What is the mechanism behind Quantum Entanglement?

[RUTA]

Summary: Quantum Entanglement

What is the mechanism behind Quantum Entanglement? Why do only subatomic particles exhibit Quantum Entanglement?

The mechanism is “average-only” conservation and that happens because everyone must measure the same value for Planck’s constant h, regardless of their orientation relative to the source, i.e., rotational invariance of h. It’s totally analogous to why we have time dilation and length contraction. Those happen because everyone must measure the same value for the speed of light c, regardless of their motion relative to the source, i.e., boost invariance of c. See https://www.physicsforums.com/insig...ciple-at-the-foundation-of-quantum-mechanics/

 

[vanhees71]

As always you forget gravity or leave it for last. Given that the spacetime background is required for formulating QFT it is a major conceptual issue. Although admittedly not a point with the most engineering applications.

/Fredrik

Sure, gravity is the big issue, but that has nothing to do with these apparent philosophical issues of QT. In the entire history of science, philosophical ideas helped only to understand the wider implications of the results of the natural sciences in a larger cultural context. Kuhn's paradigm shifts always happened due to discrepancies between scientific observations and the then valid theories. Purely philosophical speculations never helped to find new theories, and paradigm shifts are really rare (on the timescale of centuries!).

 

[vanhees71]

The mechanism is “average-only” conservation and that happens because everyone must measure the same value for Planck’s constant h, regardless of their orientation relative to the source, i.e., rotational invariance of h. It’s totally analogous to why we have time dilation and length contraction. Those happen because everyone must measure the same value for the speed of light c, regardless of their motion relative to the source, i.e., boost invariance of c. See https://www.physicsforums.com/insig...ciple-at-the-foundation-of-quantum-mechanics/

The conservation laws are not only valid "average-only" but event by event. That's a result known since the 1920ies with Bothe's coincidence measurement of the Compton effect. The Bohr-Kramers theory claiming this "average-only-validity of the conservations laws" was very short-lived ;-)).

 

[RUTA]

The conservation laws are not only valid "average-only" but event by event. That's a result known since the 1920ies with Bothe's coincidence measurement of the Compton effect. The Bohr-Kramers theory claiming this "average-only-validity of the conservations laws" was very short-lived ;-)).

What I said is exactly true and very easy to understand. I even present this to my gen ed students. Read the Insight linked, you can reference any of the published papers therein if necessary.

 

[vanhees71]

Where in this long Insight can I find the claim that the conservation laws hold on average only? As I said, this contradicts very early empirical evidence from the early history of modern quantum theory. Prominent other ideas, like the famous Bohr-Kramers theory, have been refuted by these observations and finally modern QT in its usual form has been found.

 

[Fra]

Sure, gravity is the big issue, but that has nothing to do with these apparent philosophical issues of QT.

I figured by now that you think so, but I disagree even though the the link is indeed far fetched seen in the light of the current models.

But as for the general link, there are others that is associating entanglement with potential connections to quantum gravity.
https://arxiv.org/abs/1306.0533

I don't see how the unification of gravity and QM is going to happen in a reasonable way unless one considers and reconstructs some of the foundations of QM.

Purely philosophical speculations never helped to find new theories, and paradigm shifts are really rare (on the timescale of centuries!).

I suspect many creative people keep these speculations private or inside their own heads, and only present the polished results, as it makes the process look cleaner than it really is. Noone wants to read the ugly process of creating a theory that may be wrong. Only once proven right, maybe you can read a little bit about it in biographies or so, but even there I think the ugly turns are omitted, to make it look more sexy.

/Fredrik

 

[gentzen]

The conservation laws are not only valid "average-only" but event by event. That's a result known since the 1920ies ...

What I said is exactly true and very easy to understand. I even present this to my gen ed students. Read the Insight linked, you can reference any of the published papers therein if necessary.

Well, just because you present it to your gen ed students doesn't mean that they understand it any more than the OP of this B-level thread will understand QFT and the "microcausality principle" brought-up by vanhees71:

I have not done any search in any literature. I am not a university student. I am just curious about how it works. I have no understanding of this.

Even worse, just because you believe that it is "very easy to understand" doesn't even mean that it is strictly true in all contexts.

So let us look at your Insights article how it introduces this "average-only" claim, and how it proves and explains it:

And, just as the light postulate of SR leads to time dilation and length contraction in a perfectly symmetrical fashion between different reference frames (aka the relativity of simultaneity), the “Planck postulate” of QM leads to “average-only” projection and conservation of spin angular momentum in a perfectly symmetrical fashion between different reference frames (explained below).

