The Fundamental Nature of Time by Edwin Eugene Klingman

Cristinel Stoica's essay is very relevant to points I have made above, so I show comments I made on his thread:

Cristi gets off to a great start showing the isomorphism between 'number scrabble' and 'tic-tac-toe'. He notes that "in mathematics, isomorphism's are ubiquitous", mentioning that Euclidian geometry ~ axiomatics ~ symmetries ~ numbers/equations, for example.

This supports very nicely my thesis that physicists project mathematical structure onto physical reality, and then come to believe that physical reality has that structure. While it is relatively simple for competent mathematicians to 'switch' from one formulation to another isomorphic formulation, the physicist who "freezes" the projected mathematical structure onto physical reality has a tendency to "see" reality is having that structure.

For example, spins tend to align in fields such that statistically they are aligned or anti-aligned with each other in neighborhood/domains. Based on an over-simplistic interpretation of Stern-Gerlach data, Pauli projected a 'qubit' structure, O|+> = +|+>, O|-> = -|-> onto spin, despite that the SG data is distributed almost exactly as predicted by calculations of 3D spin traversing an inhomogeneous magnetic field. Based on Pauli's 'qubit'-based Hamiltonian, Bell 'believed' the qubit to be real and thus required qubit results: A = +/-1, B = +/-1 rather than variable deflection as seen in the data. The variable data satisfies Bell's relation which he claims is impossible to satisfy.

In another comment Cristi states: "Because Bell's theorem is a theorem. Trying to refute it is like trying to find in Euclidean geometry a right triangle which violates Pythagoras's theorem. It is simply impossible." Of course Bell's theorem is a foregone conclusion, from his very first equation, in which he forces the only allowed data to be +1 or -1. There is no physics involved in this, simply an initial condition that is 'projected' onto the reality of spin.

Thus Bell's 'belief' in Pauli's mathematical projection, causes him to reject 3D spin, which does satisfy ABcos(A,B), and to claim this impossible, leading to "entanglement" as a new mystery, on which thousands of papers can be written. This is compounded by "proofs" of Bell's theorem being conducted with valid two-state experiments, where the states are detection or not of photons.

Finally, as Bell was forcing 'qubits' on spin, Feynman, who was in love with the two-slit photon experiments, realized that he could apply Pauli's 'qubit wave function' for spin in a manner analogous to the two-slit experiments and he applied this to SG, thus projecting 'superposition' onto spin. Although Feynman's gedanken experiments have never been tested, several QM texts now begin with Feynman's two-slit-spin analogy. Thus Feynman and Bell forced a 'mystical' view on spin and Aspect "confirmed" it with photon analogs.

Once these giants froze the qubit projection onto reality, other isomorphisms go to hell. Isomorphisms are formalisms, qubit spin is (believed to be) physical reality! To seriously question this "reality" can be dangerous to one's career.

I discuss qubits because the genealogy is so clear cut. I could've discussed iso-spin, in which Heisenberg replaced two real fundamental particles with an imagined particle with 'qubit-like' projections onto reality, etc.

In my essay I treat another projection onto reality. Einstein, while basing his treatment on Hertz, projected a 4D-coordinate system with a new universal time dimension onto each moving object. The addition of new time dimensions (the physical 'reality' corresponding to the math structure) of course demolished time as universal symmetry and replaced it with "the relativity of simultaneity". This 'freezing' of the 4D-projection on the moving objects has lasted 100 years, despite the fact that the 'energy-time' conjugation in one inertial frame is isomorphic to Einstein's 'space-time symmetry' in two inertial frames, and agrees with all relativistic particle physics data.

In similar fashion, one can derive Bekenstein's "holographic principle" in terms of energy alone, without ever conceiving of information. But the 'information' projection is now 'believed' by physicists, and the door is closed to isomorphisms.

In summary, as long as the isomorphisms are mathematical, they are easily seen to morph into one another. But as soon as a mathematical structure is projected onto physical reality, it becomes "frozen" in the mind of the (consensus) physicist, and the fact that other isomorphic interpretations (such as 'classical' versus 'quantum') are equally possible are dismissed or rejected with almost religious fervor.

