I Modern View of Quantum Phenomena

[bhobba]

This is not, strictly speaking, a discussion of interpretations per se.

We often see discussions based on QM as it was understood during the early days and the famous Einstein-Bohr debates. The problem with this is that things in QM have advanced tremendously since then, and the 'weirdness' that puzzles those attempting to understand QM has changed.

I recently came across a synopsis of these advances, allowing those interested in interpretational issues to understand the modern view.

https://rreece.github.io/talks/pdf/2017-09-24-RReece-Fields-before-particles.pdf

It is advanced, but I tagged it as an I-level. Beginners may not understand the details, but they should get a sense of the modern perspective.

It also provides background to my current view, based on Wienberg's Folk Theorem, that QM is the EFT that any theory will look like at large enough distances. It is very mathematically sophisticated, but after years of thinking about interpretations, I have come to believe there is no 'simple' way to understand QM. It is, by its very nature, very advanced mathematically.

The real 'mystery' is why QM is based on operators, and complex space ones at that. I have posted a heuristic view of why, but it is just that a heuristic. That said - is it a mystery? What was it Newton said - hypotheses non fingo (Latin for "I frame no hypotheses", or "I contrive no hypotheses"). Is QM any different?

Thanks
Bill

 

[Peter Morgan]

The real 'mystery' is why QM is based on operators, and complex space ones at that.

One answer to the complex structure question comes from an article by Leon Cohen in Foundations of Physics 1988, "Rules of Probability in Quantum Mechanics" (paywalled), which is available on the author's Academia page. The argument in brief is that we use both probability measures and their Fourier transforms, characteristic functions. We could work with the sine and cosine components of the Fourier transform explicitly, but —as in signal analysis, electrical engineering, et cetera— it's mathematically much more convenient to introduce a complex structure.
Operators give us a very natural way to encode a random variable's sample space and σ-algebra as the eigenvalues of an operator and as a Projection-Valued Measure. Indeed, we can introduce a commutative operator algebra model of the Kolmogorov axioms. A noncommutative operator algebra can be thought of as a classically natural extension that encodes multiple experimental contexts in a single formalism. I refined the description I offer for that in a colloquium I gave by Zoom for NSU Dhaka on May 18th, "A Dataset & Signal Analysis Interpretation of Quantum Mechanics" (EDIT: I attach a PDF of the slides for that, because why not.)

 

[Peter Morgan]

after years of thinking about interpretations, I have come to believe there is no 'simple' way to understand QM. It is, by its very nature, very advanced mathematically.

Although that's definitely true when we consider details, I think signal analysis offers a starting point for a more accessible understanding. In particular, signal analysis includes Fourier transforms of signals over time, for which Wigner functions (called time-frequency analysis) are so classically natural that there are many YouTube videos explaining the HUP in terms of that idea. Signal analysis is also closer to field theory because it uses functions of time, in a way that is very different from classical states on phase space. I discuss that aspect of signal analysis in the introduction of Annals of Physics 2020, "An algebraic approach to Koopman classical mechanics" (that's an arXiv link, DOI there).
I'm told by a first year Yale undergraduate who came to my talk at Yale on May 1st and who then dived into other videos on my YouTube channel that the Dhaka NSU colloquium I link to in my previous comment is the most accessible of what she has seen. One aspect that I emphasize more in that talk is that I break away from an ensemble interpretation, in which an operator corresponds to a particle property; instead, I take an operator's set of eigenvalues to correspond to the set of data values contained in a Dataset. Since axioms of QM typically begin with something like "a Hilbert space corresponds to a system" and I do not mention systems or their properties whatsoever, this is a huge change. Some philosophers dislike such an instrumental way to ground QM more firmly in experiment, but that grounding allows a more realist interpretation of the structures we can develop.
I'll stop there. If you're interested, you'll say so, otherwise my apologies for landing so much on PF this morning.

ps: I enjoyed the PDF you posted enough that I wrote to the author through Academia. Thank you for it.

 

[A. Neumaier]

The real 'mystery' is why QM is based on operators, and complex space ones at that.

This a mystery only for those who think the discrete quantum information approach carries the essence of quantum mechanics, and forgot the origins of modern quantum mechanics 100 years ago:

Heisenberg discovered in 1925 that the observed Rydberg-Ritz combination principle is encoded in the canonical commutation rule [p,q]=i\hbar, which necessitates both complex numbers and operators.

 

[robphy]

Possibly interesting:

• On the relation between classical and quantum observables
  Abhay Ashtekar
  Comm. Math. Phys. 71(1): 59-64 (1980).
  https://projecteuclid.org/journals/...l-and-quantum-observables/cmp/1103907394.full
  
  
  
• Quantum Mechanics as Quantum Measure Theory
  Rafael D. Sorkin
  Mod.Phys.Lett. A9 (1994) 3119-3128
  https://arxiv.org/abs/gr-qc/9401003
  https://doi.org/10.1142/S021773239400294X

 

[Lord Jestocost]

The real 'mystery' is why QM is based on operators, and complex space ones at that. I have posted a heuristic view of why, but it is just that a heuristic. That said - is it a mystery? What was it Newton said - hypotheses non fingo (Latin for "I frame no hypotheses", or "I contrive no hypotheses"). Is QM any different?

