No Preferred Reference Frame: Quantum Mechanics Interpretations

[RUTA]

This Insight is a condensed version of No Preferred Reference Frame at the Foundation of Quantum Mechanics. Reference numbers here correspond to that paper. This Insight is an expanded version of Quantum information theorists produce new ‘understanding’ of quantum mechanics.
Feynman famously said, “I think I can safely say that nobody understands quantum mechanics” [1]. Despite the fact that quantum mechanics “has survived all tests” and “we all know how to use it and apply it to problems,” Gell-Mann agreed with Feynman saying, “we have learned to live with the fact that nobody can understand it” [2]. As a result, there are many programs designed to interpret quantum mechanics (QM), i.e., reveal what QM is telling us about Nature. Per Koberinski & Mueller, we do not have “a constructive account of ontological structure” necessary to constitute a true...

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[A. Neumaier]

The information theoretic approach to quantum mechanics is very incomplete. From its axioms one cannot even derive a single thing about the harmonic oscillator, the building block of all quantum physics outside of quantum information theory. Thus it is unsuitable as a foundation of quantum mechanics.

 

[RUTA]

Here is the bottomline. The denumerable-dimensional Hilbert space structure is the “kinematic” structure underlying QM. It’s counterpart in SR is Minkowski spacetime M4. The postulates of SR + some additional mathematical assumptions give the Lorentz transformations of M4. That constrains the supervening dynamics but it doesn’t dictate them. That is, you don’t get E = mc² from the postulates of SR. Likewise, you don’t get any particular potential for the Schrödinger equation from the Hilbert space structure. Quantum information theorists wanted to find some compelling principles/axioms at the foundation of that Hilbert space structure akin to the postulates of SR at the foundation of M4. What I showed is how they have succeeded.

The reason that the harmonic oscillator is ubiquitous in quantum physics (QM and QFT) has to do with another principle altogether, i.e., the boundary of a boundary principle BBP. That’s easy to see in the lattice gauge theory approach to the low-energy approximation of the Klein-Gordon equation. The free-particle Schrödinger equation with its the harmonic oscillator form is the result. You can see that and how it relates to BBP in Section 3 of this paper for example https://ijqf.org/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf. But that has nothing to do with the topic of this Insight.

 

[Sunil]

Whether or not one believes principle accounts are explanatory is irrelevant here. No one disputes what the postulates of SR are telling us about Nature, even though there is still today no constructive account of time dilation and length contraction, i.e., there is no “interpretation” of SR.

Source https://www.physicsforums.com/insig...ciple-at-the-foundation-of-quantum-mechanics/

That's wrong. Essentially you have it already found by Lorentz before SR. Namely, he argued that if matter is held together by EM forces, time dilation and length contraction would follow. (I have lost the explicit quote, sorry). The idea gives a valid argument - once the equations are wave equations with the same c, then they follow the corresponding Lorentz symmetry. And time dilation and length contraction follow from Lorentz symmetry.

The modern variant of this Schmelzer's generalized Lorentz ether:

Schmelzer, I. (2012). A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit. Advances in Applied Clifford Algebras 22(1), 203-242, resp. arxiv:gr-qc/0205035.

It derives the Einstein Equivalence Principle from action equals reaction symmetry. The EEP is also sufficient to prove time dilation and length contraction for rulers constructed out of matter.

 

[RUTA]

That's wrong. Essentially you have it already found by Lorentz before SR. Namely, he argued that if matter is held together by EM forces, time dilation and length contraction would follow. (I have lost the explicit quote, sorry). The idea gives a valid argument - once the equations are wave equations with the same c, then they follow the corresponding Lorentz symmetry. And time dilation and length contraction follow from Lorentz symmetry.

The modern variant of this Schmelzer's generalized Lorentz ether:

Schmelzer, I. (2012). A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit. Advances in Applied Clifford Algebras 22(1), 203-242, resp. arxiv:gr-qc/0205035.

It derives the Einstein Equivalence Principle from action equals reaction symmetry. The EEP is also sufficient to prove time dilation and length contraction for rulers constructed out of matter.

Aether theory is not taught nor mentioned in the physics textbooks. Even if it were true, it does not change the postulates of SR nor the result shown in this Insight.

 

[Sunil]

Aether theory is not taught nor mentioned in the physics textbooks. Even if it were true, it does not change the postulates of SR nor the result shown in this Insight.

