The Nature of the Wave Function by Edwin Eugene Klingman

Hi All,

As noted several places, many essays build on earlier essays. For this reason I would like to reproduce a comment I made on George Ellis's thread, which treats the two-way flow of causality: top-down and bottom-up. Another essayist, Benjamin Dribus, presents a causal metric approach. And I found Carey Carlson's essay on causal set theory a helpful tutorial to causal set theory. My sense is that causal set theory is a mathematician's theory, or a physicist 'gone native'. As I understand it, one begins with time (as an ordered binary relation) and no space. Thus, to handle George's two-way causal flow we appear to need multiple time dimensions -- not a solution that appeals to this physicist.

Also mentioned were quantum phases depending on "the entire universes involved". My essay instead derives 'finite extent' wave functions from a classical field and explains how these relate to probability amplitudes and superposition of [infinite] Fourier components. There is no "quantum wave function of the universe", only local waves.

Which brings us to two-way causality. My previous essays assumed the universe as based on one physical substance (and *nothing else*) and assumed this substance (the primordial field) could evolve only through self-interaction. This led to a scale-independent solution (hence, per Nottale, motion-invariant, ie, time-invariant) with no meaningful physical interpretation of time until the original perfect symmetry breaks. In this sense I begin with space and no time versus the assumption of time and no space.

Although difficult to summarize in a comment, the point is that the essential nature of the primordial field (which turns out to be gravity) is to support self-interaction (since there is initially absolutely nothing else to interact with) and this (evolving as it has into the world as we know it) is at the root of the ability of our universe to support top-down as well as bottom-up causality.

Edwin Eugene Klingman

Dear Eckard Blumschein,

As your questions on your own thread are very relevant to my essay, I am copying my response to make the information available were. You asked about an electromagnetic (EM) wave versus the QM wave my essay postulates is the basis of the QM wave function.

I view a 'single' EM wave as a pure sine wave of 'infinite' extent. The scaled linear superposition of such components is of course the basis of Fourier analysis.

The key physical basis of such EM waves is their ability to propagate (through a medium or vacuum) far from the source of the radiation. In contrast, the wave that I describe is a circulating field (according to the weak field approximation to GR) induced by a 'mass current density' which has units of momentum density, mv where m is mass density and v is velocity. This wave is best viewed as a 'vortex' which has one field component, C, (versus two, E and B for EM waves) and does not propagate away from the source but travels *with* the source, soliton-like. There is no 'infinite' aspect to this wave but it does decay over a finite distance. Without the finite range of the 'trailing vortex' (analogous to aircraft wingtip vortices) the wave would not extend over the range of excited orbits and there would be no interference leading to quantized stable orbits.

You provided a link, http://en.wikipedia.org/wiki/Circular_polarization, to an article discussing circular polarization, that contains a nice animation showing a circularly polarized E-field wave. Note that this wave propagates far from the source, unlike the C-field wave and note also that the E-field is a radially directed field from the axis of propagation, whereas I picture the C-field wave as circular (or cylindrical) circulating about the axis of propagation, and centered on the inducing source current density, as shown in fig 2 in my essay. This is a quite different physical phenomenon.

As for the 'left-handed nature' of this wave, the GR equation is curl C = -p where p is the momentum density. I interpret the minus sign to indicate left-handed circulation. This is compatible with many left-handed aspects of particle physics, from neutrino to boson, and even shows up in biological molecules. The implications are too many to discuss in a comment, but I find them significant.

Finally, you say "You seem to add some temporal and spatial restriction which is entirely unknown to me". You are correct. I have combined de Broglie's wavelength-momentum relation p = h/lambda with the GR equation curl C ~ p to obtain: lambda (dot) curl C = h, where h is Planck's constant. This is interpreted as a quantized 'volume' (as shown on page 5) and I show how an atomic orbit can be viewed as an integer multiple of such volumes. This is a new physical relation that has never been proposed before and probably takes some digestion from those who think everything is already known about quantum mechanics -- we should just "shut up and calculate". In addition, I believe that there are other implications, based on a geometric algebra approach, which I hope to develop further in the future.

I hope that this comment is helpful.

Best,

Edwin Eugene Klingman

Hi Jonathan,

Yes there are a lot of fascinating comments on this page. Thanks for reading them! And you just added a fascinating comment. I'm fairly sure that the minus sign is indicative of handedness, but I would love to hear a topological explanation that made sense and opened up new possibilities. Keep thinking!

Best,

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

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.