The Nature of the Wave Function by Edwin Eugene Klingman

Hi Edwin,

A lot of physicists have undertaken to explain why action at a distance isn't "spooky." Aharonov's and everyone else's explanation necessarily relies on a probabilistic interpretation of reality. (Richard Gill is also among those who do not think that nonlocality is necessary to quantum mechanics -- that probability alone determines measurement outcomes.)

All of these explanations end up assuming what they intend to prove, for at least one very elementary mathematical reason (a), and one very elementary physical reason(b): a) the measure space is made of a continuous range of variables, while the measurement result is discrete (this is what makes Lamport's discovery profound); b) given that relativity is true, there can be no probabilistic distinction between past and future, which is equivalent to assuming a privileged coordinate frame.

Like Joy Christian, Aharonov et al propose nonlocality as only apparently true: " ... what appears to be nonlocal in space turns out to be perfectly local in spacetime." So far, so good -- except that it is impossible in principle to perform a probability measure on the spacetime continuum. The difference between purportedly entangled discrete particles and demonstrably correlated continuous wave functions is a strict constraint; spacetime can't be discretized without assuming either nonlocality or a privileged frame of reference. If considered to be a complete theory, quantum mechanics *cannot* discard the assumption of nonlocality, or else the theory is incoherent.

Joy does away with the conundrum, by allowing a natural, constructive, and globally continuous topological condition (all proofs of nonlocality are nonconstructive, and all topology is global) to be realized in the local discrete measurement outcomes -- without invoking probability or time, which in turn shows that quantum correlations do not result from particle entanglement, and both nonlocality and entanglement are illusions.

In other words, while Bell's theorem explicitly demonstrates that no classical theory can be derived from the principles of quantum mechanics -- it does not forbid quantum mechanical results from being derived on classical principles. This latter is what Joy has demonstrated, and which satisfies the completeness criterion for a physical theory; i.e., every element of the mathematical theory corresponds to every element of the physical measure.

Tom

Nice, Tom; nice. Very nice.

Joy

Dear Edwin

Sorry for the delay in commenting on your essay; I have been giving your essay some thought.

As you saw in my essay, I agree with you that the wave function captures a real physical wave and not just some sort of mathematical probability wave. In the example of wave interference for electrons, it is possible to take such a purely mathematical view of the situation far from the slits causing the interference pattern. The alternative is to take the view of a physical wave, where the focus is then on the slits. As these must be on the scale of the wavelength of the particle, physical intuition leads to focusing on what is going on at the scale of the wavelength of the particle - as you do in your essay. I also make the same choice of physical intuition over the mathematics as you do, and consequently agree with you on the assumptions that you challenge. The problem is that the maths doesn't agree with our choice. So either we abandon our physical intuition and go with the abstract maths, but as Roger Schlafly discussed in his essay, this could be a major source of the problem physics has had. I point with which I agree.

Models with causal linkage between the particle and wave property generally have problems with Bell-type analysis, or re-analysis. Quantum Theory has a very peculiar form of non-locality, with what can be called non-locality of identity which is confirmed by wave interference and quantum entanglement experiments. However, this is strangely not accompanied by non-locality of causation such that it could be practically used to send a signal faster than light. Unfortunately because your model has causal linkage between the wave and particle properties, when you obtain the non-locality of identity required for comparison with QT you also acquire non-locality of causation. So Joy Christian is right and the model as given in the essay does fall victim to the non-locality issue, as encountered via Bell-type analysis.

However, our physical intuition is based upon the assumption that the physical concepts we use are absolutely defined, whereas they are actually defined relative to a background, as is explicit in GR. This generally doesn't make any difference as the normal space background on which our physical intuition is based generally doesn't change dramatically enough. There is however one scenario in GR where the change in the background metric of space-time is dramatic enough to upset our expectations, and that is the ergo-region of a rotating black hole where the time component of the metric reverses sign. This change would affect what we define as being local and non-local. Consider two events with time separation dt and space separation dx - such as a causally linked particle and wave property - which would have a time-like separation ds2 = -cdt2 dx2 < 0 in normal space. Now change the background metric by simply reversing the sign of the time component - as occurs in the ergo-region - and the separation becomes space-like ds2 = cdt2 dx2 > 0. The actual time and distance separations haven't changed, but the change in the background metric has changed local causation into apparently non-local causation. So in a compound model of particle and wave with what our physics intuition would call local causal linkage in normal space, the inclusion of this sign reversal effect on the scale of the wavelength of the particle would give a non-local identity to the compound object. But because the metric is as per normal beyond the wavelength of the compound object, it wouldn't have non-locality of causation and so could be expected to avoid falling victim to Bell-type analysis.

