The Nature of the Wave Function by Edwin Eugene Klingman

Hi Jonathan,

Rather than assume that S3 topology applies to the electron, the C-field naturally evolves to a torus [ as schematically shown on page 5 in my previous FQXI essay ] with a key frequency being the Zitterbewegung frequency. The "hole" in the center has no apparent connection to the Schwartzschild radius but the topology does support the spin one half property of the electron. This is a stable configuration to which the field naturally condenses under the curl C ~ -p weak field equation with appropriate assumptions.

I don't really understand your suggestion about the Hopf fiber leaving a hole equal to the Schwartzschild radius of the particle mass or the 'always spiraling inward' aspect. I'm impressed by how quickly you've come up with such a topological solution, but the solution I describe above seems to evolve according to the weak field approximation to GR and also leads, under reasonable assumptions to the fine structure constant. The consequences of this model are developed in "The Chromodynamics War". I believe that the natural appearance of the Zitterbewegung frequency, the spin one half properties, and the fine structure constant provide points in favor of the model.

Finally, I should point out that while the 'condensing C-field' leads to a stable particle, any linear momentum of this particle then induces a *secondary* circulation which is the wave function discussed in my current essay. Thus the C-field actually accounts for both [primary] particle AND [secondary] wave in QM.

Hope this makes sense to you.

Edwin Eugene Klingman

Jonathan,

I had not heard of the recent Jenkins and Fischbach varying decay rate correlated with solar storms. My earlier interpretation [page 415 in "The Chromodynamics War"] is based on neutrino interaction with nuclear structures based on particles of the type described above. I find this far more feasible than a topological explanation. But if there is a topological explanation of the type you suggest, there appear to be enough people working in this field to eventually figure it out.

To clarify my point: I am not opposed to topology, in fact, the topology of the torus is more subtle than is usually realized [I believe] but it is one that evolves naturally from real physical fields, not one that is made up from thin air, in search of an application.

I hope others have comments on this question of decay correlation.

Edwin Eugene Klingman

Dear Hou Ying Yau,

Thanks for the comment. I am glad that you share an appreciation of a real wave as the basis of the wave function. As for the phase of the wave, I do not believe it is measurable in any way. How it is shifted, and what the effects of this will be, is an important question that must be addressed. And yes, it will help either substantiate the idea or will work against the idea. I am investigating this and other aspects but cannot yet answer the question. Many of the current essays are providing me with new ideas, as I am sure is also the case for you.

Additionally, another thread brought to my attention the PNAS article by Menzel et al. of June 12, 2012 vol 109 #24 on "Wave-particle dualism..." wherein a double-slit experiment using two entangled particles (based on down-conversion) observes the wave aspect on one leg at the same time that a particle is detected on the other leg. I believe this to be the first simultaneous experimental detection of particle and wave properties. I will write more on this after studying the paper.

I expect that we will be seeing much more experimental and theoretical support for the idea that "There *IS* Reality Beneath Quantum Theory".

Best,

Edwin Eugene Klingman

Dear Hou Ying Yau,

I will be very interested in reading your paper and am happy that you find the new information extremely useful. I too find it exciting. And I look forward to direct communication, once the rush of final essay submissions dies down. My email address is in my essay.

Sincerely,

Edwin Eugene Klingman

Dear FQXi'ers,

There are now several models for 'particles' published in this essay competition. As my essay is based on the wave function induced by a real particle, I feel it's appropriate to at least sketch my own model of how real particles are created, and I do so here:

First, the century old assumption of a 'point'-like electron is clearly wrong.

Several models assume a 'quantum loop' of some sort, often associated with Zitterbewegung. There's no realistic explanation for why a particle circles with Compton radius at light speed, and it's a stretch to obtain known particle parameters based on the Zitterbewegung model.

My own model assumes an intense C-field -- easily encountered at the big bang or in LHC collisions -- where particles are created. A vortex in the field, combined with the relevant field equations describing the self-interacting behavior of the field, results in an ever-faster spinning, ever-tightening vortex in the same way that a skater spins faster when she pulls her arms in. The significance of the Compton radius is that **this is the point where the vortex 'wall' reaches the speed of light**.

Instead of assuming that some 'point-like' particle races around a 'Compton radius' circle at the speed of light, I assume that a new phenomenon occurs here -- the creation of charge (the C-field, or gravito-magnetic field, is uncharged). This charge adds a new outward-based self-repulsion force to the inward directed centripetal force acting on the mass [energy] of the vortex wall moving in the original field [plus self-induced dipole field], and this self-repulsive force provides the limiting condition that prevents the vortex from following it's natural path which is to shrink to an infinitely dense 'point'. Instead, the charged vortex wall resists being compressed to a 'point' and the electron radius stabilizes at radius about 10^-18 meters.