Your "there is still today no constructive account of time dilation and length contraction" remains wrong even if the existing constructive accounts are ignored by the mainstream and Peter Donis does not like to see that particular reference.

I don't understand why mentioning Schmelzer's theory as a clear counterexample of a published paper is wrong simply because that theory has been "sufficiently discussed" in Peter Donis' opinion (in threads I was unable to identify - what I have found using the search engine here was not even a serious start of a discussion).

It is not my aim to question the existing principle theories. Without doubt, they remain useful tools. For example, if one wants to develop new theories, and prove they have the appropriate limit, all one has to do is to check if those principles hold in that limit.

 

[RUTA]

Your "there is still today no constructive account of time dilation and length contraction" remains wrong even if the existing constructive accounts are ignored by the mainstream and Peter Donis does not like to see that particular reference.

I don't understand why mentioning Schmelzer's theory as a clear counterexample of a published paper is wrong simply because that theory has been "sufficiently discussed" in Peter Donis' opinion (in threads I was unable to identify - what I have found using the search engine here was not even a serious start of a discussion).

It is not my aim to question the existing principle theories. Without doubt, they remain useful tools. For example, if one wants to develop new theories, and prove they have the appropriate limit, all one has to do is to check if those principles hold in that limit.

I did cite Brown & Timpson in this paper and we have cited others who advocate a dynamical account of SR in other papers:

@book{brownbook,
author = {Harvey Brown},
title = {Physical Relativity: Spacetime Structure from a Dynamical Perspective},
publisher = {Oxford University Press},
address = {Oxford, UK},
year = {2005}
}
@incollection{brownpooley2006,
title ="Minkowski Space-Time: A Glorious Non-Entity",
author ="H. Brown and O. Pooley",
booktitle ="The Ontology of Spacetime",
editor ="D. Dieks",
year ="2006",
pages ="67",
publisher ="Elsevier",
address ="Amsterdam"
}
@inbook{brownTimp2006,
publisher={Springer},
location={Berlin},
title={Why special relativity should not be a template for a fundamental reformulation of quantum mechanics},
booktitle={Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub},
author={H. Brown and C. Timpson},
editor={W. Demopoulos and I. Pitowsky},
year={2006},
pages={29-41},
note={\url{https://arxiv.org/abs/quant-ph/0601182}}
}

Those authors are cited and acknowledged in foundations of physics. I just haven't seen anything cited or discussed about actual theories of the aether anywhere. Once such a theory reaches that level of recognition in the physics community, I will certainly reference them.

 

[aabottom]

Excellent article! This clarifies my recent realization that at least some parts of "quantum mechanics weirdness" stems from No-Preferred-Reference-Frame (NPRF). E.g., quantum entanglement of two spin particles is no more weird than two clocks (moving relative to each other) ticking at different rates.

 

[Karll]

Thank you for this very readable article even for beginners like myself!
I especially enjoyed the article because this description made it very clear to me what physics is caused by special relativity and what physics by quantum mechanics! Before this article this distinction wasn't clear at all to me.

Sorry for this very basic question, I couldn't find an explanation in the cited article [4] of the following
In the paper on arxiv I didn't understand on page 9 last line

For example, suppose you want to construct the L_x

and continued on page 10

measurement operator with eigenvalues +1, 0, −1 in the L_z eigenbasis

and continued on page 11 the first 10 lines.

Even though calculating concretely the example in the paper, I fear I don't understand what leads to the chosen rotations (on page 11). Thanks!

 

[RUTA]

Thank you for this very readable article even for beginners like myself!
I especially enjoyed the article because this description made it very clear to me what physics is caused by special relativity and what physics by quantum mechanics! Before this article this distinction wasn't clear at all to me.

Sorry for this very basic question, I couldn't find an explanation in the cited article [4] of the following
In the paper on arxiv I didn't understand on page 9 last line

and continued on page 10

and continued on page 11 the first 10 lines.

Even though calculating concretely the example in the paper, I fear I don't understand what leads to the chosen rotations (on page 11). Thanks!

