Essay Abstract

Some mathematical theories in physics have claimed explanatory superiority even in the absence of new predictions. This was justified by the clarity of their postulates. In particular, mathematical derivations drive home the importance of the composition rule and the continuity assumption as two pillars of quantum theory. Our approach sits on these pillars but it combines new mathematics with a testable prediction. If the observer is defined by a limit on string complexity, information dynamics leads to an emergent continuous model in the critical regime. Restricting it to a family of binary codes describing `bipartite systems,' we find strong evidence of an upper bound on bipartite correlations equal to $2.82537$. This is measurably different from the Tsirelson bound. The Hilbert space formalism emerges from this mathematical investigation as but an effective description of a fundamental discrete theory in the critical regime.

Author Bio

Alexei Grinbaum is a researcher at CEA-LARSIM located in Saclay near Paris and member of FQXi. His main interest is in the philosophy of physics and the foundations of quantum mechanics.

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Dear Alexei Grinbaum,

I very much enjoyed your essay on the mathematical basis and understanding of quantum mechanics. I would call attention to your statement to the effect that

"Mathematical reconstruction of quantum theory... must be complemented with a quantitative bound on the amount of correlations..."

based on what is claimed to be "a fundamental fact about nature: the amount of correlation between distant subsystems is limited by a non-classical bound..."

I realize of course that this is a current statement of the quantum credo, but I would ask that you read my essay in which I present a classical local model that does not respect this bound.

As a good part of the focus of FQXi's essay question is whether mathematics can "trick" physics, I exhibit an instance in which Bell's focus on "hidden variables" has masked his imposition of "hidden constraints".

Bell's math is impeccable. If there were a math problem, it would not have survived for 50 years. But Bell's physics is not impeccable, and could easily survive 50 years given the half-dozen to dozen current "interpretations" of physics, all generally describable by Feynman's comment that "no one understands quantum mechanics", examples of which your essay is full.

Bell begins with a logical contradiction, based on effectively assuming a constant magnetic field which, in turn, yields a null result in a Stern-Gerlach experiment leading to an obvious contradiction.

Given a local model that does reproduce the quantum mechanical correlation, one must ask where the error occurs in Bell's logic. I have analyzed this and attempt to present the answer in nine pages. I hope that you will find the time to read my essay. I realize this goes completely against the quantum orthodoxy, and therefore "cannot possibly be right", but from your own essay it appears that you claim

"All mathematical alternatives to the Hilbert space must fit the experimental value of this bound."

I understand (to some degree) your derivation of the value 2.82537 for bipartite correlations that differs slightly from the Tsirelson bound, but is, as you say, consistent with available experimental results. You also say your model is highly speculative.

The model I develop is consistent with available experimental results and agrees with quantum predicted correlations, while also "in line with Bohr's well-known insistence on the role of classical concepts." Moreover it should be subject to experimental confirmation, as required for all good physics.

Templeton, in providing the funds for FQXi, was not hoping to make assorted professors happy by picking up an easy $10,000 or so for an essay. He was hoping to shake the foundations of physics. We all know how likely this is to occur in the face of fifty-year 'Gospel according to Bell', but I hope you will willingly suspend your disbelief long enough to give my essay a fair reading, and then give me your opinion and feedback.

If Bell's correlation bound is derived from a very good math analysis of very bad (because oversimplified) physics, then it is not at all necessary for reconstructions of quantum mechanics to yield this feature, despite that it is today seen as "as important as the fundamental constants or the mass of the Higgs boson."

My very best regards,

Edwin Eugene Klingman

Dear Alexei,

Well done on your essay, although I find the dose of mathematical spices more than what my philosophy taste buds prefer.

Permit me to ask a philosophical question that may or may not be eventually relevant to the new mathematical model you are formulating:

Can a Universe, along with its mathematical and/or physical objects perish? If the universe can perish, what is the possible implication for physics that mathematical/ physical objects are not eternally existing things but have a finite duration of existence varying from object to object?

Regards,

Akinbo

7 days later

Dear Alexei,

I liked much your lucid account of the status of mathematics in the modern history of physics. May be we are at a stage where mathematics will clarify misconceptions and paradoxes about quantum reality. I have much respect to coding theory in this context, algebraic and quantum. To my knowledge, self dual classical codes and the Clifford quantum computing have been found to share many concepts that are also known in the context of efficient sphere packing (Sloane, Nebe et al). What you write about algebraic codes and anomalous large correlations (encompassing quantum correlations) is an exciting mathematical perspective that is certainly welcome in this contest. Manin-Marcolli maths is difficult and you do an excellent job by relating the KMS states and CHSH. I am familiar with Bost-Connes KMS paper and the relation to RH and quantum computing. In a different direction, I would like to mention another bound 2.566 >> 2v2 for CHSH-like correlations in entangled optical qubits in the paper 1403.0805 [quant-ph] by L. Olislager et al. Thank you for the comments on my essay and the starting of my counter.

Michel

a month later

Dear Alexei,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Dear Alexei

I found interesting historical notes on you essay. In particular, the citation from Bohr:

"The use of mathematical symbols secures the unambiguity of definition required for objective description".

This makes apparent how casual was Niels in his writings, and why he was so often obscure and boring. A "symbol" does not secure anything. It is the mathematical definition beyond the symbol which secure objectivity, in the sense that we conventionally agree on everything is well defined mathematically.

Regarding your theory of the observer, I have already followed two of your talks, and have still difficulties understanding. The solution is that you will explain it to me personally, next time we meet, which I hope will be very soon (in Växjö?)

With my warmest regards

Mauro

    Dear Mauro,

    Alas, I won't be in Växjö this year but I hope we'll have another opportunity soon for a detailed conversation about these things. As for Bohr, I read his phrase as meaning that he was talking about the use of a mathematical formalism in physical theory.

    Amitiés,

    Alexei