This introduction not only postpones the proof (which is fine), but also doesn't specify what exactly is meant by "average-only". From the POV of the minimal statistical interpretation (vanhees71's preferred interpretation), the natural interpretation of "average-only" would be that there would exists experiments where actual violations of conservation of momentum, or angular momentum, or energy, or ... would actually be observable. Or to put it differently, his "event by event" conservation claim mean that no statistical significant violation of conservation should ever be observable in any properly performed series of experiments. Even so this is quite a strong claim, I am not aware of any experimental evidence against it.

So, how can this be reconsiled with your proof(s)?

However, given that the radiation is actually composed of indivisible photons, there is a non-zero lower limit to the energy passed by a polarizing filter, i.e., each quantum of energy either passes or it doesn’t. Thus, we understand that the classical “expectation” of fractional amounts of quanta can only obtain on average per the quantum reality, so we expect the corresponding quantum theory will be probabilistic.

The assumption that "the radiation is actually composed of indivisible photons" doesn't hold from the perspective of QFT (vanhees71's preferred perspective), but that is less important than that you cannot nail down individual indivisible photons in experiments. So this argument is (most probably) unable to make verifiable preditions about observable violation of conservation in experiments.

Thus, as argued by Brukner & Zeilinger, a theory of qubits must be probabilistic. Of course, the relationship between classical and quantum mechanics per its expectation values (averages) is another textbook result, e.g., the Ehrenfest theorem.

The provable (weak) relationship between classical and quantum mechanics given by the Ehrenfest theorem doesn't mean that there cannot be stronger relationships between classical and quantum mechanics when it comes to conservation laws.

 

[PeterDonis]

What I said is exactly true

No, what you said is a proposal you have made. It is not something that has been experimentally tested and verified. It's not even clear how it could be experimentally tested and verified.

 

[vanhees71]

So let us look at your Insights article how it introduces this "average-only" claim, and how it proves and explains it:

Thanks for doing the hard work, digging out the claim from a long text!

This introduction not only postpones the proof (which is fine), but also doesn't specify what exactly is meant by "average-only". From the POV of the minimal statistical interpretation (vanhees71's preferred interpretation), the natural interpretation of "average-only" would be that there would exists experiments where actual violations of conservation of momentum, or angular momentum, or energy, or ... would actually be observable. Or to put it differently, his "event by event" conservation claim mean that no statistical significant violation of conservation should ever be observable in any properly performed series of experiments. Even so this is quite a strong claim, I am not aware of any experimental evidence against it.

This has nothing to do with interpretation whatsoever, it's simply an experimentally verified fact without any counterexamples observed yet, and it's known even before or just at the time when modern quantum theory has been discovered.

So, how can this be reconsiled with your proof(s)?

The assumption that "the radiation is actually composed of indivisible photons" doesn't hold from the perspective of QFT (vanhees71's preferred perspective), but that is less important than that you cannot nail down individual indivisible photons in experiments. So this argument is (most probably) unable to make verifiable preditions about observable violation of conservation in experiments.

That's not true either. The "indivisibility of photons" is one of the stringent proves for the existence of photons, i.e., the validity of relativistic QFT. The claim by many textbooks that this were the case for leading-order treatments of the photoelectric effect or Compton scattering is not conclusive, because both follows from the quantization for charged particles (electrons in this case) alone keeping the em. field classical.

Of course one must be a bit more precise in this statement, because what's "indivisible" are the energy quanta of radiation of a certain frequency. There are, of course, processes in non-linear optics, where a photon of some frequency is absorbed and two photons with different frequencies (however with energy and momentum conservation valid) are emitted like in the celebrated parametric-down conversion process to prepare entangled photon pairs, enabling proper one-photon sources.

The provable (weak) relationship between classical and quantum mechanics given by the Ehrenfest theorem doesn't mean that there cannot be stronger relationships between classical and quantum mechanics when it comes to conservation laws.

 

[RUTA]

Where in this long Insight can I find the claim that the conservation laws hold on average only? As I said, this contradicts very early empirical evidence from the early history of modern quantum theory. Prominent other ideas, like the famous Bohr-Kramers theory, have been refuted by these observations and finally modern QT in its usual form has been found.