I'm glad you found the article useful. It was written so that a physicist in any specialty could follow the argument. The bit about L_x, L_y, and L_z is just an example to show how higher-level Hilbert spaces can be built from the 2-level Hilbert space (qubit) and SU(2). Those specific choices were made to create a set of mutually complementary measurements, but any and all measurement operators with eigenvalues +1, 0, -1 can be made that way using the qubit and SU(2). Bell notes something similar in his famous 1964 paper when he says the 2-level entangled state he discusses could be a subspace of some higher-level system and all of his analysis still follows. The point the QIT people are making is simply that the qubit structure is the basis of denumerable-dimensional Hilbert space in that sense. My example is really a pedagogical tangent :-)

 

[Karll]

Thank you! This paper was really a revelation to me.
As you mentioned, this formulation facilitates discussion not only among experts, but also for beginners like myself. I am looking forward to a textbook, which starts with your axioms!
Just to underline the last point, here are some recent papers I enjoyed, which show that uniform formulations across physics specialities are needed:
All the following papers tell us something different about the intersection between special relativity and quantum mechanics.

E.g.:

paper described in:
Does relativity lie at the source of quantum exoticism?
https://phys.org/news/2020-04-relativity-source-quantum-exoticism.html

Schmid, Manfred, and Pavel Kroupa. "The Spheronic Toy Universe: How Special Relativity may be Visualised to Emerge from a Wave-Nature of Matter." Publications of the Astronomical Society of Australia 31 (2014).
(Similar ideas like in a pedagogical paper by John Bell cited in Physical Relativity: Space-time Structure from a Dynamical Perspective by Harvey R. Brown)

Lindgren, Jussi, and Jukka Liukkonen. "Quantum Mechanics can be understood through stochastic optimization on spacetimes." Scientific reports 9.1 (2019): 1-8.

or:

Westra, Willem. "A First Principles Derivation of Classical and Quantum Mechanics as the Natural Theories for Smooth Stochastic Paths." arXiv preprint arXiv:2011.09181 (2020).

 

[gentzen]

The insight felt a bit like deja vu to me. I have the impression having read similar articles from RUTA ever since first reading "Answering Mermin’s Challenge with ...". So I wondered what it new. Then I found this:

In SR, we are concerned with the fact that everyone measures the same speed light , regardless of their motion relative to the source (light postulate). Here the inertial reference frames are characterized by motion at constant velocity relative to the source and different reference frames are related by Lorentz boosts.

This seems genuinely new, I don't remember a similar statement in previous articles. So it seems to be new, but is it also true? Well, at least it seems misleading to me.

But more seriously: What is new in this insight, compared to previous insights and similar articles by RUTA?

Let me also remark with respect to the overall approach that it is a nice start, but there is still potential for further progress of sorts that has already happened for SR. For example, Mermin in "It's About Time: Understanding Einstein's Relativity" has a chapter (9 Trains of Rockets) where it is shown that relativity of simultaneity is enough to fully explain both time dilation and length contraction. (What I am thinking about here is "QM is Nature’s way of having to avoid dealing with an infinite number of bits" as lemur put it succinctly, or in my own older words "... nature probably doesn't contain an infinite amount of information in a finite volume. So nature has to use QM (or something similar) to blur details ...")

 

[RUTA]

The insight felt a bit like deja vu to me. I have the impression having read similar articles from RUTA ever since first reading "Answering Mermin’s Challenge with ...". So I wondered what it new. Then I found this:

This seems genuinely new, I don't remember a similar statement in previous articles. So it seems to be new, but is it also true? Well, at least it seems misleading to me.

But more seriously: What is new in this insight, compared to previous insights and similar articles by RUTA?

Let me also remark with respect to the overall approach that it is a nice start, but there is still potential for further progress of sorts that has already happened for SR. For example, Mermin in "It's About Time: Understanding Einstein's Relativity" has a chapter (9 Trains of Rockets) where it is shown that relativity of simultaneity is enough to fully explain both time dilation and length contraction. (What I am thinking about here is "QM is Nature’s way of having to avoid dealing with an infinite number of bits" as lemur put it succinctly, or in my own older words "... nature probably doesn't contain an infinite amount of information in a finite volume. So nature has to use QM (or something similar) to blur details ...")

In the other articles, NPRF was applied only to Bell state entanglement. In this Insight, I used the information-theoretic principle of Information Invariance & Continuity from axiomatic reconstructions of QM to show how NPRF resides at the foundation of QM.

 

[Prishon]

The information theoretic approach to quantum mechanics is very incomplete. From its axioms one cannot even derive a single thing about the harmonic oscillator, the building block of all quantum physics outside of quantum information theory. Thus it is unsuitable as a foundation of quantum mechanics.

The harmonic oscillator the building block of all quantum physics (outside of...)? Most of these quantum phenomena are non-linear (except in laborataries).