileo and Newton, but the reason has not been
Figure 3. Apparent location of charges.
The spherical wave structures of atoms and the
electrons arrange themselves in a configuration of
minimum amplitude or minimum energy. For
example, in this crystal, the waves of adjacent
electrons overlap with opposing phases resulting
in equal spacing of the wave centers. This is
caused by Principle II. Most of the wave
amplitude of an atom and its electrons are
concentrated around a center point where energy
exchange occurs. This produces the appearance
of a particle that we emotionally expect, as
predicted by Schroedinger.
known. The total energy exchange will follow the relativistic rule from a) above,
that at small velocity becomes the familiar energy rule E=1/2mv2.
J. The New Electrodynamics
Prof. Carver Mead, an engineer at Cal Tech investigated the e-m consequences of the
WSM in his 2000 book “Collective Electrodynamics” . This book is very popular in
Silicon Valley because it shows correct ways to solve the electromagnetics of transistor
circuits. He recognized that the electron is not a point particle but a wave structure. Thus
the approximations of Maxwell’s Equation do not work when dimensions approach the
quantum region, especially magnetism. Mead made use of the electron wave structure
observed at low temperatures  to derive a vector potential in place of the erroneous
magnetic terms of Maxwell Equations – an error foreseen by Einstein. His work begins
an important future for wave-based electromagnetism.
The proposals of Clifford and Schroedinger were correct that an electron is a continuous
wave structure in space not a material particle, and our observation of point particles and
electromagnetic waves are merely appearances (schaumkommen). The Schroedinger
wave functions must be interpreted as the electron itself, not as probability numbers, as
seen at the Dean Dauger (UCLA) animation site above. Many classic paradoxes,
including, ‘renormalization’, wave-particle duality, and Copenhagen uncertainty, no
longer occur because they were caused by the notion of a material particle that does not
exist. There is no causality violation because the in-waves are real and do not run
backwards in time.
Unity of the Universe. The wave medium – the space around us – is the ONE source of
matter and the natural laws. Since the waves of each particle are inter-mingled with the
waves of other matter and all contribute to the density of the medium, it follows that
every charged particle is part of the universe and the universe is part of each charged
Principle II (extended Mach principle) states that the stars and galaxies of the universe
are essential to the laws of Nature and to the existence of the Earth and ourselves. This
important fact is not presently familiar to the physics community. For example, the
present Standard Model of the universe contain no recognition of Mach’s Principle, or
our inter-connection with the universe.
Why has the science community not sought the WSM? There is a dark side to the
development of science. It is tempting to imagine scientists as noble pioneers, questing
for the greater good of humanity, and transfixed by the wonderful mysteries of the world.
However the day to day history of nearly every radical discovery tells an entirely
different story portraying a community that will eat its own in the name of progress and
where each member usually votes his pocketbook. Scientists are no different than you or
I. All the deadly sins of man and womankind are also found in the hearts of scientists.
Knowing this helps understand why the science community has not sought the Wave
Structure of Matter. It will take a long time to dispel treasured scientific illusions even
though following the path of the discrete particle leads science down a dead end street.
L. The Future
There will be new valuable applications of the WSM in technologies concerned with the
behavior of matter at small molecular dimensions: especially the quantum world at low
temperature, the design of new alloys and catalysts, more efficient power transmission,
understanding the mechanisms of bio-physics, building molecular computers and
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Figure 4. The illusive lure of the
discrete particle. Although the
twentieth century pioneers of
physics urged their peers to
cons ider waves as the
fundamental structure of matter,
the temptations of government led
science down a dead end street
searching for discrete particles.
The government wanted to buy
weapons of high-energy and the
physics community tried to
oblige. As Prof Carver Meade
wrote: The last 70 years of the
20th century will be seen in history
as the dark ages of science.
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