Insights Why the Quantum | A Response to Wheeler's 1986 Paper - Comments

[vanhees71]

Then you believe Unnikrishnan's result is a mere coincidence? That's a pretty amazing coincidence, but you are free to believe that!

No, he simply has proven that theories obeying the "realism postulate of EPR" and Bell's inequalities are not compatible with precise angular-momentum conservation, as is predicted by QT. As far as I know, so far nobody has ever found the fundamental conservation laws violated in any quantum experiment. So I choose to use QT describing the empirical facts rather than using a theory obeying a strange notion of "realism" a la EPR, which is disproven by the Bell experiments with overwhelming significance.

 

[stevendaryl]

Fine, I've no problems with that. It only doesn't mean that angular momentum isn't conserved exactly on an "event-by-event basis". It was a very old error by Kramers and Bohr to assume that the conservation laws only hold on average. It was ingeniouly disproven by Walther Bothe with his coincidence measurement method (here applied to Compton scattering). He got the Nobel prize for this method.

But in the case where you measure spins along different axes, it's not possible for the vectorial sum of the two measured angular momenta to be zero exactly.

 

[RUTA]

Both you and Unnikrishnan show that the correlation functions for QM and the conservation laws, P(a.b,)_QM = P(a,b,)_C = - a.b. = - cosθ.
How is superposition of entangled spin 1/2 particles 1/2 (|ud} - |du}) and photons 1/2 (|H}₁ |V}₂ ± |V}₁H}₂)
in accord with conservation laws in the context of the question by @ftr above in post #345 ?

Sorry, I haven't been able to keep up with the discussion lately. If I understand your question correctly (and that in #345), the QM conservation at work here is different than in classical mechanics (CM). I tried to explain in the Insight and in other posts here, so I won't repeat all that. The major difference is that in CM there is a "true" value for the angular momentum $\vec{L}$ for each of the two particles and Alice and Bob measure some component (and therefore fraction) of $\vec{L}$ for their respective particles. In QM what Alice and Bob measure is always +1 or -1, no fractions. That means they have conservation of angular momentum only on average (unless they choose to measure along the same direction in which case they get exact cancelation). Of course, as pointed out by ftr, that leaves a mystery for the person who wants to know what makes the particles behave properly on a trial-by-trial basis, i.e., there is no hidden variable or 'causal mechanism' to account for conservation on average. So, this conservation principle leaves a mystery for those who demand dynamical explanation. That's the point of the Insight. Are you happy with the 4D constraint (conservation on average) as the fundamental explanation? Or, do you demand a dynamical/causal explanation? As with the many examples in my blockworld series, dynamical thinking creates a mystery that is resolved by blockworld constraint-based thinking.

 

[RUTA]

No, he simply has proven that theories obeying the "realism postulate of EPR" and Bell's inequalities are not compatible with precise angular-momentum conservation, as is predicted by QT. As far as I know, so far nobody has ever found the fundamental conservation laws violated in any quantum experiment. So I choose to use QT describing the empirical facts rather than using a theory obeying a strange notion of "realism" a la EPR, which is disproven by the Bell experiments with overwhelming significance.

So, it sounds like you're happy to accept the 4D constraint (conservation on average) as a sufficient explanation of Bell-inequality-violating QM correlations. No need to look for hidden variables or 'causal mechanisms'. In that case, we're in agreement.

 

[vanhees71]

But in the case where you measure spins along different axes, it's not possible for the vectorial sum of the two measured angular momenta to be zero exactly.

Of course, but here the minimal interpretation again solves this apparent quibble. The state with its probabilistic meaning refers to an ensemble. To empirically check, whether angular momentum is conserved, you prepare an ensemble and for each member you measure the spin components of both particles in the same direction. Then you'll find with 100% probability (i.e., for each event) a sum of 0, i.e., angular momentum in this direction is conserved. You can repeat the measurement as often as you like in an arbitrary direction.

Of course, the quantum state implies more statistical properties than that, namely the correlations for measurements of spin components of the two particles in different directions, among them choices, where Bell's inequality is predicted (and empirically found with high significance for e.g., polarization-entangled photon pairs) to be violated, disproving the possibility of local deterministic hidden-variable models.

 

[vanhees71]

So, it sounds like you're happy to accept the 4D constraint (conservation on average) as a sufficient explanation of Bell-inequality-violating QM correlations. No need to look for hidden variables or 'causal mechanisms'. In that case, we're in agreement.

What is the "4D constraint"? As I already said, in this case angular momentum is, according to standard QT, not only on average conserved but strictly for each individual particle pair!

There's no need for new theories if the old ones perfectly work fine. Since QT is causal, as any physical theory must be, there's also no argument against QT from this corner. Many people find QT unsatisfactory, because it's not deterministic. Well, physics is not there to please people's opinions about how Nature should work but it tries to figure out as accurately as one can how Nature in fact works.

Whether there is a deterministic HV theory consistent with all knows facts, I don't know. If there is one, it will be as puzzling as QT since it's for sure non-local, as is shown by the violation of Bell's inequality, and a non-local theory that's consistent with the relativistic space-time structure, will be very mind-boggling. Maybe it's not even possible to construct such a model, but this one cannot rule out yet.

 

[stevendaryl]

Of course, but here the minimal interpretation again solves this apparent quibble. The state with its probabilistic meaning refers to an ensemble. To empirically check, whether angular momentum is conserved, you prepare an ensemble and for each member you measure the spin components of both particles in the same direction. Then you'll find with 100% probability (i.e., for each event) a sum of 0, i.e., angular momentum in this direction is conserved. You can repeat the measurement as often as you like in an arbitrary direction.

That doesn't address the issue of what statistics you get when you measure one particle of a twin pair along one axis and you measure the other particle along a different axis.

Of course, the quantum state implies more statistical properties than that, namely the correlations for measurements of spin components of the two particles in different directions, among them choices, where Bell's inequality is predicted (and empirically found with high significance for e.g., polarization-entangled photon pairs) to be violated, disproving the possibility of local deterministic hidden-variable models.