Right after Eq. 4. A longer explanation with pictures is at the ScienceX Dialogue link. That’s the level I show my gen ed students. As long as they can understand projection, they can understand that explanation.

 

[RUTA]

No, what you said is a proposal you have made. It is not something that has been experimentally tested and verified. It's not even clear how it could be experimentally tested and verified.

What I shared are mathematical facts about the formalism of QM. It is not a mere proposal.

 

[vanhees71]

Right after Eq. 4. A longer explanation with pictures is at the ScienceX Dialogue link. That’s the level I show my gen ed students. As long as they can understand projection, they can understand that explanation.

It's really hard to discuss, if you don't give precise quotations. In your Insight Eq. 4 is something about spin. In the paragraph following it there's nothing about energy and momentum conservation.

So precisely where is this bold claim explained? I'm really puzzled that you teach students (whatever "gen ed" means) such speculative ideas which clearly contradict established empirical facts and the currently established physical theories.

 

[RUTA]

Well, just because you present it to your gen ed students doesn't mean that they understand it any more than the OP of this B-level thread will understand QFT and the "microcausality principle" brought-up by vanhees71:

I can only say that many of my gen ed students’ reactions are consistent with them understanding the explanation.

Even worse, just because you believe that it is "very easy to understand" doesn't even mean that it is strictly true in all contexts.

As I pointed out to Peter Donis, what I have presented are mathematical facts about the formalism of QM. So, they are true in the context of QM.

Here is the 2:45-sec video abstract for the paper that also explains the calculation with figures .

If you read the paper or ScienceX Dialogue, you should be able to understand what is meant by “average-only” conservation. It is relational, exactly like time dilation and length contraction, between reference frames. When Alice and Bob make measurements in different reference frames, Alice(Bob) says Bob(Alice) must average his(her) data according to her(his) partition of the data in order to conserve spin angular momentum. All of this follows from the exact conservation of spin angular momentum responsible for the Bell state with its rotational symmetry to begin with. As long as Alice and Bob are making measurements in the same reference frame (same orientation relative to source) their outcomes will be exactly in accord with conservation of spin angular momentum. And, not surprisingly, that can be easily accounted for via local realism. The “weirdness” of entanglement occurs for measurements in different reference frames. That’s where the relative “average-only” conservation holds and that’s what evades explanation via local realism.

If you want to get into the technical nature of the Bell spin states, read this Insight https://www.physicsforums.com/insights/bell-states-and-conservation-of-spin-angular-momentum/ which is an appendix in this paper https://www.nature.com/articles/s41598-020-72817-7

 

[RUTA]

It's really hard to discuss, if you don't give precise quotations. In your Insight Eq. 4 is something about spin. In the paragraph following it there's nothing about energy and momentum conservation.

So precisely where is this bold claim explained? I'm really puzzled that you teach students (whatever "gen ed" means) such speculative ideas which clearly contradict established empirical facts and the currently established physical theories.

Nothing I presented violates established physics. Quite the opposite, it follows exactly according to established textbook QM. Read the papers and it should be readily obvious to someone with your background. “Gen ed students” means “general education students”, i.e., the business, comm, ed, etc. students taking physics. Sorry, that’s a typical term here in U.S. academe, but maybe not where you’re located.

 

[vanhees71]

Ok, so which papers should I read? Is it so difficult to just give the references?

 

[PeterDonis]

What I shared are mathematical facts about the formalism of QM. It is not a mere proposal.

What you said in post #38 is not "mathematical facts about the formalism of QM". It's a proposal you have made for interpreting QM, or, if you like, for a new axiomatic foundation for QM different from all the other extant ones. Please do not misrepresent your own research.

 

[RUTA]

Ok, so which papers should I read? Is it so difficult to just give the references?

It’s linked at the outset of the Insight I linked.

 

[RUTA]

What you said in post #38 is not "mathematical facts about the formalism of QM". It's a proposal you have made for interpreting QM, or, if you like, for a new axiomatic foundation for QM different from all the other extant ones. Please do not misrepresent your own research.

Sorry but you’re mistaken. The words I used map exactly to mathematical facts. Look carefully and you’ll see that I’m not sharing an interpretation. I’m merely pointing out mathematical facts and using standard physics language to label those facts.

 

[DrChinese]

It's really hard to discuss, if you don't give precise quotations.

Without trying to be snarky, good friend: This is something I've said to you about 100 times.

 

[vanhees71]

It’s linked at the outset of the Insight I linked.