Cristi wrote on Jan. 27, 2018 @ 11:32 GMT, that while it is natural to question non-intuitive physics, one has to move on in his career. Nevertheless, he says:

"But I still think it is necessary to start by questioning everything, and you should never stop."

I believe that if one projection that leads to non-intuitive 'nonsense' can be replaced by another isomorphism that is compatible with the real data, and yet makes intuitive sense, this change of isomorphisms should be made.

So thank you, Cristi, for focusing on 'isomorphism' and 'fundamentality' as you have done. Your essay is well written and enlightening. Of course I agree with your proposition that geometric algebra is the tool we should be using. I hope my essay is read in terms of such isomorphisms.

Edwin Eugene Klingman

Dear Jeffrey Michael Schmitz,

Thank you for your gracious comments and for the welcome advice to humanize the Tavern with sights, sounds, smells, etc. I may rewrite this using your advice for another venue (although there are few venues like FQXi).

I've now read your essay, and agree with you about "the assumption that the rules of quantum mechanics apply to gravity waves and neutrinos, but we have no experimental evidence for this assumption." You might like to read my comment below [Feb. 20, 2018 @ 00:56 GMT] based on Cristinel Stoica's excellent discussion of isomorphisms.

Thanks again for reading and giving meaningful remarks.

My best regards,

Edwin Eugene Klingman

Dear Christian,

Thank you for your kind remarks and for reading my essay. In 'quantum gravity' I quote Ohanian and Ruffini:

"Principle of the equivalence of gravitation and acceleration is true only in a limited sense. If rotational degrees of freedom are taken into consideration... then the equivalence fails."

EEP ignores two things, tidal effects and rotation. One cannot replace gravity by acceleration if tidal effects cannot be ignored or if rotation cannot be ignored. In most cases the tidal effects can be ignored, but any principle that has exceptions is not a principle to bet one's theory on.

Although I do not mention it in this essay, I have described The Nature of Quantum Gravity the behavior of gravito-magnetism for ultra-dense matter. For example, the upper bound on the radius of the electron is approximately ten to the minus twentieth meters. This provides a density factor of approximately 60 orders of magnitude, and possibly even higher. When one plugs this mass density into equations(1) of my essay, the gravito-magnetic circulation ( del x C ) becomes non-negligible, and this aspect of gravitation cannot be "replaced" by acceleration. Therefore the EEP is a useful conceit in certain instances but I do not believe it is fundamental.

As I sit here, weighed down by gravity, I have trouble understanding the belief that mathematically projecting an "acceleration" on the body actually cancels local gravitational energy. Einstein's geometric equations do not handle the concept of local density well (if at all?) But the linear equations [(1) in my essay] imply the full non-linear equations, and they are based on momentum density, that is, mass density in motion.

As for the concept of general covariance, there is no physics in covariance.

I thank you for reading my essay and responding with thoughtful criticism. We do not agree on the central significance of the EEP. I see it as a useful approximation when gravito-magnetic and tidal effects are ignored. It says nothing real about "local gravity cannot exist."

I address other related issues in neighboring comments on this page.

As I remarked on your page, you have described, in very enjoyable fashion, a model of quantum normal modes of a black hole analogous to the atomic states of Bohr, and allowed Einstein to draw out various features that are addressed by your model. I am impressed with your analogy, and I am very glad that Einstein stopped by to see you after leaving the Tavern. It is always good conversing with you.

My best regards,

Edwin Eugene Klingman

Dear Peter Cameron,

Thank you for re-reading my essay. I very much appreciate it. I have also reread your essay and it is no surprise that you feel as you do. We believe too many different things for them to make sense. First let me repeat my main thesis that physicists project math structure onto reality, then come to believe that physical reality has that structure. Cristie Stoica discusses isomorphism. Mathematicians know that one structure is isomorphic to another [see his 'number Scrabble' versus 'tic-tac-toe'] and can easily switch between them. But physicists "freeze" one structure as physical reality, and get stuck there.