The point of the Insights article was to try to derive the statistics for measurements in arbitrary directions without assuming the Born rule, and without assuming the mathematics of spin states.

 

[stevendaryl]

Many people find QT unsatisfactory, because it's not deterministic.

That might have been the reason for Einstein, but that is not an accurate explanation for why everyone finds QT to be unsatisfactory. I would say that the measurement problem is the reason most people find the minimal interpretation of QT unsatisfactory.

 

[Lord Jestocost]

That might have been the reason for Einstein, but...

To my mind, Einstein didn't want to accept that "quantum probabilities" are - so to speak - irreducible. In his book “Quantum Reality - Beyond the New Physics” Nick Herbert drops the term “quantum ignorance”:

“Once you get down to the quantum randomness level, no further explanation is possible. You can’t go any deeper because physics stops here. Albert Einstein, no fan of the orthodox ontology, objected to this fundamental lawlessness at the heart of nature when he said that he could not believe that God would play dice with the universe. This new kind of ultimate indeterminism may be called quantum ignorance: we don’t know why an electron strikes a particular phosphor because there’s nothing there to know about. When the dice fall from the cup, on the other hand, their unpredictable outcome is caused by classical ignorance — by our unavoidably partial knowledge of their real situation.”

 

[RUTA]

What is the "4D constraint"? As I already said, in this case angular momentum is, according to standard QT, not only on average conserved but strictly for each individual particle pair!

There's no need for new theories if the old ones perfectly work fine. Since QT is causal, as any physical theory must be, there's also no argument against QT from this corner. Many people find QT unsatisfactory, because it's not deterministic. Well, physics is not there to please people's opinions about how Nature should work but it tries to figure out as accurately as one can how Nature in fact works.

Whether there is a deterministic HV theory consistent with all knows facts, I don't know. If there is one, it will be as puzzling as QT since it's for sure non-local, as is shown by the violation of Bell's inequality, and a non-local theory that's consistent with the relativistic space-time structure, will be very mind-boggling. Maybe it's not even possible to construct such a model, but this one cannot rule out yet.

As we've all been telling you, the only way to get conservation when the measurements are different is on average. That means the conservation principle applies not only between spatially separated outcomes but also between temporally separated pairs of outcomes, i.e., 4D. Hidden variables and 'causal mechanisms' are not required, QM is simply describing the spatiotemporal (4D) pattern of outcomes per conservation of angular momentum.

 

[vanhees71]

And I told you that this is not the right interpretation of conservation of a vector-like quantity. It means that the three components of this quantity are conserved, and this is indeed the case for the spin-singlet two-particle state discussed. It doesn't make sense to measure the spin component of one of the particles and another spin component of the other when you talk about conservation of angular momentum (on an event-by-event basis or (only) on average).

It was a historically very important finding by Bothe et al that the conservation laws hold on an event-by-event basis (in this historic case it was verified for Compton scattering using the coincidence method, for which Bothe received a Nobel prize for very good reasons).

What do you mean by "spatiotemporal pattern of outcomes per conservation of angular momentum". What's done to verify angular-momentum conservation is just what I said previously: You measure the components of the angular momentum for both particles always in the same direction, and given the preparation in the angular-momentum-zero state (in the center-momentum frame that's indeed the spin-zero state) of the pair, these components are precisely back to back, i.e., adding to 0, and this is what is usually defined as conservation of angular momentum.

Already in classical physics it doesn't make sense to measure the components of a conserved quantitiy in different directions for subsystems and then claime the total vector is not conserved, because these components don't add up to the initial total vector quantity. It doesn't even make geometrical nor physical sense to add vector components in different directions.

 

[RUTA]

And I told you that this is not the right interpretation of conservation of a vector-like quantity. It means that the three components of this quantity are conserved, and this is indeed the case for the spin-singlet two-particle state discussed. It doesn't make sense to measure the spin component of one of the particles and another spin component of the other when you talk about conservation of angular momentum (on an event-by-event basis or (only) on average).

It was a historically very important finding by Bothe et al that the conservation laws hold on an event-by-event basis (in this historic case it was verified for Compton scattering using the coincidence method, for which Bothe received a Nobel prize for very good reasons).

What do you mean by "spatiotemporal pattern of outcomes per conservation of angular momentum". What's done to verify angular-momentum conservation is just what I said previously: You measure the components of the angular momentum for both particles always in the same direction, and given the preparation in the angular-momentum-zero state (in the center-momentum frame that's indeed the spin-zero state) of the pair, these components are precisely back to back, i.e., adding to 0, and this is what is usually defined as conservation of angular momentum.

Already in classical physics it doesn't make sense to measure the components of a conserved quantitiy in different directions for subsystems and then claime the total vector is not conserved, because these components don't add up to the initial total vector quantity. It doesn't even make geometrical nor physical sense to add vector components in different directions.

Again, either the result is correct (i.e., conservation as explained in the Insight and published by Unnikrishnan) or it is just an amazing coincidence. You seem to be waffling between those two positions.

 

[vanhees71]

I read the first part of your Insights article again, i.e., the part which discusses QT, and I don't see any contradiction between what you state there with standard quantum theory, and it is precisely the statement I made in #361 concerning event-by-event conservation of angular momentum for the spin-singlet state (of course for what you call "Mermin photon state" the arguments are analogous). Of course, precise event-by-event angular-momentum conservation in the there explained sense (i.e., in both my postings and also in your Insight in the paragraph directly after the figure showing the SG experiment) holds both within QT and in all experiments done so far at high accuracy and significance. That's all I wanted to say about it.

What I don't understand is, what precisely do you consider a puzzle or "an amazing coincidence".

 

[RUTA]

I read the first part of your Insights article again, i.e., the part which discusses QT, and I don't see any contradiction between what you state there with standard quantum theory, and it is precisely the statement I made in #361 concerning event-by-event conservation of angular momentum for the spin-singlet state (of course for what you call "Mermin photon state" the arguments are analogous). Of course, precise event-by-event angular-momentum conservation in the there explained sense (i.e., in both my postings and also in your Insight in the paragraph directly after the figure showing the SG experiment) holds both within QT and in all experiments done so far at high accuracy and significance. That's all I wanted to say about it.

