Abstract. Lack of knowledge of energy transfer between particles is a major obstacle in understanding physics, matter, and the Universe. In 1945 Wheeler and Feynman sought the mechanism of energy transfer by calculating e-m radiation from an accelerated electron. The electron generated outward and inward waves and evoked a response of the universe from absorber charges. This paper compares Wheeler and Feynman’s work with a rigorous solution using the scalar wave equation that finds a quantum-wave electron structure based upon two fundamental principles of Nature. This is equivalent to replacing the material point electron with a spherical quantum-wave electron, a new structure in main-stream thinking but fulfilling a proposal by Schroedinger. Surprisingly, all the natural laws are found embedded in the wave structure of the electron – as envisioned by Schroedinger.
Wheeler and Feynman’s  use of waves to derive the energy-transfer mechanism of the electron was a pioneer attempt to quantitatively define a proposal by Clifford  in 1876 and Schroedinger  in 1939, that matter does not exist as material bodies. Instead all matter is a wave structure in a quantum medium (Space) and material bodies are only an appearance to us. Very few authors have pursued his proposal. The mechanism of energy transfer had long been sought using Maxwell's Equations (ME) and electromagnetic fields but difficulties appeared: The electron has spherical symmetry but the MEs have no wave solutions in spherical coordinates. Another problem was the infinite fields (singularities) of the point electron. Avoidance was attempted using a "renormalization" process wherein infinity was subtracted from infinity to obtain the desired result. In 1937, 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 also 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.
In 1950, Einstein  rejected the point particle and Maxwell's Equations 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.
In 1937, Schroedinger  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 material particles are not.
These famous scientists had concluded that the logical structure of matter is quantum waves in space. A goal of this paper is to show that their correct conclusions motivated Wheeler and Feynman’s far-sighted response of the universe. The mathematical proofs by Wolff [6,7], and Mead  are summarized in section D below.
Wheeler and Feynman were calculating only an electron but were mainly seeking a fundamental understanding of the universe and looked at many ideas. They discussed this with Einstein who suggested a proposal by Tetrode  that light was two-way communication between source and receiver utilizing in- and out-waves. This proposal was controversial because in-waves appear to violate the causality principle: Actions should not appear before their causes. Wheeler and Feynman wished to use in-waves but avoid violation. Their goal was to verify a formula for radiation force by Dirac who used in/out scalar quantum waves.
They assumed the accelerated electron generated both in- and out-waves. The out-waves stimulated absorber charges in the universe whose waves then returned to the initial charge, a response of the Universe. Upon arrival, those waves became in-waves of the initial charge. However, their assumed behavior of the absorber was illogical – the absorber waves began before the initial acceleration, arriving at the electron at the moment of acceleration. Further, they changed wave type, switching from vector e-m waves to scalar quantum waves, without explanation, to match assumptions.
Remarkably, but as intended, causality was not violated because in-waves from the absorbers were cancelled upon arrival by opposite in-waves of the initial 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.
Wheeler and Feynman 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 charge form an array of approximately plane waves moving 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 obtained rigorously using a scalar wave equation in Section D below. Thus we can deduce that the partial success of Wheeler and Feynman method was due to switching of the wave type during the calculation so that in effect they were calculating scalar quantum waves, even though they assumed the final sum of waves had e-m properties.
Wheeler and Feynman’s work goes beyond explaining radiation forces because energy transfer and the motion of matter are fundamental processes of nature. Further their concept, that the whole universe contributes to each electron, implies an inter-connection, i.e., Every charged particle is part of the universe and the universe is part of each charged particle. This caused much speculation and others, such as Hoyle & Narlikar , used Wheeler and Feynman's work to examine the universe. Cramer  used Wheeler and Feynman’s work to argue that quantum waves were indeed real and e-m waves were not, in a 'transactional interpretation' of QM. Unfortunately in contradiction, he also retained the material particle notion as real.
Wolff [6,7], Mead , and Haselhurst  explored the Scalar Wave Equation and found that the solutions formed an in-out quantum-wave structure possessing all the electron’s experimental properties. A material particle electron (with all its paradoxes) became un-necessary. Further, a Wave Structure of Matter (WSM) does not violate causality. Their solutions are below:
If Wheeler and Feynman had begun with the scalar wave equation they would have found only two solutions:
Outward wave = Fout = (1/r) Fo exp(iwt - kr) (1a)
Inward wave = Fin = (1/r) Fo exp(iwt + kr) (1b)
Where F is a scalar amplitude, w is frequency = 2pmc2/h, k= wave number, r = radius. These two waves can be combined in only two ways to form a wave structure of the electron:
electron = Fin - Fout + CW spin (2a)
positron = Fout - Fin + CCW spin (2b)
+ = The Spherical In and Out Waves form a Standing Wave around the Wave-Center 'particle'.
FIG 1. The spherical waves of the electron or positron. These are 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. Wave rotations of 720 degrees at the center that transform in-waves to out-waves, are also opposite. The resulting spin = ± h/4p. Thus, superposition of an electron and a positron causes annihilation since Eqn. 2a = - Eqn. 2b.