You ask me to define 'local gravity'. I feel local gravity at this moment. It pulls me toward the center of the Earth with a strength and preferred direction that differs from the gravity I find in the asteroid belt, or between galaxies. Light is deflected in gravity, and, even according to Einstein, "propagates" in gravity.

We have very different concepts of the 'wave function'. Like Bell, I believe it is real and possesses energy. In my reply to Christian Corda above, I reference The Nature of Quantum Gravity, based on the gravito-magnetism of ultra-dense matter, such as the electron. This picture is of the deBroglie-Bohm-like induced waves [ del x C ~ rho v ] and is compatible with Born's probability interpretation, so I think of it as physically realistic at the particle level. It is a wave function that is compatible with deBroglie, Born, Bohm (to some extent) and explains Bohr's 'orbits' and two-slit behaviors. It also makes sense statistically, i.e., for quantum mechanics. I do not believe this is the way in which you conceive of 'wave functions'.

Similarly, you identify a 'medium' as curvature. I do not. Einstein's 'curvature' is equivalent to energy density in Cartesian space. You note Hestenes and others demonstrated equivalence of GR in 'curved space' and gauge theory gravity in flat Minkowski space. Weinberg and Feynman separately showed the same thing. So 'curvature' is not really part of my thinking - it effectively leaves out the mass and focuses on empty space surrounding mass. It is the inverse of distributed energy density and is of limited utility. Even so, the gravito-magnetic field "curves" around ultra-dense matter in motion, but I view this as curvature of the field, not of space.

One result of the above is that I find no use for the 'vacuum wave function'. QFT is to me a "bookkeeping scheme", that ignores the physics of particles while keeping track of the results of this physics in terms of 'excitations' in the vacuum. It is generally isomorphic to the phonon excitations of condensed matter physics. Calculations of vacuum energy are off by 123 orders of magnitude, called "the worst error in physics". Again, Feynman diagrams replace continuous reality with the lattice of 'events', and provide a bookkeeping scheme based largely on conservation of energy. Sometime 'ghosts' are needed to preserve energy, but they are projected into the formalism without a second thought.

To switch topics a little, in The Nature of Quantum Gravity I discuss Ohanian and Ruffini's statement:

"That the linear equations imply the full nonlinear equations is a quite remarkable feature of Einstein's theory of gravitation."

Most physicists believe that Einstein's "weak field equations" [contained in eqns(1) of my essay], by virtue of this linearity, actually apply to linear gravity, as if removing non-linear terms from a description actually has an effect on the physical field. It does not. The non-linear terms are recovered by iteration. Gravity is always non-linear. It might be of interest to you that a treatment of Einstein's 'weak-field' equations based on Geometric Algebra makes no use at all of the concept of field strength, hence 'weak-field' is not a relevant concept for GA, only for Einstein tensors.

To summarize, I identify non-linear gravito-magnetic field as the continuum reality on which our universe is based. When Big Bang and LHC energies exist, the field behaves like a perfect fluid. Particles 'condense' according to the laws of equations(1) and then interact. The gravito-magnetic circulation and ultra-dense matter is equivalent to deBroglie's wave particle postulate that underlies quantum mechanics. It is what Bell was searching for. The 'quantum vacuum' is a figment, an isomorphism of the bookkeeping scheme that ignores gravity and keeps track only the results of such interactions. It is sufficient to solve statistical physics problems but cannot even calculate the masses of the particles. Pauli's 'qubit', Heisenberg's iso-spin, and SU(3) etc. symmetries are projections of math mistaken as realities of physics. For more on this aspect of quantum projection, see my response to Cristi Stoica above at Feb. 20, 2018 @ 00:56 GMT.

In short, it is no wonder you have trouble making sense of my essay. I respect you for trying to do so.

My very best regards,

Edwin Eugene Klingman

Dear Cristi,

Thank you for responding to my comment. You have certainly understood my main point, that we project our views onto reality. However you misinterpret me when you suggest "find where they are wrong and then conclude this was because of a wrong projection."

That is exactly what I am doing!

My essay discusses the arguments for one such wrong projection. It is hard to solve other century-old mistakes in a brief comment.

