Quantum Physics: A Brief Analysis of Richard Feynman's Quantum Electrodynamics (QED, 1945)

QED is founded on the assumption that charged 'particles' somehow generate spherical electromagnetic (vector) In and Out Waves (a dynamic version of Lorentz's Theory of the Electron, as Feynman uses spherical electromagnetic Waves, rather than static force fields). It is important to realise though, that like most post-modern physicists, Richard Feynman was a Logical Positivist. Thus he did not believe in the existence of either particles or waves, he simply used this conceptual language as a way of representing how matter behaves in a logical way. As he says;

.. some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation. (Feynman)

This explains why he had such success and such failure at the same time, as he had the correct spherical wave structure of Matter, but he continued with two further errors, the existence of the particle, and the use of vector 'electromagnetic' waves (mathematical waves of force), rather than using the correct scalar 'quantum' waves. It is this error of Feynman's that ultimately led Wolff to make his remarkable discoveries of the WSM.

The problem for QED is twofold;
Firstly, there is the Problem of 'Renormalization' - Feynman must assume finite dimensions for the particle, else the spherical electromagnetic waves would reach infinite fields strengths when the radius of the spherical electromagnetic waves tends to zero. There must be some non-zero cut-off that is arbitrarily introduced by having a 'particle' of a certain finite size. Effectively, Feynman gets infinities in his equations, and then he subtract infinity from infinity and puts in the correct empirical answer (which is not good mathematics, but it does then work extraordinarily well!)
Secondly, it is a mathematical fact that there are no vector wave solutions of the Maxwell Equations (which found electromagnetic fields) in spherical co-ordinates!
These are profound problems that have caused contradiction and paradox within Quantum Theory to the present day, and have led to the self fulfilling belief that we can never correctly describe and understand Reality.

... the more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that. (Feynman)

In fact Nature behaves in a very sensible and logical way (which explains why mathematical physics exists as a subject and can describe so many phenomena, and also explains how we 'humans' have been able to evolve a logical aspect to our minds!). That it is not Nature which is strange, but our incorrect conceptions of Nature! Most importantly, the simple sensible solutions to these problems can be easily understood once we know the correct Wave Structure of Matter.

The Solution to the Problem of 'Renormalisation'.

Richard Feynman's PhD thesis (with J. A. Wheeler, 1945) used Spherical IN (Advanced) and OUT (Retarded) e-m waves to investigate this spherical e-m field effect around the electron and how accelerated electrons could emit light (e-m radiation) to be absorbed by other electrons at-a-distant in space.
One vexing problem of this e-m field theory was that it led to infinitely high fields (singularities) at the center of the point particle electron. This was avoided with a mathematical process called renormalisation whereby infinity was subtracted from infinity and the correct experimental result was substituted into the equation. It was Dirac who pointed out that this is not good mathematics - and Feynman was well aware of this!
In 1937 Paul Dirac wrote;

I must say that I am very dissatisfied with the situation, because this so called good theory does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. 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! (Dirac, 1937)

Richard Feynman was obviously also aware of this problem, and had this to say about renormalisation.

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 renormalisation is not mathematically legitimate. (Feynman, 1985)

Albert Einstein was also aware of this problem as he explains in his critique of Lorentz's electromagnetic field theory for electrons (as it is still the same fundamental problem of the particle / electromagnetic field duality).

The inadequacy of this point of view manifested itself in the necessity of assuming finite dimensions for the particles in order to prevent the electromagnetic field existing at their surfaces from becoming infinitely large. (Albert Einstein, 1936)

Feynman's Spherical IN OUT wave theory is largely correct (and of course explains his success) but his error of using vector e-m waves resulted in infinities at the point particle as the radius tended to zero, and this led to the errors of renormalisation. In reality, Matter, as a structure of scalar spherical quantum waves, has a finite wave amplitude at the Wave-Center (as observed) and thus eliminates the infinities and the problems of renormalization found in Feynman's Quantum Electrodynamics (QED).

1.6.2 The Solution to the Problem of there being NO Vector Wave Solutions of Maxwell's Equations in Spherical Co-ordinates

James Maxwell (1876) used the experimental (empirical) results of Faraday, Coulomb, etc. to develop four equations, now famous, whose solutions described an electromagnetic (e-m) wave which correctly deduced the velocity of light c. Maxwell was correct that light is a wave traveling with velocity c - but it is a wave developed from the interaction of the IN and OUT waves of two spherical standing waves whose Wave-Centers are bound in resonant standing wave patterns. (Thus it is the interaction of four waves which probably explains why there are four Maxwell Equations.)
The Maxwell's Equations (M.E.), which describe the formation of electric fields E by a charge distribution q and changing magnetic fields H, as well as the formation of the H field by a changing E and electric currents i, cannot describe a spherical electromagnetic wave! It is a mathematical fact that there are no wave solutions of the M.E.s in spherical co-ordinates! Only the scalar 'quantum' wave equation has spherical wave solutions. Similarly, there are no imaginable M.E. solutions for a 'photon particle'. It is clear that the M.E.s are not fundamental and the photon is only a mathematical construction.
The failure of the M.E. in spherical co-ordinates can be imagined by saying, You cannot comb the hair on a tennis ball. This means that if you attempt to comb down an E field (the hair representing the electric vector) everywhere flat onto a tennis ball (a spherical surface), you must create a 'cowlick' somewhere on the ball which frustrates your attempt to comb it.