One reads from the “THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY” by Sir Isaac Newton (translated into English by Andrew Motte):

“But hitherto I have not been able to discover the cause of those properties of gravity from phænomena, and I frame no hypotheses; for whatever is not deduced from the phænomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phænomena, and afterwards rendered general by induction.”

As Aage Bohr, Ben R. Mottelson and Ole Ulfbeck put it in "The Principle Underlying Quantum Mechanics":
"In fact, the quantum mechanical formalism was discovered by ingenious guesswork which was given an interpretation in terms of probabilities for the results of measurements." The orthodox version of quantum mechanics frames no hypotheses as it is a calculational recipe, designed in the last resort to predict the probabilities of various directly observed macroscopic outcomes - phenomena.

 

[Peter Morgan]

Possibly interesting:

• On the relation between classical and quantum observables
  Abhay Ashtekar, Comm. Math. Phys. 71(1): 59-64 (1980).
• Quantum Mechanics as Quantum Measure Theory
  Rafael D. Sorkin, Mod.Phys.Lett. A9 (1994) 3119-3128

Thank you for pointing out those two articles, neither of which I had seen before.
Ashtekar's article inches towards something like the ideas I develop in the article I mentioned above, "An algebraic approach to Koopman classical mechanics", but I think it is not ultimately much different from geometric quantization (he hints at that when he says in his introduction, "these questions are rather elementary, and the answers probably well known among experts in geometrical quantum mechanics"). In contrast, we can instead find isomorphisms between Classical Mechanics and Quantum Mechanics, if we are willing to abandon the Correspondence Principle, which almost nobody was ready for in 1980. Koopman's Hilbert space formalism for CM has been developed enough, however, since Sudarshan pointed out that it is a useful tool for discussing chaotic dynamical systems in Pramana 1976, that the ground is now rather differently prepared (some of the practical aspect of that development can be found in an article in SIAM Review 2022, "Modern Koopman Theory for Dynamical Systems").
A second consideration is that Ashtekar's introduction of Planck's constant is —as is generally found in the literature— not classically motivated. As I point out already in my Annals of Physics 2020, and more clearly on slides 7-8 in the NSU Dhaka talk, if we adopt a more classical starting point, I think we have to ask how quantum noise and thermal noise are different. Quantum thermodynamics gives a clear answer that can be adopted naturally into classical physics: the quantum vacuum (where quantum fluctuations live, so to speak) is Lorentz invariant, whereas thermal fluctuations are not invariant under boost transformations. Planck's constant becomes the amplitude of Lorentz invariant quantum fluctuations, very comparably to kT being the amplitude of thermal fluctuations.
I won't rehearse here more of the discussion in my Annals of Physics 2020 and in my NSU Dhaka talk.

 

[RUTA]

This is not, strictly speaking, a discussion of interpretations per se.

We often see discussions based on QM as it was understood during the early days and the famous Einstein-Bohr debates. The problem with this is that things in QM have advanced tremendously since then, and the 'weirdness' that puzzles those attempting to understand QM has changed.

I recently came across a synopsis of these advances, allowing those interested in interpretational issues to understand the modern view.

https://rreece.github.io/talks/pdf/2017-09-24-RReece-Fields-before-particles.pdf

It is advanced, but I tagged it as an I-level. Beginners may not understand the details, but they should get a sense of the modern perspective.

It also provides background to my current view, based on Wienberg's Folk Theorem, that QM is the EFT that any theory will look like at large enough distances. It is very mathematically sophisticated, but after years of thinking about interpretations, I have come to believe there is no 'simple' way to understand QM. It is, by its very nature, very advanced mathematically.

The real 'mystery' is why QM is based on operators, and complex space ones at that. I have posted a heuristic view of why, but it is just that a heuristic. That said - is it a mystery? What was it Newton said - hypotheses non fingo (Latin for "I frame no hypotheses", or "I contrive no hypotheses"). Is QM any different?

Thanks
Bill

I read all 51 slides in that presentation, very comprehensive. However, it is missing the axiomatic reconstruction of QM via information-theoretic principles completed in 2011. I think that's the newest view of QM.

 

[Peter Morgan]

I read all 51 slides in that presentation, very comprehensive. However, it is missing the axiomatic reconstruction of QM via information-theoretic principles completed in 2011. I think that's the newest view of QM.

VERY good to see you here, @RUTA! Though it is a notable new approach, I think the information-theoretic approaches introduce axioms that I don't find obvious enough for them to be axioms.
It's not yet ready for prime-time, but please consider thinking of "A Dataset & Signal Analysis Interpretation of Quantum Field Theory" as perhaps the notable 2026 newcomer on the block. We can pull back from the abstraction of information as a basis for the axioms by taking actually recorded datasets (in computer memory or in a lab notebook) as a grounding for axioms that do not mention particles or systems or their properties, leaving those to be derived when they can be (or not to be derived when they are, as so often, problematic).
[I like to include "Signal Analysis" as a familiar hook in my titles, but it's partly a bait and switch insofar as we notice after a while that we have to work with stochastic processes as a signal analysis made more elaborate by introducing probability theory and, one step further, by introducing generalized probability theory. If I said "stochastic processes", there would still be that further step to generalized probability theory.]

 

[A. Neumaier]

the axiomatic reconstruction of QM via information-theoretic principles completed in 2011. I think that's the newest view of QM.

It does not even reconstruct the canonical commutation rules for a harmonic oscillator, hence is far from a useful reconstruction.