It does not matter why or how Pauli came up with the wrong projection, only that he did. He was brilliant, and his model was extremely useful. It is only when physicists believe in this model and assume spin is a two-state entity that things go off the track. One can very happily use 'qubits' when it is appropriate. Unfortunately, post-Bell all physicists seem to think it is always appropriate.

I believe you are wrong about Bell. He does not assume only that the particle can go up or down. He assumes the particle has two states, +1 and -1. This precludes the 3D spin that is deflected in the field by a spin-dependent amount. When one treats 3D spin versus qubit spin, one does obtain the correlation that Bell claims is impossible.

By projecting qubits onto 3D spin, Bell formulates a false theorem, falsified from his first condition. It is logic past this point, not physics. And the two-state logic ignores the distribution of SG data and is "proved" by two-state experiments on photons, having almost nothing to do with silver atoms in an inhomogeneous field.

I am surprised and pleased to learn that you do agree with me about 3D spin. That's wonderful!

You challenge me to make a model of the helium angle without entanglement. I would ask you to try and understand two types of 'entanglement' that physicists do not distinguish between. First, I remind you that I believe in a deBroglie-Bohm-like wave (function) induced by momentum density as discussed in The Nature of Quantum Gravity. The ultra-dense electron induces a gravito-magnetic wave similar to the manner in which a moving speedboat induces a wave. Boat AND wave are physically real. In helium, two electrons interact and their wave states become "entangled". This is a fancy word for simply interacting and influencing each other. It is physically sensible and not surprising in the least.

This local 'entanglement' is entirely different from Bell type 'entanglement' that exists 'faster-than-light' at any distance. That is the belief derived from Bell's logic based on qubit structure projected onto physics. In short, the entanglement one finds in a helium atom is real and local. It differs from the non-local entanglement of Bell.

Finally, you say prove Bell wrong. I do so here: Modern Classical Spin Dynamics. I do so by using 3D spins in the magnetic field and calculating the deflections. This maps perfectly over the SG data [see figure 6, page 20]. The model is simply classical spin and the correlation is the same as QM predicts for qubits. As you note, you will not study it, nor will any physicist still active in their careers. So it is a thankless task that yet yields satisfactions, and I thank FQXi for a venue in which we exchange information densely and pleasantly.

Thanks again for your thoughtful response, and good luck in the contest.

Best wishes,

Edwin Eugene Klingman

Dear Cristi,

After responding to you I started looking through 26 Jan 2018 copy of Physical Review Letters I received in the mail today. I was interested to find article 040406 titled

"Violation of Bell's Inequality Using Continuous Variable Measurements"

That is essentially the argument I was making above about the continuous variable deflection of silver atoms instead of Bell's constraint of +1 and -1. The current article is based on quantum optics, and therefore does not translate directly into atomic tests, but I hope you can see that it is an isomorphism of the paper I linked to above. The authors [Thearle, e al.] note that for continuum variable quantum optics the Bell test is harder to realize. But, significantly, they state

"Bell argued that quantum states with positive definite Wigner function would not violate a Bell inequality with respect to continuous variable measurements."

They claim the first observation of Bell correlations in a continuous variable system. As I said, this does not translate directly into Stern-Gerlach type of atomic tests, but I believe it is isomorphic to the continuous variable deflection measurements that I describe and that I have shown to violate Bell's inequality.

Best regards,

Edwin Eugene Klingman

Author Cristinel Stoica replied on Feb. 21, 2018 @ 08:34 GMT

Dear Edwin,

There are some important parts where I agree with you. I wanted to state this from the beginning of my comment, in order to facilitate reading without feeling that I opposed you too much. There is something where we disagree too, but you will see there is some important part where I tend to agree with you.

But first let me clarify something. When I say that spin is 3D, I refer to the Block sphere representation (plus the phase), not that spin is a mere 3D rotation. To me the spin is perfectly described by a spinor. I agree with the Pauli spinor as the nonrelativistic limit of the Dirac spinor. If you want to describe the Pauli spin of the electron in a basis, ignoring the position and other degrees of freedom, the basis has two vectors. There are not only two states, there are infinitely many, it seems to be two states because the measurement is done in a particular basis, and by the projection postulate yields two possible outcomes. This description of the spin works perfectly and it is very simple and natural. By "simple" I don't mean is simple to our classical intuition, I mean that it arises naturally when combining special relativity with the requirement of unitarity, see Wigner's theorem. The "3D spin" I mention is the Bloch sphere representation, and the state vector, represented up to a phase factor by a 3D vector, is completely determined by the expectation values of the spin operators along the three axes (which give the components of that vector along the three axes).