What I don't understand is, what precisely do you consider a puzzle or "an amazing coincidence".

You keep ignoring the situation when Alice and Bob do different measurements, the co-aligned case is trivial. The significance of the result is how conservation obtains for different measurements, as Unnikrishnan showed and I explain in the Insight. That such average, frame-independent conservation yields exactly the QM correlation is either expressing a deep fact of Nature or it is just an amazing coincidence.

 

[vanhees71]

But you explain yourself correctly what happens for measurements in different directions. However, what's puzzling with that? It's a pretty simple calculation, and that there are correlations, even those violating Bell's inequality and other correlation measures contradicting the assumption of deterministic local models, is the very point of doing such "Bell-test experiments". This expresses a deep fact of Nature, but it doesn't imply that angular-momentum conservation is valid only on average. In fact in this case it's precisely valid on an event-by-event basis. This is the very point of the connection between conservation laws and entanglement. You yourself explain this in the first part of your Insights article!

 

[RUTA]

But you explain yourself correctly what happens for measurements in different directions. However, what's puzzling with that? It's a pretty simple calculation, and that there are correlations, even those violating Bell's inequality and other correlation measures contradicting the assumption of deterministic local models, is the very point of doing such "Bell-test experiments". This expresses a deep fact of Nature, but it doesn't imply that angular-momentum conservation is valid only on average. In fact in this case it's precisely valid on an event-by-event basis. This is the very point of the connection between conservation laws and entanglement. You yourself explain this in the first part of your Insights article!

When the measurements are not co-aligned, there is no way to get strict conservation for any given trial, it can only obtain on average. The assumption of conservation of this type is independent of QM (as Unnikrishnan explains), so it could just be a coincidence that it yields the QM correlations.

 

[vanhees71]

Sigh. I seem not to be able to make this obvious point. It doesn't make sense to measure the components of the single-particle spins in different directions and then claim that you don't have strict conservation of angular momentum. The algebra of vectors implies that adding vectors is component by component and not components of different directions. Even in classical physics although the total angular momentum of two particles is 0, in general $J_{1x}+J_{1y} \neq 0$. So this has nothing to do with quantum mechanics but it's simply a statement about angular-momentum conservation which doesn't make any sense!

 

[RUTA]

Sigh. I seem not to be able to make this obvious point. It doesn't make sense to measure the components of the single-particle spins in different directions and then claim that you don't have strict conservation of angular momentum. The algebra of vectors implies that adding vectors is component by component and not components of different directions. Even in classical physics although the total angular momentum of two particles is 0, in general $J_{1x}+J_{1y} \neq 0$. So this has nothing to do with quantum mechanics but it's simply a statement about angular-momentum conservation which doesn't make any sense!

You’re absolutely correct when you say that this type of conservation isn’t necessarily related to QM. That’s why it has to be postulated as the basis for QM correlations. That’s why I asked if you thought it was just an amazing coincidence that it reproduces the QM correlations. So, one last time, which do you believe?

 

[vanhees71]

Nothing nonsensical like that has to be postulated "as the basis for QM correlations". Everything is within the well-established formalism of standard QT. I still seem not to get what's "the hype" about whichever "amazing coincidence". All you need to understand the measured "QM correlations" is standard QT, where entanglement is common. In the 21st century entanglement shouldn't be puzzling to anybody anymore since it's a well-established empirical fact to describe the corresponding correlations right.

 

[RUTA]

Nothing nonsensical like that has to be postulated "as the basis for QM correlations". Everything is within the well-established formalism of standard QT. I still seem not to get what's "the hype" about whichever "amazing coincidence". All you need to understand the measured "QM correlations" is standard QT, where entanglement is common. In the 21st century entanglement shouldn't be puzzling to anybody anymore since it's a well-established empirical fact to describe the corresponding correlations right.

So, if that conservation principle is "nonsensical," then the fact that it reproduces the QM correlations is just an amazing coincidence.

 

[RUTA]

Nothing nonsensical like that has to be postulated "as the basis for QM correlations". Everything is within the well-established formalism of standard QT. I still seem not to get what's "the hype" about whichever "amazing coincidence". All you need to understand the measured "QM correlations" is standard QT, where entanglement is common. In the 21st century entanglement shouldn't be puzzling to anybody anymore since it's a well-established empirical fact to describe the corresponding correlations right.

This paper https://arxiv.org/pdf/1703.11003.pdf might help you accept the proposed conservation principle as reasonable. He doesn't invoke the conservation principle at all, but he sets it up using single-particle measurements. In fact, he could avoid his conclusion

the exhortation that “correlations cry out for explanation” is one that was learned in the context of a different kind of (classical) physical thinking and therefore not appropriate in a discussion of quantum entanglement.

if he would take his reasoning one step further as Unnikrishnan did.

 

[RUTA]

I used Unnikrishnan's conservation principle to explain the Mermin device in this paper. It's written at the level of Am. J. Phys. (where it's under review), so you should be able to follow it if you've had an introductory course in physics.

 

[vanhees71]

I'll try to read your preprint, but still it is clear that angular-momentum conservation holds exactly and it's the very reason for the spin entanglement in this setup used to perform the Bell experiment. It's not only conserved on average!

 

[RUTA]

I'll try to read your preprint, but still it is clear that angular-momentum conservation holds exactly and it's the very reason for the spin entanglement in this setup used to perform the Bell experiment. It's not only conserved on average!

Does whatever form of conservation you're referring too for different settings reproduce the quantum correlation function without using QM? That's what Unnikrishnan's conservation principle does.

 

[vanhees71]

Of course QM produces the quantum correlation function. How else should I reproduce them? The very point of Bell's ingeneous work was to show that local deterministic HV theories can't reproduce the correlations. So what's the goal of your investigation? Is it to find a non-local deterministic model/theory?