Figure 1 shows the spherical wave pairs, Eqns. (2a & 2b), of an electron or positron. Note that Wheeler and Feynman in Section B above, described almost perfectly the behavior of the actual waves of the electron or positron even though Eqns. (2a & 2b) were not known at that time. Missing from the Wheeler and Feynman description was the 720 degree rotation of the in-wave that changes it to an out-wave, with continuous spin = h/4p. This wave origin of spin is new, not known at that time.
The Wave Equation is Principle I of two principles of a complete description of matter used by Wolff [6,7]. The second Principle II provides the origin of the wave medium – the apparently empty space all around us. The source of the medium was foreseen by Ernst Mach  who asserted: The law of inertia (F=ma) is determined by the matter of all the fixed stars. Wolff used an extended Mach's principle to quantitatively calculate the density of the wave medium, proportional to the sum of waves from all the matter (10^80 particles) of our Hubble universe. This calculation yields a finite electron density at the wave center thus the need for ‘normalization’ was a figment of the particle electron notion.
The wave structure of the electron Eqns. (2a & 2b) was found
to contain the natural laws as experimentally observed. They are derived in
detail by Wolff [6,7] and summarized as follows:
a) Electron and positron waves annihilate when super-imposed. i.e. Eqn. 2a = - Eqn.2b.
b) Spin occurs due to 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 .
c) The Doppler effect between two moving wave structures produces the relativistic mass increase as well as Compton and deBroglie wavelengths and the Schroedinger Equation.
d) Energy is conserved 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 appear like point charges.
f) Gravity - The in-wave, on arrival at the center, establishes the position and motion of a particle. Matter nearby modifies the density of the surrounding medium, according to Principle II. The changed medium density changes in-wave motion, moving the particle toward the matter. This is the force of gravity.
g) Inertia - The acceleration of matter changes Doppler frequency equilibrium in the medium. This produces energy exchanges with the medium that appear as local force F=ma.
Prof. Carver Mead at Cal Tech investigated the e-m consequences of the WSM in 'Collective Electrodynamics' . This book, very popular in Silicon Valley, shows correct ways to solve the electromagnetics of transistor circuits using the wave structure of the electron and a vector potential in place of the erroneous (predicted by Einstein- above) Maxwell Equations. He recognized that the electron is not a point particle but a wave structure.
FIG 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 waves generated become a Huygens combination, the in-wave of the initial electron. This intermingled exchange of waves between all particles makes each particle a hologram of the others – the universe, Wolff .
The proposals of Clifford and Schroedinger are correct that an electron is a continuous wave structure of equal inward and outward waves, not a material particle, whereas point particles and electromagnetic waves are merely appearances (schaumkommen). Figure 2 shows the in-wave Huygens wave fronts traveling towards their wave-centers, a continual process analogous to the response of the universe. There is no causality violation because the in-waves are real and do not run backwards in time.
The wave medium is the space around us that, although we do not interact directly with it, governs our observations of inertia such as the laser gyro. It has an energy density exceeding 10^40 Mev/cc. The Schroedinger wave functions are not probabilities. They must be interpreted as the matter itself. Many classic paradoxes, including, ‘renormalization’, wave-particle duality, and Copenhagen uncertainty, no longer occur. They were caused by the notion of a material particle that does not exist.
1. J. A. Wheeler, and R. Feynman, Rev. Mod. Phys. 17, 157 (1945)
2. Wm. Clifford,(1876) “On the Space Theory of Matter” in The World of Mathematics, p568, Simon and Schuster, NY 1956
3. E. Schroedinger. In Schroedinger- Life and Thought, Cambridge U. Press, 327, (1989)
4. P.A.M. Dirac, Proc. Roy. Soc. London A117, 610 (1929)
5. A. Einstein, Relativity, Crown Books (1950)
6. M. Wolff, Physics Essays 6, No 2, 181-203 (1993)
7. M. Wolff, Gravitation and Cosmology in From the Hubble Radius to the Planck Scale, R. L. Amoroso et al (Eds.), pp 517-524, Kluwer Acad. Publ. (2002)
8. C. Mead, Collective Electrodynamics, MIT Press (2000)
9. H. Tetrode, Zeits. F. Physik 10, 312 ((1922)
10. F. Hoyle and J. Narlikar, Rev. Mod. Phys. 67, No. 1, pp113-155 (1995)
11. J. Cramer, Rev. Mod. Phys. 58, 647 (1986)
12. G. Haselhurst, (to be published) What is the Electron, Apeiron Press (2004)
13. E. Batty-Pratt and T. Racey, Int. J. Theor. Phys. 19, 437 (1980)
14. E. Mach, (1883 German). English: The Science of Mechanics, Open Court (1960)
15. Wolff, M. Spin, the Origin of the Natural Laws, and the Binary Universe, APS meeting, Wash. DC, April 30, 2001
For more information on Dr Milo Wolff and his contributions to the Wave Structure of Matter please see the following articles and Digital Video Interviews.