Ok, obviously you don't want to give the precise reference.

 

[PeterDonis]

Sorry but you’re mistaken.

You're referencing an Insights article of yours, which in turn references a published paper of yours. That paper is not just "stating mathematical facts". It's a proposal of yours which is still under review by the physics community in general. Referencing that work here is fine, since it's based on published peer-reviewed work. Claiming that it is mainstream QM is not fine, because, no matter how much you might fervently believe that is true, the physics community in general has not come to agreement with you. And that is the standard we use here at PF for whether something is mainstream. The personal opinion of the person who published the research, by itself, is not enough.

 

[vanhees71]

Sigh. Which of the papers quoted in the Insight are we talking about?

 

[physika]

,
.

What is the mechanism behind Quantum Entanglement?

That is wicked!

Not a true entanglement.
The relevant question is, what is the source or origin (mechanism) of quantum correlations.

quantum entanglement is just a kind of Quantum Correlation.

The Advantages of Not Entangling Macroscopic Diamonds at Room Temperature​

https://www.hindawi.com/journals/jamp/2012/469043/

"The recent paper entitled by K. C. Lee et al. (2011) establishes nonlocal macroscopic quantum correlations, which they term “entanglement”, under ambient conditions. Photon(s)-phonon entanglements are established within each interferometer arm. However, our analysis demonstrates, the phonon fields between arms become correlated as a result of single-photon wavepacket path indistinguishability, not true nonlocal entanglement"

"Nonlocal interactions can be from either entanglement or path indistinguishability (the path integral for larger systems), with the latter being further subdivided as discussed. These two distinct phenomenon have recently been treated often in the literature as essentially identical, which is problematic when utilizing them for practical applications"

"the phonon fields between arms become correlated as a result of single-photon wavepacket path indistinguishability, not a true nonlocal entanglement"

Nonlocal Quantum Correlations: Beyond Entanglement​

https://arxiv.org/abs/1209.1081

​

Quantum Correlations beyond Entanglement and Discord​

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.170404

"Dissimilar notions of quantum correlations have been established, each being motivated through particular applications in quantum information science and each competing for being recognized as the most relevant measure of quantumness. In this contribution, we experimentally realize a form of quantum correlation that exists even in the absence of entanglement"

Quantumness beyond entanglement: The case of symmetric states​

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.022433

"Nowadays, it is accepted that truly quantum correlations can exist even in the absence of entanglement. For the case of symmetric states, a physically trivial unitary transformation can alter a state from entangled to separable, and vice versa."

,


.

 

[bhobba]

Regarding ideas as to the 'mechanism' of QM I feel it is important to emphasise that QM is different to other physical theories (and of course, those theories are limiting cases of QM). We do not have direct experience with the subatomic world (ie the QM world) as we do with Newtonian Mechanics. To know about the QM world, we interact with it using what we have direct experience with here in the macroscopic world. We have a mathematical theory about these interactions (ie observations), but as to what is 'really' going on, this makes QM difficult, perhaps nearly impossible, to grasp at that level. I was once really interested in such things, but slowly, over time, I realized it might be something at our current level of knowledge these may not be good questions to ask as they mostly lead down a rabbit hole. Occasionally we get progress, like with Bell, PBR etc, but by and large, it is tough going. I am happy with the idea QM is a phenomenological probabilistic theory about observations. At that level, there is no issue. We know the 'mechanism' of entanglement. It is simply a consequence of the principle of superposition. Suppose we have two systems that can be in state |a> or state |b>. States are simply bookkeeping devices that help us predict the probabilities of observational outcomes. If system 1 is in state |a> and system 2 is in state |b>, that is written as |a>|b>. Conversely if system 1 is in state |b> and system 2 in state |a> it is written as |b>|a>. But the principle of superposition says a possible state is 1/root(2) |a>|b> + 1/root(2) |b>|a>. This is a peculiar state of affairs with no classical analogue. My view is that is the mechanism. But I know opinions on this differ.

Thanks
Bill

 

[RUTA]

You're referencing an Insights article of yours, which in turn references a published paper of yours. That paper is not just "stating mathematical facts". It's a proposal of yours which is still under review by the physics community in general. Referencing that work here is fine, since it's based on published peer-reviewed work. Claiming that it is mainstream QM is not fine, because, no matter how much you might fervently believe that is true, the physics community in general has not come to agreement with you. And that is the standard we use here at PF for whether something is mainstream. The personal opinion of the person who published the research, by itself, is not enough.