 

[RUTA]

Of course QM produces the quantum correlation function. How else should I reproduce them?

You're missing the entire point: Unnikrishnan's conservation of angular momentum on average reproduces the quantum correlations without using QM. That's why I said you're free to dismiss his conversation principle as "mere coincidence." It wouldn't be a coincidence if he had used QM.

The very point of Bell's ingeneous work was to show that local deterministic HV theories can't reproduce the correlations. So what's the goal of your investigation? Is it to find a non-local deterministic model/theory?

Suppose you accept that Unnikrishnan's conservation of angular momentum on average is in fact a reasonable constraint responsible for the quantum correlations violating Bell's inequality, i.e., it's not just an amazing coincidence. In that case, you fall into the overwhelming majority of physicists who have discussed this with me. This conservation principle as a constraint is compelling. The question then is, do you require more? [This assumes you're not already content to "shut up and calculate."]

This conservation principle serves as the compelling constraint in and of itself, i.e., no 'deeper mechanism' a la hidden variables or 'causal influences' is required and none is offered. Do you require more? If so, you're just like Albert Michelson who said of his famous Michelson-Morley experiments, "It must be admitted, these experiments are not sufficient to justify the hypothesis of an ether. But then, how can the negative result be explained?'' In other words, even Michelson required some `deeper mechanism' to explain the light postulate of special relativity, i.e., why ``the speed of light c is the same in all reference frames.'' Postulates, by definition, serve as the explanans (that which explains) not the explananda (that which is to be explained). Likewise here, if you require some `deeper mechanism' to explain the conservation of angular momentum on average, then this constraint is simply one mystery replacing another and cannot serve as a postulate or explanans.

That brings us to the theme of "Beyond the Dynamical Universe." Therein, we show over and over where physics understood via dynamical or causal mechanisms leads to mysteries that disappear when using constraints. So, this is yet another such example (see my Insights series Blockworld and its Foundational Implications). The point is, maybe it's time to ascend from the "ant's-eye view" of physical reality to the "4D view" of physical reality, as Wilczek challenged. Physics hangs together beautifully without "conundrums, mysteries, or paradoxes" when you do.

 

[stevendaryl]

I just don't understand exactly how the quantum criterion follows from conservation of angular momentum.

In the EPR experiment with spin-1/2 twin particles, let $\overrightarrow{S_1}$ be the measured spin of the first particle, and let $\overrightarrow{S_2}$ be the measured spin of the second particle. We pick two directions $\overrightarrow{A}$ and $\overrightarrow{B}$ and we restrict our attention to those measurements such that

$\overrightarrow{S_1} = + \frac{1}{2} \overrightarrow{A}$
$\overrightarrow{S_2} = \pm \frac{1}{2} \overrightarrow{B}$

The quantum prediction is that $\langle (\overrightarrow{S_1} + \overrightarrow{S_2}) \cdot \overrightarrow{B} \rangle = 0$ (where $\langle ... \rangle$ means expectation value).

I don't see how conservation of angular momentum implies that $\langle (\overrightarrow{S_1} + \overrightarrow{S_2}) \cdot \overrightarrow{B} \rangle = 0$ Why is the sum $\overrightarrow{S_1} + \overrightarrow{S_2}$ projected onto the $\overrightarrow{B}$ direction?

 

[vanhees71]

I cannot make sense of @RUTA 's ideas yet, maybe I get it by reading his preprint over the weekend, but within QT the issue is very clear.

Concerning #377: You cannot measure $\vec{S}=\vec{S}_1+\vec{S}_2$, nor $\vec{S}_1$ or $\vec{S}_2$. You can measure always one component, say $\vec{S} \cdot \vec{n}$ as well as arbitrary components $\vec{S}_1 \cdot \vec{n}_1$ and $\vec{S}_2 \cdot \vec{n}_2$. If the particle pair is prepared in the spin-singlet state, i.e., if $S=0$ this implies that $\vec{S} \cdot \vec{n}=0$ (exactly!) for all $\vec{n}$.

This you also get, of course, when measurin $\vec{S}_1 \cdot \vec{n}$ and $\vec{S}_2 \cdot \vec{n}$, but a measurement of $\vec{S}_1 \cdot \vec{n}_1$ and $\vec{S}_2 \cdot \vec{n}_2$ with $\vec{n}_1 \neq \pm \vec{n}_2$ doesn't tell you anything about angular-momentum conservation. Of course, you get the correlations due to entanglement, and with clever arrangements for the directions you measure the spin you can verify the violation of Bell's inequality.

 

[RUTA]

I just don't understand exactly how the quantum criterion follows from conservation of angular momentum

Unnikrishnan shows how the quantum correlation function follows from conservation of angular momentum on average where the angular momenta measured by Alice and Bob are the angular momenta contributing to the conservation—not components. His derivation is independent of QM that’s why it’s interesting. It’s in my Insight. I don’t know what else to say

 

[RUTA]

This you also get, of course, when measurin $\vec{S}_1 \cdot \vec{n}$ and $\vec{S}_2 \cdot \vec{n}$, but a measurement of $\vec{S}_1 \cdot \vec{n}_1$ and $\vec{S}_2 \cdot \vec{n}_2$ with $\vec{n}_1 \neq \pm \vec{n}_2$ doesn't tell you anything about angular-momentum conservation.

Unnikrishnan’s derivation of the quantum correlation doesn’t use QM. Read his derivation in my Insight or my AJP preprint, it’s very simple. It’s clear what he means by “conservation of angular momentum on average” by his derivation. I don’t know what else I can say

 

[stevendaryl]

Unnikrishnan shows how the quantum correlation function follows from conservation of angular momentum on average where the angular momenta measured by Alice and Bob are the angular momenta contributing to the conservation—not components. His derivation is independent of QM that’s why it’s interesting. It’s in my Insight. I don’t know what else to say

Well a key result is not argued, but is just asserted:

The average outcome for Alice’s set of +1 results is +1, so we expect that the average outcome of Alice’s results at $\theta$ for that set would be $cos(\theta)$. Conservation of angular momentum therefore says Bob’s results corresponding to Alice’s set of +1 outcomes would average to $- cos(\theta)$

I don't see why that follows from conservation of angular momentum. Angular momentum conservation says that the two spins should add up to zero. When the measurements are along different axes, then getting the vectorial sum of the two measurements to be zero is impossible.So what is the motivation for replacing this impossible requirement by the requirement that $(\overrightarrow{S_1} + \overrightarrow{S_2}) \cdot \overrightarrow{B} = 0$?