The questions arise, Why did theorists continue to favour the e-m field, the photon, and M.E. for 70 years in spite of the well-known flagrant failure of the mathematical description to agree with observation? Why were alternative descriptions of nature not sought? We suspect the answer is because it worked once the errors were removed with a bit of 'hocus pocus' mathematics and the aid of empirical data.
Unfortunately, this logical positivist view to retain the point particle and vector force fields has been the root cause of the many paradoxes and mysteries surrounding quantum theory. The resulting confusion has been increasingly exploited in the popular press. Instead of searching for the simple behaviour of nature, the physics community found that 'wave-particle duality' was an exciting launching pad for more complex proposals that found support from government funding agencies. The search for truth was put into limbo and wave-particle duality reigned.
Once we understand though, that the particle theory of matter is a mathematical (logical positivist) description of nature, then it becomes less confusing. Essentially the particle is a mathematical construction to describe energy exchange. It says nothing about the energy exchange mechanism and thus makes no comment about how the particle exists, how it moves through Space, what the Space around the particle is made of, and how matter particles 'emit' and 'absorb' photon particles with other matter particles distant in Space.

Let us then consider one fundamentally important argument of Feynman's that light must be a particle.

For many years after Newton, partial reflection by two surfaces was happily explained by a theory of waves,* but when experiments were made with very weak light hitting photomultipliers, the wave theory collapsed: as the light got dimmer and dimmer, the photomultipliers kept making full sized clicks - there were just fewer of them. Light behaves as particles.
* This idea made use of the fact that waves can combine or cancel out, and the calculations based on this model matched the results of Newton's experiments, as well as those done for hundreds of years afterwards. But when experiments were developed that were sensitive enough to detect a single photon, the wave theory predicted that the clicks of a photomultiplier would get softer and softer, whereas they stayed at full strength - they just occurred less and less often. No reasonable model could explain this fact.
This state of confusion was called the wave - particle duality of light. (Feynman, 1985)

Feynman though is incorrect in two ways;
Firstly, he is making unjustified assumptions beyond what is observed. It is true that light energy is emitted and absorbed in discrete amounts between two electrons. But we DO NOT OBSERVE any 'Particles' - we only observe discrete energy exchanges!
Secondly, the solution is to realize that the Spherical Standing Wave Structure of Matter actually demands that all energy exchanges for light be of discrete amounts because this is what occurs for 'Resonant Coupling', and for standing Wave interactions in general.

It is also interesting to see how simply Feynman summarizes QED;

So now, I present to you the three basic actions, from which all the phenomena of light and electrons arise.
-Action #1: A photon goes from place to place.
-Action #2: An electron goes from place to place.
-Action #3: An electron emits or absorbs a photon.

This can now be simplified to two actions with the WSM;
Action #1: An Electron, as the Wave-Center of a Spherical Standing Wave, goes from place to place in Space (as determined by the spherical In-Waves.)
Action #2: An Electron resonantly couples with another Electron (emits or absorbs a photon)

Once we realise that there are no separate electron or photon particles, thus we remove the problem as to how an electron particle can interact with a separate photon particle! Thus this solution is actually more consistent (and simpler) than Feynman's QED, particularly when we consider Feynman's further explanation of a positron being an electron which goes backwards in Time.

The backwards-moving electron when viewed with time moving forwards appears the same as an ordinary electron, except that it is attracted to normal electrons - we say it has a positive charge. For this reason it's called a positron. The positron is a sister particle to the electron, and is an example of an anti-particle. ..This phenomena is general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle. (Feynman, 1985)

As Wolff explains this is simply a mathematical truth caused by the fact that a negative time in the wave equations changes the phase of the standing waves to be equal and opposite, which corresponds to antimatter. (Antimatter does no move 'backwards in time'!)
Further, notice what Feynman says about photons, which are treated as particles in QED, and thus by Feynman's logic there should also be anti-photons, whereas the WSM is clear on this point - there are anti-electrons (positrons) which are opposite phase Spherical Standing Waves, but there are no separate photon particles, thus no anti-photons!

And what about photons? Photons look exactly the same in all respects when they travel backwards in time, so they are their own anti-particles. You see how clever we are at making an exception part of the rule! (Feynman, 1985)

While it may be clever, it is not good philosophy, and it has led to a very confused and absurd modern physics. Surely it is time for physicists to start considering the fundamental theoretical problems of the existing theories and to appreciate that the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter is a simple, sensible, and obvious way to solve these problems!
 

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