 

[RUTA]

It took me a lot of study and application before I realized what the quantum reconstruction had accomplished. On the surface it doesn't look like much, but it's all in there. Let me give you an executive summary. It took an entire book (Einstein's Entanglement) to explain why this is true, so don't feel bad if you don't see it from this simple summary. Here is an open access paper that serves as a 17-page summary. Or you can watch this 11-min YouTube video.

Special relativity is introduced as follows in:
Physics for Scientists and Engineers with Modern Physics 5e
R. Knight
Pearson, San Francisco
p. 1057 (2022)

Quantum mechanics could be introduced in analogous fashion:

 

[A. Neumaier]

It took me a lot of study and application before I realized what the quantum reconstruction had accomplished. On the surface it doesn't look like much, but it's all in there. Let me give you an executive summary. It took an entire book (Einstein's Entanglement) to explain why this is true, so don't feel bad if you don't see it from this simple summary. Here is an open access paper that serves as a 17-page summary. Or you can watch this 11-min YouTube video.

Special relativity is introduced as follows in:
Physics for Scientists and Engineers with Modern Physics 5e
R. Knight
Pearson, San Francisco
p. 1057 (2022)
View attachment 364606

Quantum mechanics could be introduced in analogous fashion:

View attachment 364608

The Schrödinger equation is nonrelativistic, hence violates your principle!

 

[RUTA]

The Schrödinger equation is nonrelativistic, hence violates your principle!

You're confusing the relativity principle with the theory of relativity. Newtonian mechanics obeys the relativity principle and it's certainly not relativistic. Newton made a big deal out of that, even repeating Galileo's argument.

 

[PeterDonis]

Newtonian mechanics obeys the relativity principle

It obeys a relativity principle, but it's the wrong one, as we now know by experiment. It obeys the Galilean relativity principle, but we now know by experiment that the Lorentzian relativity principle is the correct one.

 

[RUTA]

It obeys a relativity principle, but it's the wrong one, as we now know by experiment. It obeys the Galilean relativity principle, but we now know by experiment that the Lorentzian relativity principle is the correct one.

As appears in Serway & Jewett: Einstein's relativity principle, "The laws of physics must be the same in all inertial reference frames" is generalized from Galileo's relativity principle, "The laws of mechanics must be the same in all inertial frames of reference." Since "the laws of mechanics" is a subset of the "laws of physics," anything that obeys Galileo's version also obeys Einstein's version.

 

[pines-demon]

Since "the laws of mechanics" is a subset of the "laws of physics," anything that obeys Galileo's version also obeys Einstein's version.

I guess I can try to understand what you mean here. But reading it for the first time, it looks like a complete fallacy. What you can say is that in their domain of validity, the laws of non-relativistic mechanics follow Galilean relativity, but this is just an approximation.

 

[gentzen]

It took me a lot of study and application before I realized what the quantum reconstruction had accomplished. On the surface it doesn't look like much, but it's all in there.

Do you believe that you can communicate your "realization" to me (or PeterDonis, or PeroK, or ...)?

Let me give you an executive summary. It took an entire book (Einstein's Entanglement) to explain why this is true, so don't feel bad if you don't see it from this simple summary.

Do you believe that I would get your "realization", if I would read your entire book?

Here is an open access paper that serves as a 17-page summary. Or you can watch this 11-min YouTube video.

I guess there is a decent chance that after reading your 17-page paper, I would once again have trouble to see what has changed compared to your previous papers? Or do you disagree?

And I already learned that your 11-min video ends with referring me to part 2 and 3, and part 2 ends with referring me to part 3, but part 3 doesn't exist yet. And independent, I guess there is still a decent chance that I won't get what should be different this time, compared to your older videos or papers.

OK, I did notice one thing which I really like: You mention Bob Coecke and his latest book, in part 1. For him, I really agree that reading his older longer book is currently the only way (for me) to really learn and understand what he found. The book has a summary at the end of each chapter, but already those summaries no longer did the trick for me, even so they really do summarize the important parts of the content.

 

[PeterDonis]

anything that obeys Galileo's version also obeys Einstein's version

Only if you ignore all the actual experimental results.

 

[RUTA]

Only if you ignore all the actual experimental results.

I think you're confusing the relativity principle with the light postulate. The relativity principle holds for G4 and M4, but the light postulate only holds in M4.

 

[robphy]

Conservation of Galilean-momentum holds in Galilean relativity.
Conservation of relativistic-momentum holds in Special relativity.

Conservation of Galilean-momentum does not hold in Special relativity.

Conservation of Galilean-momentum is only a small relative-velocity approximation of Conservation of relativistic-momentum.

 

[RUTA]

I guess I can try to understand what you mean here. But reading it for the first time, it looks like a complete fallacy. What you can say is that in their domain of validity, the laws of non-relativistic mechanics follow Galilean relativity, but this is just an approximation.

Again, don't confuse the relativity principle with the theory of relativity.

 

[RUTA]

Conservation of Galilean-momentum holds in Galilean relativity.
Conservation of relativistic-momentum holds in Special relativity.

Conservation of Galilean-momentum does not hold in Special relativity.

Conservation of Galilean-momentum is only a small relative-velocity approximation of Conservation of relativistic-momentum.

Again, don't conflate the relativity principle with the theory of relativity.

 

[RUTA]

Do you believe that you can communicate your "realization" to me (or PeterDonis, or PeroK, or ...)?

