Quantum Correlations without Many Worlds or Determinism

[msumm21]

TL;DR Summary

Trying to understand things I read in other posts about correlation like EPR-Bell

I'm trying to understand the comment by bhobba below from another thread. A related followup from RUTA is provided for reference. After reviewing these I still don't understand. If I think in terms of a single-world (not Everette) and assume Alice and Bob are free to adjust their SG measurement orientation at will (not predetermined), then is there another way to understand these correlations (with needing non-local influence)?

Comment: I'm not saying many-worlds or determinism are wrong, just saying IF they are wrong then ...

There is no proof of non-locality in QM. All Bell, and its experimental confirmation, shows is a non-classical statistical correlation. What it means is simply QM is not a classical probability model - its a generalized probability model. Want it to be one - then you need non-local influences. But the world may simply not be classical in its statistical behavior - it does not have to be non-local.

Here is an explanation suitable for anyone who knows intro physics: https://arxiv.org/abs/1809.08231. In fact, I had several of my Honors students in intro physics read and comment on it before posting. Here is a generalized version just published in Entropy: https://www.mdpi.com/1099-4300/21/7/692/pdf. Here is the talk I gave on that paper: which is pretty basic.

The bottom line in all these is that contrary to popular myth, QM and SR are self-consistent as they are ultimately based on the same principle — no preferred reference frame. This explains the one difference between the quantum and classical joint distributions per Garg and Mermin (see citation in either paper), i.e., that Bob and Alice both always measure +1/-1 regardless of their reference frame. That fact alone then accounts for the “weird” QM correlation just like the light postulate accounts for the “weird” relativity of simultaneity in SR. In other words, what people find so weird about modern physics is due to the fact that no one’s sense experiences can provide a favored perspective on the real external world (to borrow from Einstein). Specifically here wrt the measurements of fundamental constants (c and h).

 

[DarMM]

Summary: Trying to understand things I read in other posts about correlation like EPR-Bell

If I think in terms of a single-world (not Everette) and assume Alice and Bob are free to adjust their SG measurement orientation at will (not predetermined), then is there another way to understand these correlations (with needing non-local influence)

In essence the correlations only need to be nonlocal if you insist on what is sometimes called unicity or the existence of counterfactuals.

So if Alice can measure spin along two axes $S_a , S_b$ and Bob can measure them along two others $S_c ,S_d$ we only get nonlocality if we assume there are values for each variable in each round.

Now in Classical Mechanics this is always the case. If you measure angular momentum along one axis $L_z$ there is still a value for the other two axes, you just don't know them. So you are allowed discuss the counterfactual case: "What if I had measured $L_x$?" in a meaningful way.

In QM only the axis you measured has a result, thus trying to discuss the values of all four of Alice and Bob's axes is meaningless as only two have a defined value in a given round.

The violation of Bell's inequalities just reflect the fact that correlations when not all variables have well-defined values are stronger than when they do.

That is the Copenhagen view.

@RUTA has another view that doesn't require nonlocality, but isn't the Copenhagen view I've given here. It's a Relational Acausal view. It's very interesting, but I don't want to overload this post so I won't explain it here.

 

[msumm21]

OK thanks, I think I see it now. I had to re-read Bell's derivation.

RUTA's view is included in the 2 links he provided? Another reference for that? I will try to read those linked papers soon.

 

[DarMM]

OK thanks, I think I see it now. I had to re-read Bell's derivation.

I'd suggest reading the account of it in Asher Peres's "Quantum Theory: Concepts and Methods".

RUTA's view is included in the 2 links he provided? Another reference for that?

@RUTA 's view is most completely given in his book "Beyond the Dynamical Universe: Unifying Block Universe Physics and Time as Experienced".

Have you taken a graduate QM class or gone through a book equivalent to it if you are an autodidact?

 

[msumm21]

I'd suggest reading the account of it in Asher Peres's "Quantum Theory: Concepts and Methods".

Will try to check this out.

I just read RUTA's Entropy paper in the original post (https://www.mdpi.com/1099-4300/21/7/692/pdf ). I didn't understand some of the logic. Here are a couple questions I'm stuck on, below.

On page 3 it says NPRF in this context means all outcomes must be either hbar/2 or -hbar/2. I realize that +/- hbar/2 is what's seen experimentally, but don't see how that follows from NPRF.

Also, when equation 17 is derived (page 10) it was assuming the QM average values from equation 15 & 16, right? If so, isn't this paper really arguing that NPRF+conservation+someQuantumValues implies the Tsirelson bound? The argument doesn't work without that third component, right?

 

[DarMM]

Yeah, discrete outcomes combined with conservation laws and NPRF gives you the quantum correlations.

Asher Peres in the book I mentioned above shows discrete outcomes and the continuous space of measurement settings forces probabilistic reasoning and the absence of values for counterfactuals.

 

[RUTA]

Will try to check this out.

I just read RUTA's Entropy paper in the original post (https://www.mdpi.com/1099-4300/21/7/692/pdf ). I didn't understand some of the logic. Here are a couple questions I'm stuck on, below.

On page 3 it says NPRF in this context means all outcomes must be either hbar/2 or -hbar/2. I realize that +/- hbar/2 is what's seen experimentally, but don't see how that follows from NPRF.

Also, when equation 17 is derived (page 10) it was assuming the QM average values from equation 15 & 16, right? If so, isn't this paper really arguing that NPRF+conservation+someQuantumValues implies the Tsirelson bound? The argument doesn't work without that third component, right?