Now here is a bridge over the gap between our views. While I take the spinor seriously, it is not directly observable. The observables are build out of the Dirac spinor by taking various products of Dirac matrices and evaluating the result on the spinor field. You know these are scalar, vector (the electromagnetic four-current), bivector (where the angular momentum is), trivector (or pseudovector), and a pseudoscalar (a tetravector). These quantities are observable, and for a single spin 1/2 particle they behave in many situations quite classically. Now by "classically" I mean a classical spinor field, not a quantized field (as in the so-called second quantization), but the point is that these quantities are differential forms. And in the nonrelativistic limit we can treat an external field as a classical field too, in particular the magnetic field of the Stern-Gerlach device. So I am pretty sure that a quasiclassical analysis of the electron in the magnetic field is useful and relevant. You can even approximate the particle with a ball following a classical trajectory, as long as it is not too localized so that Heisenberg's principle makes the trajectory too fuzzy. This bridge I try to present here to you is something I always found reasonable to be true, and thought that it is important to have such an analysis. My brief glance to your paper gave me the impression that you are doing this in a careful and serious way. I always pictured for myself the electron as interacting continuously with the Stern-Gerlach device and exchanging momentum, energy, and angular momentum with it. I didn't do a careful reading of your paper, but I think you do this, and if I am wrong please let me know.

As a general approach to quantum mechanics and quantum field theory, I think it is important to understand what happens. I don't belive in magical projectors, and I think measurements are not sharp, they are just interactions. But I don't think there is a description consistent with both L and SI. I will come back to this later. For now, I want to say that I see nothing wrong with the particle passing through a Stern-Gerlach device and landing either in the up region or in the down region, without a collapse or projection. Even though I see this in terms of spinor fields, I think we see this picture similarly. So probably if I will check all your math and physics I expect I will agree with your figure at page 20. If you did this analysis without adding new physics, with the right math, and got that picture at page 20, I think it is an important result.

Now, I have the feeling that you are not satisfied with this analysis, and want more, namely to disprove Bell. If you are interested in my 0.02$, here is what I would advise you. Take that paper, clean it for claims that Pauli and Bell were wrong (I will explain later why), and try to publish it. If I am right, you can make it be some "mainstream" analysis of the Stern-Gerlach experiment. And I think you can get it published in a journal with ISI IF.

Now, I promised you I will come back to Bell's theorem. It is completely irrelevant if he labels the two outcomes with +1 and -1, or +1/2 and -1/2, or |up> and |down>, or just "up" and "down". If you think it is relevant, let's consider then another version of Bell's theorem, one which I say is the same, and you may say is a weakened version. Let us refer only to spin being up or down along an axis, not to Pauli matrices, not to two-level systems. By up and down I call the two places where the particle arrives after going through the S-G device, those two regions you reproduce in your picture at page 20. This is also in agreement with my views, because there are no sharp measurements. So we just think in terms of yes/no measurements, answering to questions like "did the particle land on this "lip" of the iconic postcard, when oriented along this particular axis?"

If you want to prove that Bell was wrong, then your task (for a second paper I would recommend) is to provide an explanation of the EPR experiment based on your theory, in terms of these up and down along diferent axes. So we stick only with what we can see in the experiment, not with the projections you said Pauli made. Maybe you think you already have this proof, but I still suggest you to put it in a second paper, separate from the one-particle paper.