Note: as @vanhees71 says, spin measurements actually only give a number, not a vector, but I'm defining $\overrightarrow{S_1}$ to be $\overrightarrow{A}$ times the component of the spin of the first particle along axis $\overrightarrow{A}$ and $\overrightarrow{S_2}$ to be $\overrightarrow{B}$ times the component of the spin of the second particle along axis $\overrightarrow{B}$.

 

[RUTA]

Well a key result is not argued, but is just asserted:

I don't see why that follows from conservation of angular momentum. Angular momentum conservation says that the two spins should add up to zero. When the measurements are along different axes, then getting the vectorial sum of the two measurements to be zero is impossible.So what is the motivation for replacing this impossible requirement by the requirement that $(\overrightarrow{S_1} + \overrightarrow{S_2}) \cdot \overrightarrow{B} = 0$?

Note: as @vanhees71 says, spin measurements actually only give a number, not a vector, but I'm defining $\overrightarrow{S_1}$ to be $\overrightarrow{A}$ times the component of the spin of the first particle along axis $\overrightarrow{A}$ and $\overrightarrow{S_2}$ to be $\overrightarrow{B}$ times the component of the spin of the second particle along axis $\overrightarrow{B}$.

This is reference-frame-independent conservation of angular momentum, this is not your usual conservation of angular momentum. At some particular angle, Alice measures +1 and -1 (with equal frequency) over many trials. Consider all the trials where she measured +1 at that angle. She says her +1 result in each trial was the `right' value, i.e., the `true' magnitude of her particle's angular momentum $\vec{S1}$. Had Bob measured his particle at the same angle, he would have gotten -1 which is the `right' value at that angle, i.e., the `true' magnitude of his particle's angular momentum $\vec{S2}$ for that trial. Instead, Bob measured at $\theta$ relative to Alice, so he should only get a component of $\vec{S2}$, i.e., $-cos(\theta)$, which is less than 1. Unfortunately, Bob only measures +1 or -1 himself, so he can't get the `right' value (fraction) at $\theta$ for any given trial. But, his +1 and -1 outcomes at $\theta$ can average to the `right' value $-cos(\theta)$. Of course, the argument is symmetric, so Bob says the same thing about Alice's results.

So, who is measuring the `right' value of their $\vec{S}$ for any given trial at $\theta$ and who is only measuring the `right' value on average? Indeed, if each particle had a definitive (hidden) $\vec{S}$ with magnitude S it would be amazing that Alice and Bob always measured +1 or -1. Why should that happen? Why don't they get random fractions of S? In Unnikrishnan's view, there is no underlying or hidden $\vec{S1}$ and $\vec{S2}$. What Alice and Bob measure is all that is needed to give average conservation of angular momentum. No hidden variables, no `causal influences', all you need to invoke is reference-frame-independent conservation of angular momentum as just described and you get a correlation that equals that from QM.

 

[vanhees71]

I've still to read your AJP preprint, but please think about your understanding of conservation laws in quantum theory. It's obviously flawed. Physical quantities are frame independent by construction and as such conserved (or non-conserved) in any frame of reference!

 

[RUTA]

I've still to read your AJP preprint, but please think about your understanding of conservation laws in quantum theory. It's obviously flawed. Physical quantities are frame independent by construction and as such conserved (or non-conserved) in any frame of reference!

You’re still missing the point. I have a more explicit way to explain how this conservation of angular momentum on average yields the QM correlation (keep in mind, again, this principle is independent of the formalism of QM). It’s a bit long, so I’ll do that later today.

 

[vanhees71]

I'll read your paper. It's a challenge to read about physics in terms of so much text and so few formulae ;-)).

 

[RUTA]

Ok, let me try to explain Unnikrishnan's conservation principle as transparently as possible. We have two sets of data, Alice's set and Bob's set. They were collected in N pairs with Bob's(Alice's) SG magnets at $\theta$ relative to Alice's(Bob's). We want to compute the correlation of these N pairs of results which is

$\frac{(+1)_A(-1)_B + (+1)_A(+1)_B + (-1)_A(-1)_B + ...}{N}$

Now organize the numerator into two equal subsets, the first is that of all Alice's +1 results and the second is that of all Alice's -1 results

$\frac{(+1)_A(\sum \mbox{BA+})+(-1)_A(\sum \mbox{BA-})}{N}$

where $\sum \mbox{BA+}$ is the sum of all of Bob's results corresponding to Alice's +1 result and $\sum \mbox{BA-}$ is the sum of all of Bob's results corresponding to Alice's -1 result. Notice this is all independent of the formalism of QM. Now, we rewrite that equation as

$\frac{(+1)_A(\sum \mbox{BA+})}{N} + \frac{(-1)_A(\sum \mbox{BA-})}{N} = \frac{(+1)_A(\sum \mbox{BA+})}{2\frac{N}{2}} + \frac{(-1)_A(\sum \mbox{BA-})}{2\frac{N}{2}}$

which is

$\frac{1}{2}(+1)_A\overline{BA+} + \frac{1}{2}(-1)_A\overline{BA-}$

with the overline denoting average. Again, this correlation function is independent of QM formalism. All we have assumed is that Alice and Bob measure +1 or -1 with equal frequency at any setting in computing this correlation. Now we introduce our proposed conservation principle as I justified in #382 which is

$\overline{BA+} = -\cos(\theta)$

and

$\overline{BA-} = \cos(\theta)$

This gives

$\frac{1}{2}(+1)_A(-\cos(\theta)) + \frac{1}{2}(-1)_A(\cos(\theta)) = -\cos(\theta)$

which is exactly the same correlation function as the quantum correlation obtained using conditional probabilities for the spin singlet state in QM. However, again, none of the QM formalism is used in obtaining this result. In deriving the quantum correlation function in this fashion, we assumed two key things: 1) Bob and Alice measure +1 or -1 with equal frequency in any setting and 2) Alice(Bob) says Bob(Alice) conserves angular momentum on average when Bob's(Alice's) setting differs from hers(his) by $\theta$. Those two assumptions are what I mean when I say the result is "reference frame independent."