NPRF entails the quantum outcomes which then means the conservation principle can hold only on average. I just finished a video series on this idea for my students, so it’s not very detailed, but the part you missed is made very clear. Here is the last episode (only 8 min). It recaps the other episodes and the idea you missed. Let me know if you want links to any of the other episodes. The video series is still Unlisted while I wait for feedback, but will be Public soon. Let me know if you find any mistakes before it goes Public :-)

 

[msumm21]

Here is the last episode

Nice video, thanks for the link. I still haven't convinced myself that NPRF implies the quantum $\pm \hbar/2$ measurements. For instance, take a "classical type" theory where particle 1 gets spin $\hat{x}\hbar/2$ and particle 2 gets $-\hat{x}\hbar/2$ with $\hat{x}$ random (uniform over all directions) in each run of the experiment. When spins are measured about an axis $\hat{A}$ the outcome is just the projection onto that axis. Doesn't this satisfy NPRF (and also conservation, on average)? There's no reliance on any preferred frame here, as far as I can tell.

 

[RUTA]

Nice video, thanks for the link. I still haven't convinced myself that NPRF implies the quantum $\pm \hbar/2$ measurements. For instance, take a "classical type" theory where particle 1 gets spin $\hat{x}\hbar/2$ and particle 2 gets $-\hat{x}\hbar/2$ with $\hat{x}$ random (uniform over all directions) in each run of the experiment. When spins are measured about an axis $\hat{A}$ the outcome is just the projection onto that axis. Doesn't this satisfy NPRF (and also conservation, on average)? There's no reliance on any preferred frame here, as far as I can tell.

The classical explanation for the deflection per variable magnetic moment orientation in the inhomogeneous magnetic field yields variable deflection. So, the having the same deflection in all directions does not conform to the classical prediction. That alone differentiates the classical from the quantum joint distribution yielding the TB (Garg and Mermin, PRL 49(13), 901-904, 1982). If the magnetic moment is uniform in all directions for a given trial, that's a zero magnetic moment. Regardless, NPRF, as I've defined it (there are other definitions, as I point out in the paper), for the spin singlet state simply means that Alice and Bob measure the same outcome for all orientations of their SG magnets.

 

[DarMM]

Nice video, thanks for the link. I still haven't convinced myself that NPRF implies the quantum $\pm \hbar/2$ measurements. For instance, take a "classical type" theory where particle 1 gets spin $\hat{x}\hbar/2$ and particle 2 gets $-\hat{x}\hbar/2$ with $\hat{x}$ random (uniform over all directions) in each run of the experiment. When spins are measured about an axis $\hat{A}$ the outcome is just the projection onto that axis. Doesn't this satisfy NPRF (and also conservation, on average)? There's no reliance on any preferred frame here, as far as I can tell.

To try another explanation, by measuring the projections onto different axes you'd know the "true" axis that aligned with the angular momentum as the one with the maximum projection. However if nobody's axis is preferred at all, i.e. a sense of NPRF stronger than in classical mechanics, that shouldn't happen.

The values then can't be continuous as you can always use such a maximizing operational procedure in that case.

I think.

 

[msumm21]

To try another explanation, by measuring the projections onto different axes you'd know the "true" axis that aligned with the angular momentum as the one with the maximum projection. However if nobody's axis is preferred at all, i.e. a sense of NPRF stronger than in classical mechanics, that shouldn't happen.

The quantum behavior also has this property, right? If Alice measures about axes x and -x she will find the true momentum to be about x or -x. So I could claim x or -x was a preferred frame having all the angular momentum, right?

 

[DarMM]

The quantum behavior also has this property, right? If Alice measures about axes x and -x she will find the true momentum to be about x or -x. So I could claim x or -x was a preferred frame having all the angular momentum, right?

I'm not sure what you mean here. $x$ and $-x$ would basically be vectors referring to the same axis and she would find $\frac{\hbar}{2}$ or $-\frac{\hbar}{2}$ along that axis. In QM every axis has the same projection.

 

[msumm21]

I'm not sure what you mean here. xxx and −x−x-x would basically be vectors referring to the same axis and she would find ℏ2ℏ2\frac{\hbar}{2} or −ℏ2−ℏ2-\frac{\hbar}{2} along that axis. In QM every axis has the same projection.

Sorry, I interpreted the post below to say: NPRF is violated because we can perform measurements and find an axis aligned with the angular momentum. So I was just commenting that we can do the same thing in the quantum version. Is there a consensus as to the definition of NPRF? I (maybe incorrectly) envision it as one in which the physical rules don't have any preferred frame/axis (and the classical example presented above does not as far as I can tell), but yours is maybe stronger, referencing results of multiple measurements in various directions?

To try another explanation, by measuring the projections onto different axes you'd know the "true" axis that aligned with the angular momentum as the one with the maximum projection. However if nobody's axis is preferred at all, i.e. a sense of NPRF stronger than in classical mechanics, that shouldn't happen.

 

[DarMM]

Sorry, I interpreted the post below to say: NPRF is violated because we can perform measurements and find an axis aligned with the angular momentum. So I was just commenting that we can do the same thing in the quantum version. Is there a consensus as to the definition of NPRF? I (maybe incorrectly) envision it as one in which the physical rules don't have any preferred frame/axis (and the classical example presented above does not as far as I can tell), but yours is maybe stronger, referencing results of multiple measurements in various directions?

@RUTA's explanation of QM involves a stronger form of NPRF than the one currently used in Relativisric physics. Classical mechanics violates this form because one can look for the axis with a maximization of the angular momentum projection and then explain projections along other axes as simply being due to them being misaligned with the "true" axis of rotation.

In @RUTA's explanation the same discrete values being found along all axes prevents any from being the "real" axis of rotation. Or more accurately if we privilege no observer's view of the angular momentum then no axis of measurement should display signs of being the true one and since continuous projection values would allow one to opertionally define a true axis, as per the above method, the outcomes must be discrete.

 

[DarMM]

So I was just commenting that we can do the same thing in the quantum version

The point is it seems we can't.