My essay discusses this effect in the context of deriving quantum field theory via a change in mathematical representation because the wave expansion about a particle-like black hole on the Planck scale can be proven to be mathematically incomplete in terms of countable particle (black hole) numbers. However, it does suggest that an approximate causal model of a particle-wave compound object could be possible if it included this effect of sign reversal in the time component of the metric.

Hope this is helpful.

Michael

Mr. Klingman, this is something particular interest to me of how energy and time related to 1 another. I am rather unfamiliar with this concept. Where might a good resource be that I could look into this more? Thanks.

Dwaynefries1@gmail.com

Hello Edwin,

I've never disagreed with your emphasis on continuous functions. I just never have seen a way for your program to satisfy the completeness criterion, which of course is my chief concern.

Lamport's contribution is a strict local barrier to completeness; overcoming it requires a global solution.

Tom

Hi Erwin, first of all, a very understandable essay about the essence of physics today. Physicists based in the Uk think that they have proof that ithere is more then meets the eye. (see New Scientist 28 july 2012, : Ghost in the atom, page 28-31, by Marcus Chown) They concoted a thought experiment which involved bringing two independent atoms together and making a particular measurement on them. Their results showed that the wave function cannot be a mere abstract mathematical device, IT MUST BE REAL (?). Their conclusion : Quantum Theory makes no sense if the wave function is merely a probability distribution instead, the wave function HAS TO BE A REAL THING associated with a single quantum system, informing it how to behave. I wonder what your opinion is here, I am doubting this view, because i think that a quantum system has true properties, even before any measurement (observation) has been made on it., further moer in my new essay "THE CONSCIOUNESS CONNECTION" which has still to be accepted by FQXi, I introduce the so called "subjective simultaneity" which is in fact a universal web of interactions (decoherence) in which almost every system influences every other system. The second doubt I have is that the wave function ofv two particles (in their view) exist in an abstract six-dimensional space and for three particles nine-dimensional and so on, this is not logical I think. Furthermore once you accept a wave as a reality (stuff) in an atom where is the origin of this wave ? It means that the wave must be created sometime as a result of particles merging but then ?

thanks in advance for your appreciated answer. Wilhelmus

Dear Edwin Eugene,

I think, demonstrating the relativity of simultaneity in accordance with the wave functions of two identical particles, may evolve consistency of wave mechanics with string dynamics within the framework of quantum mechanics.

With best wishes

Jayakar

Dear Wilhelmus de Wilde,

Great comments and great questions! And thanks for the link to "Ghost in the atom". I'll start with that. The animation is actually wrong in my view. They say that if the wave function is 'real' then you get a 'taco-dog-burger' in the box until you look at it. That is the 'collapse of the wave function' interpretation that I explain to be incorrect. It surprises me that physicists can insist that the wave function is real and still believe it is a mathematical superposition.

But I do agree with you (and them) that "the wave function cannot be a mere abstract mathematical device, IT MUST BE REAL" and that "Quantum Theory makes no sense if the wave function is a mere probability distribution, instead, the wave function HAS TO BE A REAL THING."

Recent measurements of the wave function (discussed in my essay) agree with a recent proof by Pusey, Barrett, and Rudolph ('PBR') than an "information only" wave function cannot predict quantum results. This is consistent with the work you mention and with my essay.

I also agree with you that the system has true ('real') properties before it is measured [that is, it is a dog or a taco or a burger before you open the box, not a mysterious 'superposition' taco-dog-burger]. To not believe this leads to the situation I described in "down the rabbit hole" above where the first measurement shows what values the experimenter will choose **in the future**, before they have even made their choice. In other words, acting as if Bell's theorem [or the Copenhagen interpretation] is true leads to nonsense.

You describe the wave as "informing it how to behave". I would not interpret this literally. The particle and physical wave function form one inseparable system. The motion of the particle induces the field that constitutes the wave and changes in the wave feed back to the particle. Neither is "boss".