The paper:

No Preferred Reference Frame at the Foundation of Quantum Mechanics​

and this earlier one:

Answering Mermin’s challenge with conservation per no preferred reference frame​

do indeed merely state mathematical facts about the Bell spin states that are mainstream QM. "Average-only" conservation is a characterization of relational partitions by different reference frames (related by spatial rotations) of Bell state data per mainstream physics. It's no more a matter of opinion than the relativity of simultaneity, which is a characterization of relational partitions by different reference frames (related by Lorentz boosts) of the events in M4. Here is the Science X Dialogue related to the "Answering Mermin's Challenge" paper:

Einstein's missed opportunity to rid us of 'spooky actions at a distance'​

What makes entanglement mysterious isn't Alice and Bob's measurements of the same spin, those correlations are easy to explain using conservation of spin angular momentum, e.g., Fact 1 about case (a) for the Mermin device. The mystery arises because of the correlations between Alice and Bob's measurements of different spins, e.g., Fact 2 about case (b) for the Mermin device, given their correlations when measuring the same spins. Those correlations satisfy "average-only" conservation in relative fashion. This was shown in 2005 for the singlet state by Unnikrishnan in this paper:

Unnikrishnan, C. Correlation functions, Bell’s inequalities and the fundamental conservation laws. Europhysics Letters 69, 489–495 (2005) (arxiv:quant-ph/0407041).

Unnikrishnan's mistake was to claim this average conservation principle resolves the mystery of entanglement when in fact it is simply another way to characterize the mystery, since it is just a mathematical fact about the Bell spin states. Indeed, you can say that average-only conservation is simply the result of an empirical fact we call spin when spin angular momentum is conserved but measured in different reference frames.

So, there is no opinion or proposal or interpretation going on here when I say the mystery ("mechanism" in the OP) of entanglement is characterized by "average-only" conservation.

 

[RUTA]

Sigh. Which of the papers quoted in the Insight are we talking about?

See my Post #62. You can add this one as well:

Stuckey, W.; Silberstein, M.; McDevitt, T.; Kohler, I. Why the Tsirelson Bound? Bub’s Question and Fuchs’ Desideratum. Entropy 2019, 21, 692 https://www.mdpi.com/1099-4300/21/7/692

 

[RUTA]

We know the 'mechanism' of entanglement. It is simply a consequence of the principle of superposition. Suppose we have two systems that can be in state |a> or state |b>. States are simply bookkeeping devices that help us predict the probabilities of observational outcomes. If system 1 is in state |a> and system 2 is in state |b>, that is written as |a>|b>. Conversely if system 1 is in state |b> and system 2 in state |a> it is written as |b>|a>. But the principle of superposition says a possible state is 1/root(2) |a>|b> + 1/root(2) |b>|a>. This is a peculiar state of affairs with no classical analogue. My view is that is the mechanism. But I know opinions on this differ.

Thanks
Bill

In the axiomatic reconstructions of QM, this is called Information Invariance & Continuity. It is indeed equivalent to the mechanism of "average-only" conservation, as detailed in the first paper linked in my Post #62.

 

[vanhees71]

What makes entanglement mysterious isn't Alice and Bob's measurements of the same spin, those correlations are easy to explain using conservation of spin angular momentum, e.g., Fact 1 about case (a) for the Mermin device. The mystery arises because of the correlations between Alice and Bob's measurements of different spins, e.g., Fact 2 about case (b) for the Mermin device, given their correlations when measuring the same spins. Those correlations satisfy "average-only" conservation in relative fashion. This was shown in 2005 for the singlet state by Unnikrishnan in this paper:

I think we had this discussion a while ago. In fact in the here described EPR-paradox version with angular momentum (spin) a la Bohm, it's easy to see that of course the conservation laws hold event by event. To prove this, of course, you have to measure the angular-momentum component in the same direction on both particles, because you can only determine one momentum component due to the commutator relations of angular-momentum components. The $J=0$ state of the total system is an exception, because for this state all three components take simultaneously the same value, 0.

If you measure different components of the angular momentum on both particles, of course you cannot verifty angular-momentum conservation, because the outcomes of the measurements are random with a probabilities for the possible outcome for the two angular-momentum components given by Born's rule. This also includes, of course, the violations of Bell's inequality, which cannot be described with local deterministic hidden-variable theories. This has, however, nothing to do with the claim that the conservation laws only hold "on average".