It has been known for 80 years that the electron must "spin faster than the speed of light" to account for the magnetic moment but no one has ever explained why this is forbidden. Nowhere in the relevant equations does 'c' show up to limit this action. In fact, if the skater could pull her arms in to a radius approaching zero, she too would spin faster than the speed of light. If angular momentum is conserved, then the speed is determined by the radial arm -- there is no 'natural' limit. It is *NOT* the same as 'boosting' linear velocity to the speed of light. And the spin frequency is identically equal to the Zitterbewegung frequency!

My key assumption is that electric charge appears when the vortex wall reaches the speed of light at the Compton radius. Then everything else, including the fine structure constant, falls out. All particles are automatically 'indistinguishable' since there is no possible "marking" that could be seen on a particle spinning faster than light. This stable particle possesses a finite radius, a spinning charge that induces the correct magnetic moment, spin-one half and the particle spin provides the Zitterbewegung frequency. I present this process in great detail in The Chromodynamics War where I also treat all of the other particles of the Standard Model [except the Higgs].

A number of recent experiments have shown that the de Broglie model of real particle plus real-field-based wave function provides the best explanation of the observed results. To see how such a non-point electron induces a wave function, please read my essay [top of page].

In summary, electron properties derive from structure and it's high time that physicists focus on this structure. This is inconvenient from the perspective of point-based quantum field theories and QCD, but these theories have a number of problems.

Edwin Eugene Klingman

Dear Ben Baten,

The C-field is my abbreviation for the gravito-magnetic field that is meant to be used with the gravito-electric G field in a manner analogous to the E and B fields of electromagnetism. Equations very similar to Maxwell's equations fall out of the weak-field approximation to general relativity, as described in reference 10 of my essay. Since I am concerned with non-relativistic QM in weak gravity, this seems to me to be the appropriate approximation. Hoyle, many years ago called his "Creation-field" the C-field, and this has the unfortunate effect of bringing up Hoyle in Google searches. For a while I tried to avoid the term, C-field, but it is too convenient, with only 26 characters, and Hoyle's field is dead, except on Google. I regret this inconvenient similarity in names.

Units of the G-field are acceleration, L/T^2 while units of the C-field are frequency, 1/T. The Lorentz-like force equation is F=m(G plus v x C) where m is mass and v is the velocity of the mass in an external C-field. A mass in motion also induces its own C-field circulation, according to the relativity equation curl C ~ -p where p is the particle momentum.

Unknown at the time of Einstein's general relativity was a coherency factor, kappa, measured by Martin Tajmar (see appropriate reference). For particles and superconducting matter, this coherency factor provides a very large multiplier for the C-field effects. For thermal matter (like the Earth) this coherency is lost, and a much weaker C-field is measured (as the recent Gravity Probe B results).

I hope this helps.

Hi Jonathan,

Thanks for reviewing the comment. One never knows how reduced explanations will be received and interpreted. In fact, I should probably state that it is actually the outward-acting self repulsive force of charge working against the inward-acting force of the C-field on the mass of the C-field [energy] that actually provides the limiting mechanism that prevents the particle from shrinking to a point. I do not believe that the speed of light applies to angular momentum, only Planck's constant.

As for the Menzel experiment, I haven't yet had a chance to study it -- trying to keep up with the final flood of essays. But it appears to prove that a particle and a wave aspect have been detected **simultaneously** which does not agree with the Copenhagen interpretation of 'either particle OR wave'. It is, as my essay claims, 'both particle AND wave'.

Best,

Edwin Eugene Klingman

Yes, it's a big deal!

Dear Shawn,

Thank you for reading and commenting. I have truly enjoyed your comments on other threads and am very happy that you found my essay and associated comments of interest. As you note, there are many thoughtful comments here.

I have also noted elsewhere that I would like to drink whatever you guys are drinking in Saskatoon!

Edwin Eugene Klingman

Shawn, if by 'professional' you mean that one gets paid for doing physics, then be thankful. Those whose livelihood depends on being a member of the guild are very constrained, whether they admit it or not, to following the party line. Those of us who never or no longer depend on money connected to our physics are not so constrained. There are other constraints (being called 'crackpot', etc) but these are of a lesser sort. Of course this does not imply that non-professionals are any more likely to be correct than professionals, but they can look for truth in a larger field.

I am glad so many accepted the invitation as well.