You propose a universal web of interactions in which every system influences every other system. We know that we have something like this (in the gravitational field, for instance) but the real question is how fast the influences travel. If they travel at the spead of light, then one side of the 'web' may not influence the other side for 14 billion years or so. But what if the changes are instantaneous (as you seem to imply with the word 'simultaneity')? Then every change propagates instantly to every other system, the reaction propagates back immediately, and the reaction-to-the-reaction propagates to all other systems immediately and all possible future changes and all reactions to these changes all happen at once, resulting, I believe, in nothing happening. So there must be a finite speed, but then one is back to such long delays that only local interactions seem to make much sense.

You note that two particles are represented in an abstract 6-dimensional space, three particles in a 9-dimensional space and N particle in a 3N or abstract 'configuration' space. I also treat this is my essay (page 7). Einstein and others, believing that wave could exist *without particles*, concluded that momentum and energy were conserved *only statistically* in 3-space. Schrodinger then FORCED the 3N-dimensional solution to conserve energy (after all, Schrodinger's equation is just the conservation of energy relation, written using operators!) As explained in the essay, this seems to imply (in view of Einstein's confused 'statistical conservation' idea) a certain 'non-locality' that has haunted us to this day. I believe this is also the conceptual source of the "stronger correlations" that Joy interprets in a different fashion. It's complicated, but I believe that reading and rereading pages 7-9 in my essay will help clear it up.

Finally, you ask about "the origin of this wave". It is the gravito-magnetic field ('discovered' by Maxwell and 'built-into' Einstein's relativity field equations). Just as an electric charge moving in an electric field induces electro-magnetic circulation, a mass particle moving in a gravitational field induces gravito-magnetic circulation. It's always there as a physical wave and I show in the essay how and why it corresponds to the probability amplitude.

Thanks for those questions. I hope this helps.

Edwin Eugene Klingman

Dear Edwin,

I read with interest your essay. I think that one of the major questions in physics is to understand the wavefunction, and how is it able to give the results we observe. I congratulate you for attacking this problem in such a beautiful essay. Good luck with the contest.

Best regards,

Cristi

Thank you Edwin for the reply, and excuse for my typo error of Erwin, I will come back to you after the acceptation of my essay by FQXi (there was a refernce which was not 100%) I am now rereading your essay. Wilhelmus

Hi Edwin

I really enjoyed reading your well written essay. You did a very nice work, quite intelligible. I do agree that the wave function represents a real particle. I understand your line of reasoning and why it is important for you the references you asked me.

Eckard Blumschein mentioned in his essay the following:

Hermann Weyl warned: We are less certain than ever about the ultimate foundations.

- Feynman smugly declared quantum mechanics something that nobody understands.

You said: So quantum mechanics is based on real local particle-plus-induced-wave, not on mystical non-local superposition of non-real wavefunctions of the kind Bohr, Feynman and others insist "no one can understand".

And also: 'No one can understand this theory until he is willing to think of as a real objective field rather than just a 'probability amplitude'.

I made the following comment to Eckard's essay which I think also apply to yours:

...I believe my essay offers viable solutions to the understanding of QM. Since the beginning of the XX, physics became so abstract that the physical and intuitive sense were demoted to a second plane. By the 1930s Heisenberg himself gave up trying to find an intuitive picture of quantum mechanical phenomena. He concluded that it was impossible to understand quantum mechanics intuitively; Schrondinger, Born, Bohr, Neumann, Feynman and others agreed with him. I believe that the reason for this is because they no longer had in mind some physical concepts that are crucial to accomplish the intuitive picture that they were looking for, namely: the PSR, the aether, the idea that particles are actually waves, and the notion that a field is a state of the aether. Once these concepts are restored in the physical conception of reality all the mysteries of quantum mechanics automatically disappear.

Perhaps, you may not see clearly the connection but the last paragraph is highly connected with entanglement, as you said:

Thus Bell is wrong --quantum mechanics is local.. Yet some physicists believe that quantum mechanics is inherently non-local...'non-locality' is fictitious, and the non-locality disappears from quantum mechanics.

I agree with this. I think you are in the correct track, but if you really wish your view to be widely accepted you must grant your works with a different philosophical framework in which the physical conceptions I mention in my paragraph are included. The reason for this is not only because your works could acquire more physical and intuitive meaning but also because it could lead you to new unobserved physical phenomena. As long as you maintain your ideas within the current paradigm, they will gain very few attention from the physics community. As an example of this just bring to mind both Bohm's quantum mechanics and consistent quantum mechanics. The latter argues that there is no collapse of the wave function. But both attempts predict no new physics they are only different interpretations. Your case, at first sight, is similar, it appears only a different interpretation of the wave function.

Good luck in the contest

Israel