Do you believe that I would get your "realization", if I would read your entire book?

I guess there is a decent chance that after reading your 17-page paper, I would once again have trouble to see what has changed compared to your previous papers? Or do you disagree?

And I already learned that your 11-min video ends with referring me to part 2 and 3, and part 2 ends with referring me to part 3, but part 3 doesn't exist yet. And independent, I guess there is still a decent chance that I won't get what should be different this time, compared to your older videos or papers.

OK, I did notice one thing which I really like: You mention Bob Coecke and his latest book, in part 1. For him, I really agree that reading his older longer book is currently the only way (for me) to really learn and understand what he found. The book has a summary at the end of each chapter, but already those summaries no longer did the trick for me, even so they really do summarize the important parts of the content.

Everyone requires different experiences to "understand" something; the term means different things to different people. Physicists typically play with the math to see how it maps to physical phenomena and once they see that they feel like they "understand" the physics. Given that superposition, complementarity and entanglement are so widely applied today in physics, most physicists feel like they understand quantum mechanics, so they don't care about the axiomatic reconstruction of QM via information-theoretic principles. Those of us in quantum foundations want a bit more (see Becker's book "What is Real?" for example), so we struggle with the interpretations program. The quantum reconstruction program offers us a principle alternative to the quagmire that is the interpretations program.

So, I'm not sure what of the three options I posted will suffice for you. I'm sorry about not having episodes 3-5 posted on YouTube yet. They're ready to be recorded, but I broke my back three weeks ago and I can't stand or sit upright for more than 30 min, plus I can't reach or lift anything, so it might be another week or two before I can get them recorded and posted. Try the paper and if that doesn't work, go to the book. If you read the book, check the Preface to see which chapters you should skip based on your interest.

 

[PeterDonis]

I think you're confusing the relativity principle with the light postulate.

No, I'm not. I'm pointing out that "the relativity principle", as far as physics is concerned, is not one thing. Galilean invariance is not the same thing as Lorentz invariance.

 

[RUTA]

No, I'm not. I'm pointing out that "the relativity principle", as far as physics is concerned, is not one thing. Galilean invariance is not the same thing as Lorentz invariance.

Galilean transformations between inertial reference frames in G4 are time translations, spatial translations, spatial rotations, and Galilean boosts. Poincare transformations between inertial reference frames in M4 are time translations, spatial translations, spatial rotations, and Lorentz boosts. The only difference is in their boosts and that has nothing to do with the relativity principle, that difference is due to the light postulate.

Note that it is the observer-independence of h under spatial rotations (e.g., spin-1/2 and photon polarization qubits) and spatial translations (e.g., double-slit and Mach–Zehnder qubits) that leads to the Hilbert space kinematics for QM.

 

[PeterDonis]

The only difference is in their boosts

But the Lorentz boosts cannot be invariantly separated from the spatial rotations. So it's the entire Lorentz group that's different.

that has nothing to do with the relativity principle, that difference is due to the light postulate.

Sorry, but I disagree. You can't separate out the two things that way. They're inseparably linked.

Note that it is the observer-independence of h under spatial rotations (e.g., spin-1/2 and photon polarization qubits) and spatial translations (e.g., double-slit and Mach–Zehnder qubits) that leads to the Hilbert space kinematics for QM.

And since, as above, spatial rotations can't be invariantly separated from Lorentz boosts, this works differently for the two relativity principles. The only way to limit things as you state them here is to go to the non-relativistic approximation, which is useless if you're talking about foundations.

 

[pines-demon]

Galilean transformations between inertial reference frames in G4 are time translations, spatial translations, spatial rotations, and Galilean boosts. Poincare transformations between inertial reference frames in M4 are time translations, spatial translations, spatial rotations, and Lorentz boosts. The only difference is in their boosts and that has nothing to do with the relativity principle, that difference is due to the light postulate.

Note that it is the observer-independence of h under spatial rotations (e.g., spin-1/2 and photon polarization qubits) and spatial translations (e.g., double-slit and Mach–Zehnder qubits) that leads to the Hilbert space kinematics for QM.

You seems to want to say that something can follow the first postulate of relativity independent if it is a relativistic or a non-relativistic equation. Fine, but no need to claim that what follows Galilean transformation follows Lorentzian ones.

 

[RUTA]

But the Lorentz boosts cannot be invariantly separated from the spatial rotations. So it's the entire Lorentz group that's different.

Lorentz boosts stand alone as a transformation between inertial reference frames in M4. You're conflating group structure with functionality. Spacetime translations are a group. SO(3) is a group. Lorentz boosts with SO(3) form the restricted Lorentz group. These are the subgroups of the Poincare group.

Sorry, but I disagree. You can't separate out the two things that way. They're inseparably linked.

The relativity principle says: The laws of physics are the same in all inertial reference frames. It stands as stated regardless of what transformations you use between inertial reference frames. If that wasn't true, then the relativity principle and light postulate wouldn't both be needed for special relativity. As John Norton wrote, "Maxwell’s theory entails the constancy of the speed of light and that constancy, along with the principle of relativity, entails the relativity of simultaneity." It is the relativity of simultaneity that differentiates G4 and M4.

And since, as above, spatial rotations can't be invariantly separated from Lorentz boosts, this works differently for the two relativity principles. The only way to limit things as you state them here is to go to the non-relativistic approximation, which is useless if you're talking about foundations.