I have added this to my Insight. I also added an explicit calculation of the quantum correlation function using the conditional probabilities for the spin singlet state from QM, so you can see how the two derivations differ.

 

[vanhees71]

Can you also explain this strange notation. Already the first equation is not clear to me. What does it mean? It's an average of what? What's in the numerator? In this way it's indeed a mystery compared to quantum theory, which is not a mystery but the solution to the mystery of the observed behavior of microscopic particles as well as the then ununderstandable stability of macrocsopic matter surrounding us.

That said, let me come to your AJP preprint. I'll got through it as I'd be a referee.

Section I is confusing and doesn't make sense to me to begin with.You should explain Mermin's apparatus to make your paper self-consistent. You don't explain it but rather open several other topics (4D spacetime views and Fermat's principle) which are completely unrelated to the "conundrum of entanglement". Since Bell it's the more clear that quantum theory is not the mystery but the solution to describe the behavior of subatomic particles, in this case spin-entangled states of two particles.

As a referee, I'd suggest to cancel Sect. I and use Sect. II as the introduction, explaining clearly Mermin's apparatus. You should explain what's entangled. It's the spins of the two particles emitted from the middle box. It doesn't make sense to say "two particles are entangled" in QM. You have to say which observables are entangled. Figs. 3 and 4 are unexplained. What are they good for? To make the paper understandable to at least a physics student who has heard the QM 1 lecture, you should just explain the experiment in terms of standard QT, i.e., say that the two spin-1/2 particles are prepared in the pure $j=0$, $j_3=0$ state represented by the state vector
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle - |-1/2,1/2 \rangle),$$
where the notation for the two-particle spin states is the usual one, i.e.,
$$|\sigma_{z1},\sigma_{z2} \rangle \equiv |\sigma_{z 1} \rangle \otimes |\sigma_{z2} \rangle.$$
To make your paper as mysterious as you can you don't even tell this your reader anywhere.

What you describe then is completely ununderstandable to me. It doesn't reflect at all what QT predicts to be measured in A's and B's measurements. It's not clearly explained. You can calculate it easily of course. You simply quote the result in Eqs. (2) and (3) without clearly saying what's measured. Obviously what's meant is that A and B choose a plane (say the $xy$ plane for simplicity since due to the total isotropy of the entangled state it doesn't matter anyway which plane they choose). Then with two unit vectors $\vec{n}(\alpha)=(\cos \alpha,\sin \alpha,0)$ what's measured are the spin components of A's and B's particles in directions $\vec{n}(\alpha)$ and $\vec{n}(\beta)$ respectively. The probabilities quoted in Eqs. (2) and (3) are then, written in standard notation
$$P(\sigma_{1\alpha},\sigma_{2\beta})=|\langle \vec{n}(\alpha) \cdot \vec{\sigma}_1,\vec{n}(\beta) \cdot \vec{\sigma}_2|\Psi \rangle|^2.$$
On the left-hand side of the equation I denoted spin components in direction $\alpha$ in the above defined sense as $\sigma_{\alpha}=\vec{n}(\alpha) \cdot \vec{\sigma})$. I'll use this abbreviation from now on.

Of course the possible outcomes for each single-particle spin component are $\pm 1/2$, and you give the correct probs. for all four possible simultaneous outcomes in Eqs. (2) to (3). But why don't you give this simple explanation rather than the very complicated description so far?

Fig. 6 and its caption is absolutely enigmatic to me. I still don't get the meaning of the words "angular momentum is conserved on average" should mean for unaligned measurements, i.e., for $\alpha-\beta \neq 0$ or $\pi$. In which sense should there be angular-momentum conservation be measured. I've brought this argument again and again already several times in this thread, and it's not answered. It doesn't even make sense in a classical context to check angular momentum conservation of a system by measuring components of angular momenta on different parts of the system in different directions! Also what's represented in this space-time diagram? Measurement outcomes of A's and B's measurements? Why do I need a space-time diagram to depict this?

I've no clue what $\langle \alpha,\beta \rangle$ should mean either. What's summed over? I can only guess it is
$$\langle 4 \sigma_{1 \alpha} \sigma_{2 \alpha} \rangle=\sum_{\sigma_{1 \alpha},\sigma_{2 \alpha} =-1/2}^{+1/2} 4 \sigma_{1 \alpha} \sigma_{2 \alpha} P(\sigma_{1 \alpha}, \sigma_{2 \alpha}).$$
Then at least I can reproduce Eq. (4).

That Alice's and Bob's "spin angular momenta cancel on average" is the next mysterious statement. Do you mean that for any single-particle spin component the average is 0? That's of course true due to the complete isotropy of the spin-singlet state. Of course, this follows also from the probabilities given by Eqs. (2) and (3). Of course, everything is completely determined by the probabilities (2) and (3). So to translate the very complicated text, what you claim is that in some way you can get these quantum probabilities by a not precisely defined "principle of angular-momentum conservation on average"? I cannot invisage how I can make sense of that, although so far I could make some conjectures about what you wanted to say. As I repeatedly said, I've no clue what the fact that in this setup the single-particle spin components have a 0 expectation value to do with angular-momentum conservation.