http://www.spaceandmotion.com/Wolff-Wave-Structure-Matter.htm - Abstract: The structure of the electron is investigated and found closely entwined with the origin of the natural laws. The natural laws had been measured for hundreds of years but no one knew how Nature creates them. Richard Feynman wrote, speaking of the Conservation of Energy, Nature has a hidden accountant who keeps honest books of energy input and output but we don't know how she does it. The origins had been proposed earlier by Clifford and Schrodinger, who pointed out that only a Wave Structure of Matter (WSM), can explain natural laws (i.e. Wave Mechanics). Further, Einstein realised that matter was spherical and spatially extended and thus the Electron was not a point particle, but rather, a structure of space. He writes;
Physical objects are not in space, but these objects are spatially extended. In this way the concept empty space loses its meaning. ... Since the theory of general relativity implies the representation of physical reality by a continuous field, the concept of particles or material points cannot play a fundamental part, nor can the concept of motion. The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. (Albert Einstein)
error was to represent matter as a continuous spherical field in space-time
rather than as a Spherical Wave in continuous Space which causes
the spherical force field effects (as we shall shortly explain).
Using the WSM a quantitative origin has been found based on the wave structure of the electron. It is shown that Space (the quantum wave medium) is a single entity underlying electron structure and the laws. Three Principles are found describing the wave medium, enabling calculation of particles and the laws. The predictive power of the WSM is shown by deriving the previously unknown physical origin of electron spin and making experimental predictions which solve the paradoxes of the famous EPR experiment. The WSM has important implications for research, industry, and our human role in the universe.
http://www.spaceandmotion.com/Wolff-Einstein-EPR-Experiment.htm - Abstract: In l935, Einstein, Podolsky, and Rosen (EPR) put forward a gedanken (thought) experiment whose outcome they thought was certain to show that there existed natural phenomena that quantum theory could not account for. The experiment was based on the concept that two events cannot influence each other if the distance between them is greater than the distance light could travel in the time available. In other words, only local events inside the light sphere can influence one another.
Their experimental concept was later used by John Bell (1964) to frame a theorem which showed that either the statistical predictions of quantum theory or the Principle of Local Events is incorrect. It did not say which one was false but only that both cannot be true, although it was clear that Einstein expected The Principle to be affirmed.
When later experiments (Clauser & Freedman 1972; Aspect, Dalibard, and
Roger, 1982; and others) confirmed that quantum theory was correct, the conclusion
was startling. The Principle of Local Events failed, forcing us to recognize
that the world is not the way it appears. What then is the real nature of our
The important impact of Bell's Theorem and the experiments is that they clearly thrust a formerly only philosophical dilemma of quantum theory into the real world. They show that post-modern physics’ ideas about the world are somehow profoundly deficient. No one understood these results and only scant scientific attention has been paid to them. With the recent discoveries on the Wave Structure of Matter we can now understand the cause of these apparently 'spooky' actions at a distance.
http://www.spaceandmotion.com/Wolff-Feynman-QED.htm - Abstract: Lack
of knowledge of energy transfer between particles is a major obstacle in understanding
physics, matter, and the Universe. In 1945 Wheeler and Feynman sought the mechanism
of energy transfer by calculating e-m radiation from an accelerated electron.
The electron generated outward and inward waves and evoked a response of the
universe from absorber charges.
This paper compares Wheeler and Feynman’s work with a rigorous solution using the scalar wave equation that finds a quantum-wave electron structure based upon two fundamental principles of Nature. This is equivalent to replacing the material point electron with a spherical quantum-wave electron, a new structure in main-stream thinking but fulfilling a proposal by Schrodinger (Quantum Wave Mechanics). Surprisingly, all the natural laws are found embedded in the wave structure of the electron – as envisioned by Schrodinger.
Milo Wolff Digital Video Interview (Windows Media, 1,100K). 'I
was curious! ... ' - On his lifelong (slightly obsessive!) motivation
to find the cause of the de Broglie wavelength of Quantum
Theory / Wave Mechanics. His discovery (in 1986) that a Spherical
Wave Structure of Matter deduced Doppler shifts (due to
relative motion of the Spherical In and Out-Waves and the Wave-Center) that
correctly corresponded to the de Broglie Wavelength of matter. Of even more
significance is the fact that within these same simple wave equations were
the correct terms for the Frequency-Mass-Energy increases
with Motion as deduced by Einstein' Special Relativity.
Thus for the first time finding a fundamental theoretical and mathematical
unification of these two famous theories. (REAL).
More video interviews of Dr Milo Wolff on Physics and the Wave Structure of Matter.
Milo Wolff: Thinking Mind - Mathematical Physicist Dr Milo Wolff on how his mind thinks in terms of models rather than mathematics. Interesting and important to maths physics!
Discoveries of Milo Wolff & Geoff Haselhurst - A list of the independent discoveries of Mathematical Physicist Dr Milo Wolff and Natural Philosopher Geoff Haselhurst on the Wave Structure of Matter.
http://www.QuantumMatter.com (Milo Wolff's Website on the Wave Structure of Matter)
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