I'll try to read the papers, as soon as I find the time.

 

[gentzen]

I can only say that many of my gen ed students’ reactions are consistent with them understanding the explanation.

Thanks for answering me. Maybe I was a bit snarky (as DrChinese puts it) towards you and vanhees71. But if I would have tried to explain in a B-level thread how the (dagger) compact closed category structure typical of the QM of small systems leads to a nicer duality between observation and action compared to classical mechanics, I probably would have gotten quite some flak.

What I said is exactly true and very easy to understand.

The more interesting question for me is how easy it will be to discuss details of "interpretation" and "language" of your proposal with you.

Your claim that "the mechanism is average-only conservation" at first seems to contradict my experience that assuming "event-by-event conservation" typically is the right thing to do for theoretical computations or Monte-Carlo simulations of atomic phenomena. This raises the question of what you mean exactly by your claim. In "Answering Mermin’s challenge with conservation per no preferred reference frame" I found:

In short, the explicit conservation that obtains for Alice and Bob’s Stern-Gerlach spin measurement outcomes in the same reference frame holds only on average in different reference frames, not on a trial-by-trial basis.

So you even mention that explicit conservation will be observed if the measurement is done in a way that this outcome is even possible to begin with. Therefore your "trial-by-trial" means something different from my "event-by-event". But then we are back to a sort of measurement problem, how non-conservation in a "trial including preparation and measurement" should be possible, if no single physical process by itself violates conservation.

I have a bit the impression that your "non-conservation in a single trial" arises from a sort of Copenhagen like collapse interpretation of single trials. Therefore, Heisenberg's defense that collapse arises from a sort of boundary condition for open system might help to bring some more clarity: We are looking here at experiments whose boundary conditions are incompatible with the symmetries corresponding to exact conservation. So the boundary conditions have broken a symmetry. This makes sense, because a Stern-Gerlach magnet does its magic in a certain sense by suitably breaking a symmetry.

Of course, you probably won't be happy with this reinterpretation of your nice "reference frames" as "boundary conditions that break symmetries in various ways". But it allows to ask a related question: will "conservation trial-by-trial" always hold, when the "implicit boundary conditions" would in principle allow it? (One problem here is that the idealized implicit boundary conditions are not identical to the boundary conditions realized in an actual experiment.)

That is, “there is no mention in relativity of exactly how clocks slow, or why meter sticks shrink” (no “constructive efforts”), nonetheless the principles of special relativity are so compelling that “physicists always seem so sure about the particular theory of Special Relativity, when so many others have been superseded in the meantime

I thought the mechanism would be "relativity of simultaneity," together with a definition of how to measure lengths based on measuring times (for why meter sticks shrink). However, there is also a second component, why it can be an advantage that the universe does not need a global perfectly synchronized clock. If you do parallel computation, the requirement to always be in perfect sync would slow you down badly.

So even for QM, if the principle explanation is to be perfectly similar to the principle explanation of SR, then I would also expect a similar explanation of the advantages of violating the classical principles.

 

[bhobba]

In the axiomatic reconstructions of QM, this is called Information Invariance & Continuity. It is indeed equivalent to the mechanism of "average-only" conservation, as detailed in the first paper linked in my Post #62.

I know a bit about those reconstructions, and I think you may be correct. But would like to see what others say on the issue. I also like the video you posted. I know the five reasonable axioms paper well but have not kept up with developments beyond that. Since reading that paper years ago, I have always thought of QM as a generalised probability theory - the simplest after ordinary probability theory that allows 'continuity' as you put it and hence the methods of calculus. It reaches its full flowering when generalised to Rigged Hilbert Spaces, which I also have noticed books are now pointing out is the real QM space - not Hilbert Spaces (although Von Neumann did show how it could be formulated using just Hilbert Spaces).

Thanks
Bill

 

[bhobba]

I thought the mechanism would be "relativity of simultaneity," together with a definition of how to measure lengths based on measuring times (for why meter sticks shrink).

I think in modern times, the foundations of Special Relativity are well known to be the symmetries of an inertial reference frame and the POR. C is simply a constant that appears in the theory that needs to be fixed by experiment. From both theoretical and experimental considerations, it is the speed of light but is not an axiom at its foundations. See a paper I post a lot:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Thanks
Bill

 

[RUTA]

I think we had this discussion a while ago. In fact in the here described EPR-paradox version with angular momentum (spin) a la Bohm, it's easy to see that of course the conservation laws hold event by event. To prove this, of course, you have to measure the angular-momentum component in the same direction on both particles, because you can only determine one momentum component due to the commutator relations of angular-momentum components. The $J=0$ state of the total system is an exception, because for this state all three components take simultaneously the same value, 0.