That's trivial for the physical situation I guessed you really want to described, given the completely isotropic preparation of the two-particle state (the $j=0$ state). Formally you get the statistics of the single-particle spins by "tracing out the other particle", and this leads to
$$\hat{\rho}=\frac{1}{2} \hat{1}=\frac{1}{2} \left (|\sigma_{\alpha}=1/2 \rangle \langle \sigma_{\alpha}=1/2| + |\sigma_{\alpha}=-1/2 \rangle \langle \sigma_{\alpha}=-1/2| \right )$$
for any $\alpha \in [0,2 \pi)$.

I'd be very interested, how your referee reports come out from AJP...

 

[RUTA]

Again, you're missing the point which is to answer Mermin's challenge to explain how his device works to the "general reader." He's able to introduce the conundrum via the Mermin device in a way accessible to the "general reader," but I wasn't able to get the explanation quite down to that level. However, I did get it down to the level of someone who completed introductory physics. So, all you need from QM to do that are the quantum probabilities for the state in question -- no Hilbert space, no density matrix, no Pauli spin matrices. The probabilities alone suffices to explain the mystery from the QM formalism. The first equation is a conventional way to write the correlation, so I'm surprised you don't recognize it. Anyway, since Unnikrishnan's conservation principle reproduces the quantum correlation (first equation plus QM probabilities), I have to translate the conundrum from probabilities to correlations. The spacetime or 4D view is necessary to justify Unnikrishnan's conservation principle as a constraint that fully resolves the conundrum, which I explain in Sec I.

 

[vanhees71]

There is no other way today to explain the behavior of matter on the fundamental level than quantum theory. That's the important result of Bell's work on local deterministic hidden-variable theories. There are also no mysteries to be resolved. You only have to accept that there are correlations in quantum physics which cannot be described by such a classical theory but are a natural consequence of quantum theory, named entanglement. These correlations can be "long-ranged", i.e., there can be correlations between properties of distinguishable parts of a quantum system which are very far away.

What's confusing in my point of view is to call this "non-locality". As Einstein already wrote in 1948 (in a paper which is much more to the point than the famous EPR paper which Einstein didn't particularly like so much) the key issue he was uneasy about was the inseparability of quantum systems through the possiblitiy of an entanglement of observables of far-distant parts of a quantum system.

Your example of the spin-entangled spin-singlet state of two-particles is paradigmatic. It's usually easier to realize with polarziation-entangled photon pairs, which nowadays are easily produced through parametric downconversion, but the principle issue is the same. In principle the polarization-entanglement can persist for arbitrary long times (as long as there's no interaction of one of the particles or photons with something else and no decoherence occurs), and thus the particles or photons can be registered by as far distant observers as one likes, and each observer can choose his observable he likes to measure (i.e., in your example which spin component he likes to measure or which polarization state he likes to filter out), but the correlations described through entanglement will be observed.

All this is fully concistent with relativistic local microcausal QFTs. For photons everything is well understood within standard quantum optics, based on QED (with the optical devices treated in hemiclassical approximation, which is of sufficient accuracy for the usual experiments). Since for QED, as for any local QFT, the linked-cluster theorem holds there are "spooky actions at a distance", but the long-ranged "stronger than classically possible" correlations are simply there because of the preparation of the two-particle/two-photon system in an entangled state. Thus although the single-particle spins (resp. single-particle photon polarizations) are maximally indetermined, there's still this strong correlation beween measurement outcomes.

Admittedly this is hard to swallow as long as you don't accept that Nature behaves as she does and doesn't care about our philosophical prejudices due to our everyday experience with macroscopic matter, which behaves pretty classical also according to QT since we don't resolve (and don't need to resolve) every microscopic detail, such that the quantum fluctuations of the corresponding macroscopic coarse-grained obserervables are practically not visible.

In your paper there's nothing explained differently from QT. All you do is to assume the probabilities of QT to be valid and then calculate expectation values due to the rules. That the average of any of the single-particle spin components in any direction is 0 is simply due to the symmetry of the sytem. That's implied by the fact that the total angular momentum is precisely 0 due to the preparation of the particle pair in this state, and this state is a maximally entangled Bell state.

Bell's brillant analysis of this state in terms of a deterministic local theory clearly shows that QT is different from any such theory, and you have to give up either locality or determinism. Since local QFTs are the most successful consistent descriptions of matter we have today in terms of the Standard Model, my personal conclusion is that we have to give up determinism, but that was known since 1926 when Born got the so far only consistent interpretation of quantum states, namely their probabilistic meaning in terms of what we now rightly call "Born's Rule".

 

[RUTA]

Again, you've missed the point entirely. Did you even read Mermin's paper? His `Mermin device' produces outcomes he calls "case (a)" and "case (b)." Case (a) outcomes obtain for like settings on his device and case (b) outcomes obtain for unlike settings. The only way he knows to explain the workings of the device in accord with case (a) outcomes, his "instruction sets," is incompatible with the case (b) outcomes, thus the conundrum. You don't need any QM to understand this conundrum, just simple probabilities. He then asks the "physicist reader" to explain how his device works to the "general reader," analogously to how he was able to explain the conundrum of the device to the "general reader." Density matrices, spin operators, and Hilbert space won't cut it. My paper is very close to meeting his challenge. In addition to simple probabilities, which are allowed, I used conservation of angular momentum, which is a bit more. Can you do better? If so, write it up and submit it!

 

[vanhees71]

I haven't missed the point. You have failed to convince me that there is a point. There's nothing non-trivial derived in your paper, and it's written in a way that one has to guess what you want to tell and there's a lot of off-topic ballast in it. Excuse me for being harsh.

 

[RUTA]

I haven't missed the point. You have failed to convince me that there is a point. There's nothing non-trivial derived in your paper, and it's written in a way that one has to guess what you want to tell and there's a lot of off-topic ballast in it. Excuse me for being harsh.