Lorentz boosts need SO(3) to close as a group, but the converse is not true. SO(3) is a subgroup of both the Galilean and Poincare transformations between inertial reference frames. And, again, the relativity principle doesn't say anything about transformations between inertial reference frames. To get those transformations, you need to add an additional postulate.

 

[RUTA]

You seems to want to say that something can follow the first postulate of relativity independent if it is a relativistic or a non-relativistic equation.

That is exactly correct. Here are two more quotes from Norton:

the principle of relativity tells us that we recover a full description of a moving asteroid with its satellite by merely taking the easy case of the asteroid at rest and setting it into uniform motion by means of a Galilean transformation.

While not present by name, the principle of relativity has always been an essential part of Newtonian physics. According to Copernican cosmology, the earth spins on its axis and orbits the sun. Somehow Newtonian physics must answer the ancient objection that such motions should be revealed in ordinary experience if theyare real. Yet, absent astronomical observations, there is no evidence of this motion. All processes on earth proceed just as if the earth were at rest. That lack of evidence, theNewtonian answers, is just what is expected. The earth’s motions are inertial to very good approximation; the curvature of the trajectory of a spot on the earth’s surface issmall, requiring 12 hours to reverse its direction. So, by the conformity of Newtonian mechanics to the principle of relativity, we know that all mechanical processes on the moving earth will proceed just as if the earth were at rest. The principle of relativity is a commonplace of modern life as well. All processes within an airplane cabin, cruising rapidly but inertially, proceed exactly as they would at the hangar. We do not need to adjust our technique in pouring coffee for the speed of the airplane. The coffee is not left behind by the plane’s motion when it is poured from the pot.

 

[PeterDonis]

Lorentz boosts stand alone as a transformation between inertial reference frames in M4

No, they don't. They're not a group in 3+1 spacetime; they're not closed under composition. Only in 1+1 spacetime do Lorentz boosts by themselves form a group.

The relativity principle says

I understand that your version of it says that. I just don't agree with your version. I don't think you can just ignore the fundamental difference between Galilean invariance and Lorentz invariance, or say that it's not part of the relativity principle.

Lorentz boosts need SO(3) to close as a group

Which means your claim that I quoted at the start of this post is false, as I said.

the converse is not true.

Spatial rotations about a specific point in a specific inertial frame are a group, yes. But you have to pick a frame--or, equivalently, you have to pick a particular spacelike hypersurface of constant time for the rotations to operate in. If you change frames in Minkowski spacetime, you change which set of transformations are "spatial rotations", because you change which spacelike hypersurfaces are surfaces of constant time. So I stand by my statement that in Minkowski spacetime you cannot invariantly separate spatial rotations and boosts.

 

[RUTA]

No, they don't. They're not a group in 3+1 spacetime; they're not closed under composition. Only in 1+1 spacetime do Lorentz boosts by themselves form a group.

Now you're conflating transformation with group

I understand that your version of it says that. I just don't agree with your version. I don't think you can just ignore the fundamental difference between Galilean invariance and Lorentz invariance, or say that it's not part of the relativity principle.

It's not "my version," I'm following introductory physics textbooks like Knight above. Here is Serway & Jewett
Physics for Scientists and Engineers with Modern Physics, Cengage, Boston 10th ed., Section 38.3 (2019)

Here is Essential College Physics Vol II, A. Rex and R. Wolfson, Cognella Academic Publishing, USA, 2nd ed., p. 438 (2021)

Here is Sears & Zemansky's University Physics with Modern Physics, H. Young and R. Freedman
Pearson Education, USA, 15th ed., p. 1218 (2020)

Which means your claim that I quoted at the start of this post is false, as I said.

Spatial rotations about a specific point in a specific inertial frame are a group, yes. But you have to pick a frame--or, equivalently, you have to pick a particular spacelike hypersurface of constant time for the rotations to operate in. If you change frames in Minkowski spacetime, you change which set of transformations are "spatial rotations", because you change which spacelike hypersurfaces are surfaces of constant time. So I stand by my statement that in Minkowski spacetime you cannot invariantly separate spatial rotations and boosts.

Ibid

 

[PeterDonis]

Now you're conflating transformation with group

I'm saying that if the transformations don't form a group, IMO it's highly questionable, to say the least, to use them in any kind of foundational argument.

 

[PeterDonis]

It's not "my version,"

It's the version you're using in your foundational argument. The sources you cite aren't making that kind of argument; they're just declaring the principle by fiat, because they're introductory textbooks, not peer-reviewed papers making foundational arguments.

 

[RUTA]

I'm saying that if the transformations don't form a group, it's highly questionable, to say the least, to use them in any kind of foundational argument.

But you do have to add SO(3) to Lorentz boosts to get the Lorentz group. And you can clearly do a boost (generator K) or a spatial rotation (generator J for angular momentum) independently. That's what I'm talking about, independent functionality. So invariance with respect to SO(3) doesn't distinguish between G4 and M4.

 

[RUTA]

It's the version you're using in your foundational argument. The sources you cite aren't making that kind of argument; they're just declaring the principle by fiat, because they're introductory textbooks, not peer-reviewed papers making foundational arguments.

Here are peer-reviewed papers where we have published this idea:

“Answering Mermin’s Challenge with Conservation per No Preferred Reference Frame,” W.M. Stuckey, Michael Silberstein, Timothy McDevitt, and T.D. Le. Scientific Reports 10, 15771 (2020)

“Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s,” Michael Silberstein, W.M. Stuckey, and Timothy McDevitt. Entropy 23(1), 114 (2021).