If you measure different components of the angular momentum on both particles, of course you cannot verifty angular-momentum conservation, because the outcomes of the measurements are random with a probabilities for the possible outcome for the two angular-momentum components given by Born's rule. This also includes, of course, the violations of Bell's inequality, which cannot be described with local deterministic hidden-variable theories. This has, however, nothing to do with the claim that the conservation laws only hold "on average".

I'll try to read the papers, as soon as I find the time.

Now that would be, as Peter Donis said, an interpretation of the mainstream view of Bell state data.

The mainstream view of the data is that when Alice and Bob measure a Bell state (say, a triplet state in the symmetry plane) at some particular SG magnet orientation, then both will always get the same result, half the time they will both get +1 and half the time they will both get -1. If Bob changes his SG magnet orientation making an angle $\theta$ with Alice's orientation, then they will observe "average-only" conservation. By that I mean that if Alice partitions the data according to her equivalence relation (her +1 and -1 results), she will see that Bob's results average to $\pm \cos{\theta}$, respectively. If Bob partitions that same data according to his equivalence relation, he will see that Alice's results average to $\pm \cos{\theta}$. I'm using the phrase "average-only" conservation per standard physics lingo to characterize this mainstream view of Bell state data as follows.

Alice can say that if Bob had not changed his SG magnet orientation, he would have measured +1 when she measured +1, as required to conserve spin angular momentum. So, when he measured at angle $\theta$ with respect to her, he should have gotten the projection of his +1 result, i.e., $\cos{\theta}$ (analogously with their -1 result). So, his results are only satisfying the conservation of spin angular momentum on average according to her partition of the data. Indeed, his results are not a Gaussian about $\cos{\theta}$, but they give a binary distribution whereby he never measures $\cos{\theta}$ (thus, "average-only" conservation). Of course, Bob can say the same thing about Alice's results per his partition of the data.

This is totally analogous to their partitions of M4 when they occupy different reference frames related by Lorentz boosts, i.e., uniform relative motion. There Bob can partition the events of M4 per his equivalence relation (his surfaces of simultaneity) and say that Alice's meter sticks are short and her clocks run slow. And, of course, Alice can partition the events of M4 per her equivalence relation (her surfaces of simultaneity) and say that Bob's meter sticks are short and his clocks run slow. This is called the relativity of simultaneity and was a key concept in Einstein's development of special relativity (according to John Norton, anyway).

You can make the analogy stronger by noting that the different SG orientations are related by spatial rotations and spatial rotations relate inertial reference frames in both Galilean and Lorentz transformations. So, you could characterize the relativity of simultaneity and "average-only" conservation as consequences of the relativity principle (as Einstein did for the former), i.e., "no preferred reference frame." But, that would be a proposal, as Peter Donis said, because these facts could also hold where there is a preferred reference frame. Indeed, Unnikrishnan is a strong advocate for a preferred reference frame, that's why he does not support our proposal to invoke NPRF to explain his average conservation. He believes average conservation is enough to resolve the mystery of entanglement and a universal preferred reference frame resolves other mysteries for him.

Sorry for the confusion. Despite the fact that I've been teaching college physics for over 40 years, I'm not a very good teacher as it turns out :-(

 

[RUTA]

I think in modern times, the foundations of Special Relativity are well known to be the symmetries of an inertial reference frame and the POR. C is simply a constant that appears in the theory that needs to be fixed by experiment. From both theoretical and experimental considerations, it is the speed of light but is not an axiom at its foundations. See a paper I post a lot:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Thanks
Bill

Here is an interesting paper by John Norton (I mentioned this in my Post #69, but did not reference it) "Einsteinʼs Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies that Led him to it." On p. 6 at the outset of Section 2.2 "Relativity of simultaneity" he writes:

Einstein pointed out immediately that the two postulates were “apparently irreconcilable.” His point was obvious. If one inertially moving observer measures c for the speed of some light beam, what must be measured by another inertially moving observer who chases after the light beam at high speed—say 50% of c or even 99% of c? That second observer must surely measure the light beam slowed. But if the light postulate respects the principle of relativity, then the light postulate must also hold for this second, inertially moving observer, who must still measure the same speed, c for the light beam.