If you don't understand the conundrum, then you won't appreciate Unnikrishnan's solution and my qualification thereto. I did revise the manuscript according to my efforts to explain it to you, so these exchanges did prove useful :-)

 

[vanhees71]

Well, I've just looked up the following paper by Unnikrishnan:

DOI: 10.1209/epl/i2004-10378-y

He got the issue with the conservation law correct, i.e., precisely as I stated several times. Maybe it helps to sharpen also your manuscript if you use his explanation on pages 490 and 491 in his paper, particularly the statement on the conservation law directly under item 2) on page 491. Then it becomes really a non-trivial and interesting issue which sheds further light on Bell's inequality in showing that there's no local deterministic HV theory that obeys the angular-momentum-conservation law on average. This is weaker than to assume the conservation law to be valid for any individual system as is the case for quantum theory for the spin-singlet state.

 

[RUTA]

Well, I've just looked up the following paper by Unnikrishnan:

DOI: 10.1209/epl/i2004-10378-y

He got the issue with the conservation law correct, i.e., precisely as I stated several times. Maybe it helps to sharpen also your manuscript if you use his explanation on pages 490 and 491 in his paper, particularly the statement on the conservation law directly under item 2) on page 491. Then it becomes really a non-trivial and interesting issue which sheds further light on Bell's inequality in showing that there's no local deterministic HV theory that obeys the angular-momentum-conservation law on average. This is weaker than to assume the conservation law to be valid for any individual system as is the case for quantum theory for the spin-singlet state.

Here is his item 2:

The theory of correlations obeys the conservation of angular momentum on the average over the ensemble, and for the case of singlet state,STotal = 0, there is rotational invariance. Note that this is a weak assumption, since we do not insist on the validity of the conservation law for individual events.

He says, immediately thereafter

The second criterion is the main assumption, physically well motivated, in the proof that follows. Since the main assumption is applied only for ensemble averages and not for individual events, I do not make any explicit assumption on locality or reality.

That is exactly the point I make when I say Bob can't satisfy conservation of angular momentum on a trial-by-trial basis when he and Alice make measurements at different angles. He can only satisfy the conservation principle an average in such cases. [Of course, he can say the same about Alice.] The correlation function obtained per Unnikrishnan's conservation principle is not satisfied by "instruction sets," which is the Mermin equivalent of saying Unnikrishnan's conservation principle cannot be satisfied by any "local deterministic HV theory." Again, did you read Mermin's paper?

 

[vanhees71]

But you didn't make the point clear! Unnikrishnan does. Even under the assumption of angular-momentum conservation on average, which is less than what's the case for QT, where angular-momentum conservation holds on an event-by-event basis, he can show that there's no local deterministic HV model which leads to the violation of Bell's inequality as predicted by QT. I've not read Mermin's paper, but I don't think it's necessary, because in Unnikrishnan's paper everything is clear.

 

[RUTA]

But you didn't make the point clear! Unnikrishnan does. Even under the assumption of angular-momentum conservation on average, which is less than what's the case for QT, where angular-momentum conservation holds on an event-by-event basis, he can show that there's no local deterministic HV model which leads to the violation of Bell's inequality as predicted by QT. I've not read Mermin's paper, but I don't think it's necessary, because in Unnikrishnan's paper everything is clear.

What I had in the paper was just Unnikrishnan's summary paragraph. Obviously, I can't include all the explication he provides in his paper after that summary, but I didn't think it necessary since his summary was very clear to me. Apparently, it wasn't clear to you, so I revised the paper here replacing his summary with my "no preferred reference frame" argument for his conservation of angular momentum on average. My argument is just another way of looking at his argument or just another way of looking at Boughn's argument here. However you justify it, the key insight of Unnikrishnan is to use conservation of angular momentum on average to provide $\overline{BA+}$ and $\overline{BA-}$ in the correlation function (see post #386). That gives you the quantum correlation function without ever using quantum mechanics. This is akin to deriving the Lorentz transformations from the light postulate (in more ways than one, as I will point out).

As for articulating the fact that Unnikrishnan's result rules out "local HV theories," that's trivially clear from the fact that his conservation principle reproduces the quantum correlation function which rules out local HV theories (I have included that very statement in the paper). In the Mermin paper (had you bothered to read it), he goes to great lengths to explain how his "instruction sets" are the equivalent of any local HV theory. As with the Unnikrishnan paper, I can't include Mermin's entire paper in mine, so I must expect the reader to have read the Mermin paper. The Mermin device is a metaphor for the formalism of QM in this particular experimental set-up. So, when Mermin shows that his device cannot be explained with instruction sets, he's showing how QM rules out local HV theories. The conundrum of the Mermin device is then, "If it doesn't work via instruction sets, how the hell does it work?" Since Unnikrishnan's conservation principle gives the quantum correlation function responsible for the mysterious outcomes of the Mermin device, his conservation principle invoked as a constraint (as with the light postulate) then answers that question, i.e., resolves the conundrum of the Mermin device. However, ...

As I point out, Unnikrishnan's conservation principle only resolves the conundrum of the Mermin device if you can accept the conservation principle as a constraint on the distribution of outcomes in space and time with no `deeper mechanism' to account for the constraint proper. In other words, you have to accept the conservation principle as a constraint in and of itself without further explanation. Prima facie the conservation of angular momentum on average sounds like a perfectly reasonable constraint. But, this constraint does not provide a `deeper mechanism' at work on a trial-by-trial basis to account for the average conservation. So someone might still say, "But, what mechanism is responsible for the conservation? How do the particles `know' how to behave in each trial so as to contribute properly to the ensemble? Each particle has `no idea' what the outcomes were at both locations in preceding trials, nor does it `know' what the other device setting is in their particular trial. How the hell does this average conservation pattern in space and time get created?"

And that leads us to the other analogy with the light postulate. Even Michelson of the Michelson-Morley experiment said, "It must be admitted, these experiments are not sufficient to justify the hypothesis of an ether. But then, how can the negative result be explained?" In other words, even Michelson required some `deeper mechanism' to explain why "the speed of light c is the same in all reference frames." In general, if one cannot accept a constraint or postulate in and of itself as the fundamental explanans, that constraint or postulate is just as mysterious as the explanandum. That's the point of my paper and that is the point of our book, "Beyond the Dynamical Universe." So, my paper is just another argument for constraint-based explanation as fundamental to dynamical/causal explanation.