“‘Mysteries’ of Modern Physics and the Fundamental Constants c, h, and G,” W.M. Stuckey, Timothy McDevitt and Michael Silberstein. Honorable Mention in the Gravity Research Foundation 2021 Awards for Essays on Gravitation, May 2021. Quanta 11(1), 5-14 (2022).

“No Preferred Reference Frame at the Foundation of Quantum Mechanics,” W.M. Stuckey, Timothy McDevitt, and Michael Silberstein. Entropy 24(1), 12 (2022).

“Unifying Special Relativity and Quantum Mechanics via Adynamical Global Constraints,” W.M. Stuckey and Michael Silberstein. Journal of Physics: Conference Series 2948, 012009 (2025).

We had three reviewers for our book "Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit" W.M. Stuckey, Michael Silberstein, and Timothy McDevitt. Oxford University Press, Oxford (2024). Markus Mueller was kind enough to review it for us and it was blurbed by Adlam, Brukner, Bub, and Wharton.

I've presented it to physicists and philosophers at:
2022 American Physical Society March Meeting (online), Foundations 2023 (Bristol), Physics and Reality (Helsinki, June 2024), Q 100: Examining Quantum Foundations 100 Years On (Chapman University, March 2025), Fundamental Problems in Quantum Physics 2025 (Trieste), Quantum Information and Probability: from Foundations to Engineering (Vaxjo, June 2025), at the Institute for Quantum Optics and Quantum Information (Vienna, April 2022), and at University Roma Tre (June 2025).

No referee, reviewer or audience member has disagreed with our use of the relativity principle as stated above. How much more refereed do you need?

 

[PeterDonis]

you do have to add SO(3) to Lorentz boosts to get the Lorentz group.

Yes.

And you can clearly do a boost (generator K) or a spatial rotation (generator J for angular momentum) independently.

Only once you've chosen a specific frame. As I've said, there is no invariant way to separate boosts and rotations. The K and J definitions are frame-dependent.

 

[PeterDonis]

No referee, reviewer or audience member has disagreed with our use of the relativity principle as stated above.

Your use, yes. That was my point. All those other referees, reviewers, and audience members didn't publish those papers and books. You (and your coauthors--but they're not posting here) did.

 

[RUTA]

Your use, yes. That was my point. All those other referees, reviewers, and audience members didn't publish those papers and books. You (and your coauthors--but they're not posting here) did.

And Norton's references and the four intro physics textbooks. It's not idiosyncratic and it has found widespread acceptance. That's my point.

 

[PeterDonis]

It's not idiosyncratic and it has found widespread acceptance.

As a principle declared by fiat. Again, all those other references aren't making the foundational argument that you and your coauthors are. That makes a difference.

 

[RUTA]

As a principle declared by fiat. Again, all those other references aren't making the foundational argument that you and your coauthors are. That makes a difference.

Assuming the relativity principle is fundamental (not derived from something else, but "declared by fiat" as the starting point of a theory) is not unique to us. Again Norton and those four textbook authors all think that about SR and I have other quotes from Rovelli, Mueller and others in the quantum reconstruction program saying they want to follow that for QM (as we did). Here is a quote from Lorentz:

It will be clear by what has been said that the impressions received by the two observers A0 and A would be alike in all respects. It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other, nor for saying that either of them is in possession of the ``true'' times or the ``true'' lengths. This is a point which Einstein has laid particular stress on, in a theory in which he starts from what he calls the principle of relativity, ... .

I cannot speak here of the many highly interesting applications which Einstein\index{Einstein, Albert} has made of this principle. His results concerning electromagnetic and optical phenomena agree in the main with those which we have obtained in the preceding pages, the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle.

 

[PeterDonis]

Assuming the relativity principle is fundamental

That's not the assumption I'm questioning. The assumption I'm questioning is that "the relativity principle" is the same for Galilean and Lorentzian invariance.

A principle that says "The laws of physics must be the same in all inertial reference frames", to me, depends on a definition of "inertial reference frames" that includes how you transform between them. If you don't know which transformation to use between inertial reference frames, you can't test the principle. And that means the principle with two different transformations is not the same principle.

 

[gentzen]

If you change frames in Minkowski spacetime, you change which set of transformations are "spatial rotations", because you change which spacelike hypersurfaces are surfaces of constant time. So I stand by my statement that in Minkowski spacetime you cannot invariantly separate spatial rotations and boosts.

I upvoted this, because I didn't realize it before.
This raised the question for me, what we actually measure in spin measurement, if rotations are not allowed.
In an actual measurement, we can "in principle" rotate the detector (or Stern Gerlach device) around the beam. This is only a 1-parameter group, so 2-parameters are still missing for general "spatial rotation". I think I have seen in the past how to get at least one more parameter, but maybe the details are not important at the moment.

But important for me is that it is not as trivial as simply rotating a detector in 3D space.

 

[RUTA]

That's not the assumption I'm questioning. The assumption I'm questioning is that "the relativity principle" is the same for Galilean and Lorentzian invariance.

A principle that says "The laws of physics must be the same in all inertial reference frames", to me, depends on a definition of "inertial reference frames" that includes how you transform between them. If you don't know which transformation to use between inertial reference frames, you can't test the principle. And that means the principle with two different transformations is not the same principle.