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.

The mystery of entanglement (understood via spin measurements, anyway) follows from the structure of an elementary piece of quantum information, i.e., the quantum bit or qubit. Contrary to the classical bit, it is possible to change the SG magnet orientations in continuous fashion and still get your binary $\pm 1$ outcomes for a qubit. A classical bit has discrete choices of measurement, e.g., open box A or box B, to go along with its discrete binary outcomes, e.g., a ball is in the box or not. Your classical intuition applied to spin would be to expect fractions of $\pm 1$ as you rotate your SG magnets, e.g., $\pm \cos{\theta}$. But, you don't, you always get $\pm 1$ for all $\theta$. That's what Hardy discovered in what is considered to be the first axiomatic reconstruction of QM based on information-theoretic principles,

Quantum Theory From Five Reasonable Axioms​

He writes, "If Axiom 5 (or even just the word "continuous" from Axiom 5) is dropped then we obtain classical probability theory instead." Here is what Koberinski and Mueller had to say about it in "Quantum Theory as a Principle Theory: Insights from an Information-Theoretic Reconstruction":

We suggest that (continuous) reversibility may be the postulate which comes closest to being a candidate for a glimpse on the genuinely physical kernel of ``quantum reality''. Even though Fuchs may want to set a higher threshold for a ``glimpse of quantum reality'', this postulate is quite surprising from the point of view of classical physics: when we have a discrete system that can be in a finite number of perfectly distinguishable alternatives, then one would classically expect that reversible evolution must be discrete too. For example, a single bit can only ever be flipped, which is a discrete indivisible operation. Not so in quantum theory: the state |0> of a qubit can be continuously-reversibly ``moved over'' to the state |1>. For people without knowledge of quantum theory (but of classical information theory), this may appear as surprising or ``paradoxical'' as Einstein's light postulate sounds to people without knowledge of relativity.

But, while you always get $\pm 1$ instead of $\pm \cos{\theta}$ per your classical intuition for the spin qubit, the $\pm 1$ do average to $\pm \cos{\theta}$ when, say, you're making measurements at $\theta$ with respect to the z axis on the spin up/down z state. As Weinberg said in "The Trouble with Quantum Mechanics", measuring an electron's spin via SG magnets constitutes the measurement of "a universal constant of Nature, Planck's constant h." So, demanding all SG orientations (inertial reference frames related by spatial rotations) must measure the same value of h, just like the light postulate, we can use "average-only" projection (and normalization) for the qubit to obtain the probabilities $P(+1|\theta) = \cos^2{\left(\frac{\theta}{2}\right)}$ and $P(-1|\theta) = \sin^2{\left(\frac{\theta}{2}\right)}$, which gives "average-only" conservation for qubits entangled in a Bell state.

So, there are a lot of analogies with SR if you consider the relativity principle and light postulate, but this is a proposal, not a statement of mathematical facts alone :-)

 

[PeroK]

Certainly a nice paper, but my goal was for RUTA to acknowledge that "relativity of simultaneity" is indeed a concrete mechanism in case of SR, actually explaining why meter sticks shrink.

Alternatively, "simultaneity" is not a concept that has any physical significance. And metre sticks "shrink" when they are rotated in spacetime.

 

[gentzen]

Alternatively, "simultaneity" is not a concept that has any physical significance. And metre sticks "shrink" when they are rotated in spacetime.

Sorry, I deleted my answer for the moment, to have a bit more time for editing, and better understanding how the papers relate to that answer to vanhees71. For example, table 3 in "Answering Mermin’s challenge with conservation per no preferred reference frame" (the paper which triggered my comment) reads:

Empirical Fact: Alice and Bob both measure c,	Empirical Fact: Alice and Bob both measure $\pm 1(\frac{\hbar}{2})$,
regardless of their motion relative to the source	regardless of their SG orientation relative to the source
Alice(Bob) says of Bob(Alice): Must correct time and length measurements	Alice(Bob) says of Bob(Alice): Must average results
NPRF: Relativity of simultaneity	NPRF: Relativity of data partition

So the totally analogous thing for "relativity of simultaneity" was not "average-only conservation" (which provoked the reactions by vanhees71 and me), but instead "relativity of data partition". And this "relativity of data partition" is indeed quite a quantum thing, where often the quantum mysteries arise via post-selection.