If I am right, then you are wasting a great opportunity by mixing your one-particle analysis with the idea that this disproves Bell. I think your reasoning is the following sillogism: "(1) I explained the S-G experiment without Pauli matrices and spin operators, (2) Bell assumes Pauli spin, therefore (3) I disproved Bell". I don't think this works, because I don't think you can get the same correlation as QM with your model, unless you add something that breaks either L or SI. If I am right, you can publish the one-particle paper. If you are right, you can publish the one-particle paper, and then make it easier for the reader to accept your model and to read your second paper, where you will explain EPR. So no matter who is right, I think your analysis may result in a paper, which I think will be useful for physics (but I repeat, this is based on a brief glance of your paper, maybe I project my own views on it).

Best regards,

Cristi

Dear Cristi,

Thank you for your extended reply. I am retired and have plenty of time for this. You are in the middle of your career and have very little time, therefore I appreciate your gracious behavior. I take your criticism very seriously - you are certainly correct that all 'animus' must be removed from any paper on Bell. With that understood may I provide another link to a paper [please ignore the title!]: Bell was Simply Wrong , in which you might look at page 5 and 6 for the Bell test result figures. On page 5 is the model and page 6 shows the results obtained for +1 and -1 [which fail the Bell test] and for variable A and B based on the classical model [which produces the desired Bell cosine correlation]. Both are based on 10,000 runs generating random spin and SG orientations.

As I have so little opportunity to exchange thoughts with you, and since you mentioned the Dirac spinor, I link to an analysis of Dirac's equations: Spin: Newton, Maxwell, Einstein, Dirac, Bell. It is not generally known that Dirac's 4-component Dirac wave function is not an eigenvalue equation [see page 13] due to coupling between the positive and negative components. It yields a Pauli-like eigenvalue equation only after a Foldy-Wouthuysen transformation which 'smears out' the Dirac point particle, decoupling the positive and negative states, but occupying the region over which the integration is performed. Even then the equation does not yield spin, but helicity! Dirac is treated pages 10-17.

Finally, let me mention that Steven Kauffmann has analyzed the Dirac equation and shown that the speed of the electron is greater than 1.7c, where c is the speed of light, and other anomalies follow. Kauffmann attributes this to Dirac's desire for 'space-time symmetry' [per Einstein] which causes Dirac to forsake the Correspondence Principle in favor of 'symmetry in space and time variables'. [The same space-time symmetry I address in my essay.] Kauffmann has developed a unique relativistic extension of the Pauli Hamiltonian which does not produce the Dirac anomalies, but the world is not currently begging for any improvements to the Dirac equation. I include the link to his paper simply for your convenience, in case you ever desire to look more closely into the situation: Unique Relativistic Extension of the Pauli Hamiltonian.

Once again I thank you for your generous response. You need not respond to this comment. I simply present the information to you.

I see at the moment you are number one. Congratulations.

Best regards,

Edwin Eugene Klingman

Dear Vladimir Nikolaevich Fedorov,

Thank you for commenting on my essay. This year, as last year, I find we are in agreement about the fundamental nature of gravito-magnetism. You state that:

"The nature of the fundamental elements in the universe can be in two basic phase states: in the form of toroidal gravitational waves and in the form of photons."

It's not clear to me that our understanding of toroidal gravity is the same. In 'The Nature of Quantum Gravity', I see induced gravito-magnetic circulation as the deBroglie wave induced by the electron's momentum density. Association of photons and neutrinos is not compatible with my understanding. I believe the gravito-electro-dynamics represented by eqns(1) in my essay iteratively yield appropriate solutions.

You seem to say that the speed of gravitational interaction is 770 times greater than photon propagation; this seems to conflict with the recent data from colliding neutron stars, which indicate gravity and light propagate at the same speed. We do agree that "distortion of space-time is more of an abstract concepts and physical process." And, as last year, when you say "there are no fundamental particles ... with a greater mass than the electron", I believe this should be "greater mass density".

So we agree on the fundamental importance of gravito-magnetism however the details must, in my opinion, be worked out from the dynamic equations. The non-linearity of gravity makes this quite a difficult task, probably accounting for the lack of solutions in this area. It seems your calculations are heavily based on harmonics, and it is not clear to me that that is sufficient. I encourage you to continue developing your model.

My best wishes for continued development of your very interesting theory. I shall continue developing mine, and perhaps we will converge to a best theory.

Edwin Eugene Klingman