Norton studied the history of Einstein's work on SR (here and here are two websites) and it was difficult because unlike his later work, there isn't much material on Einstein pre-SR. Anyway, what you said is precisely what Einstein struggled with in coming up with SR. It's not the principle of relativity that changed from Newton to SR, but the kinematic assumptions leading to different transformations between inertial reference frames. Indeed he thought Maxwell's equations were incompatible with the relativity principle until he realized it was his tacit kinematic assumptions, not the relativity principle, that were wrong. Here is a quote from Einstein then Norton (from one of those Norton websites linked above):

"The difficulty to be overcome lay in the constancy of the velocity of light in a vacuum, which I first believed had to be given up. Only after years of [jahrelang] groping did I notice that the difficulty lay in the arbitrariness of basic kinematical concepts."

The key to the puzzle is the relativity of simultaneity. If Einstein gives up the absoluteness of simultaneity, then the principle of relativity and the constancy of the speed of light are compatible after all. The price paid for the compatibility is that we must allow that space and time behaves rather differently than Newton told us.

Here is also from Norton https://sites.pitt.edu/~jdnorton/papers/companion.pdf:

Einstein’s special theory of relativity is based on two postulates, stated by Einstein in the opening section of his 1905 paper. The first is the principle of relativity. It just asserts that the laws of physics hold equally in every inertial frame of reference. ...

Einstein’s second postulate, the light postulate, asserts that “light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.” ...

Einstein pointed out immediately that the two postulates were “apparently irreconcilable.” His point was obvious. ...

How could these conflicting considerations be reconciled? Einstein’s solution to this puzzle became the central conceptual innovation of special relativity. Einstein urged that we only think the two postulates are incompatible because of a false assumption we make tacitly about the simultaneity of events separated in space. If one inertially moving observer judges two events, separated in space, to be simultaneous, then we routinely assume that any other observer would agree. That is the false assumption. According to Einstein’s result of the relativity of simultaneity, observers in relative motion do not agree on the simultaneity of events spatially separated in the direction of their relative motion.

See what I'm saying? There aren't two different forms for the relativity principle, but you have to take into account the relationships between inertial reference frames to apply the one form properly. And that requires empirically investigation.

 

[RUTA]

I upvoted this, because I didn't realize it before.
This raised the question for me, what we actually measure in spin measurement, if rotations are not allowed.
In an actual measurement, we can "in principle" rotate the detector (or Stern Gerlach device) around the beam. This is only a 1-parameter group, so 2-parameters are still missing for general "spatial rotation". I think I have seen in the past how to get at least one more parameter, but maybe the details are not important at the moment.

But important for me is that it is not as trivial as simply rotating a detector in 3D space.

That's why you have three Pauli matrices. You can see how the Bell spin states are invariant wrt transformations generated by those matrices and what it means physically in the Methods section of this paper.

 

[PeterDonis]

See what I'm saying?

I see what you're saying. I just don't agree with it. I'll bow out at this point.

 

[Fra]

No, I'm not. I'm pointing out that "the relativity principle", as far as physics is concerned, is not one thing. Galilean invariance is not the same thing as Lorentz invariance.

I can symphatize with RUTA's logic here in that he tries to add several "constraints" he calls principles and see what they imply for the theory.

I always views the first postulated of SR as a special case of what I consider the even more general principle that says that the laws of physics should be the same; as seem by all observers (observer equivalence)

I think this principle is separate and stands on its own, regardless of how the set of all possible "observers" are generated in a particular theory.

The special cases are then because you only consider subclasses of observers. As we know in SR as well as GR, "observer", really means just observers that differ by spacetime transformations. And in SR, we consider inertial frames only.

The postulate that there must exists a max limit to signal propagtion, that all observers agree upon, I definitely see as a separate postulate as well. But of course when ADDING them, it changes the spacetime structure. But as constructing constraints, I see them as separate, I think this is what RUTA suggests and emhpasize as identifying principal constraints is his main focus?

So for me, the principle of observer equivalence is the more genereal version of "relativity principle", which tends to apply only to spacetime frames; but an observer undeniably consists of more than a spacetime index (internal structure). But this is where already things start to reveal itself, as the only reasonable way I ever understood spin1/2 is precisely as an "internal transformation" - not external. So surely they constraints may start to conflict or interfere at some point.

/Fredrik

 

[gentzen]

That's why you have three Pauli matrices. You can see how the Bell spin states are invariant wrt transformations generated by those matrices and what it means physically in the Methods section of this paper.

I read that method section now. Obviously, you didn‘t understand my remark, or what I would like to measure. This makes me wonder whether you actually understood what PeterDonis said.

Let me try to make the connection clear: if the measurement device can only be rotated around the beam, then the direction of the beam can also be used to restrict the allowed movements of the measurement device: It is only allowed to move parallel to the beam. This now allows us to define the 1-parameter group of rotations that has invariant meaning in this scenario, and provides a connection to the Lorentz group.

But the remaining 2-parameters for the full 3-parameter rotation group apparently don‘t have such a nice invariant connection to the Lorentz group.

 

[RUTA]

I can symphatize with RUTA's logic here in that he tries to add several "constraints" he calls principles and see what they imply for the theory.

The postulate that there must exists a max limit to signal propagtion, that all observers agree upon, I definitely see as a separate postulate as well. But of course when ADDING them, it changes the spacetime structure. But as constructing constraints, I see them as separate, I think this is what RUTA suggests and emhpasize as identifying principal constraints is his main focus?

/Fredrik

Sorry, I didn't make the context clear. What we did in the papers and book I referenced above is part of the quantum reconstruction program involving many other researchers beginning in 1996 as part of the "second quantum revolution." Let me share some quotes so you don't get the impression that we are the ones who came up with this idea.

Rovelli 1996:

Quantum mechanics will cease to look puzzling only when we will be able to derive the formalism of the theory from a set of simple physical assertions (‘postulates’, ‘principles’) about the world. Therefore, we should not try to append a reasonable interpretation to the quantum mechanics formalism, but rather to derive the formalism from a set of experimentally motivated postulates. … The reasons for exploring such a strategy are illuminated by an obvious historical precedent: special relativity. ... Special relativity is a well understood physical theory, appropriately credited to Einstein’s 1905 celebrated paper. The formal content of special relativity, however, is coded into the Lorentz transformations, written by Lorentz, not by Einstein, and before 1905. So, what was Einstein’s contribution? It was to understand the physical meaning of the Lorentz transformations.

Zeilinger (1999):

Physics in the 20th century is signified by the invention of the theories of special and general relativity and of quantum theory. Of these, both the special and the general theory of relativity are based on firm foundational principles, while quantum mechanics lacks such a principle to this day. By such a principle, I do not mean an axiomatic formalization of the mathematical foundations of quantum mechanics, but a foundational conceptual principle. In the case of the special theory, it is the Principle of Relativity, ... . In the case of the theory of general relativity, we have the Principle of Equivalence ... . Both foundational principles are very simple and intuitively clear. ... I submit that it is because of the very existence of these fundamental principles and their general acceptance in the physics community that, at present, we do not have a significant debate on the interpretation of the theories of relativity. Indeed, the implications of relativity theory for our basic notions of space and time are broadly accepted.

Fuchs (2016):

Associated with each system [in quantum mechanics] is a complex vector space. Vectors, tensor products, all of these things. Compare that to one of our other great physical theories, special relativity. One could make the statement of it in terms of some very crisp and clear physical principles: The speed of light is constant in all inertial frames, and the laws of physics are the same in all inertial frames. And it struck me that if we couldn’t take the structure of quantum theory and change it from this very overt mathematical speak -- something that didn’t look to have much physical content at all, in a way that anyone could identify with some kind of physical principle -- if we couldn’t turn that into something like this, then the debate would go on forever and ever. And it seemed like a worthwhile exercise to try to reduce the mathematical structure of quantum mechanics to some crisp physical statements.

Hardy (2013):

The standard axioms of QT are rather ad hoc. Where does this structure come from? Can we write down natural axioms, principles, laws, or postulates from which can derive this structure? Compare with the Lorentz transformations and Einstein’s two postulates for special relativity. Or compare with Kepler’s Laws and Newton’s Laws. The standard axioms of quantum theory look rather ad hoc like the Lorentz transformations or Kepler’s laws. Can we find a natural set of postulates for quantum theory that are akin to Einstein’s or Newton’s laws?The real motivation for finding deeper postulates for quantum theory is that it may help us go beyond quantum theory to a theory of quantum gravity (just as Einstein’s work helped him go beyond special relativity to his theory of General Relativity).

Grinbaum (2017):

If, despite Einstein's wish, no constructive theory has materialized as a replacement of special relativity, it is not impossible to imagine that our intuitive desire to `fill the box' with physical systems for the purposes of better explaining physics is as illusory. The device-independent approach might stay as a legitimate way of doing physics, without any need to `fill the box,' much in the same sense as principle-based special relativity has not been surpassed by any constructive theory.

Mueller (website):

Can quantum theory be derived from simple principles, in a similar way as the Lorentz transformations can be derived from the relativity principle and the constancy of the speed of light? The exciting answer is ‘yes!'

Berghofer (2024):

The cornerstones of the quantum reconstruction program (QRP) have been independently formulated by Carlo Rovelli (1996) and Anton Zeilinger (1999). In both works, it is explicitly argued that quantum mechanics needs to be based on a set of simple physical principles. Both suggest concrete information-theoretic principles that could play such a role. And both mention special relativity as a role model in this regard: a physical theory that has counter-intuitive consequences but is widely accepted since it conceptually rests on clear physical principles. ... The success of and booming interest in quantum information theory convinced more and more researchers that the notion of information is crucial for understanding the foundations of quantum mechanics. In the year 2000, Christopher Fuchs and Gilles Brassard co-organized a conference with the programmatic title “Quantum Foundations in the Light of Quantum Information.” Fuchs’ paper of the same name has been highly influential, summarizing the methodology of this project as follows: “to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears to be better calibrated for a direct assault than quantum information theory” (Fuchs 2001).

I could post more such quotes, but hopefully this is enough to show that our work is contributing to a much larger effort.

 

[Fra]

I could post more such quotes, but hopefully this is enough to show that our work is contributing to a much larger effort.

I absolutely got that! But thanks for the nice array ot quotes! I just wrote RUTA's logic to express that I share the distinction of different principles you tried to make.

/Fredrik

 

[selfsimilar]

Here is an open access paper that serves as a 17-page summary.

So in what sense this tells us where the electron was before measurement, among other properties.