Implications of Bell's theorem (Laloe paper)

[atyy]

[this thread was forked from another thread, as it is an interesting topic in its own right]

Yes, a variant of Bell's theorem says that quantum mechanics is truly random as long as we cannot signal faster than light.
http://arxiv.org/abs/quant-ph/0508016
http://arxiv.org/abs/0911.2504

 

[stevendaryl]

Yes, a variant of Bell's theorem says that quantum mechanics is truly random as long as we cannot signal faster than light.
http://arxiv.org/abs/quant-ph/0508016
http://arxiv.org/abs/0911.2504

I don't see how Bell's theorem implies anything about randomness. It proves that there is no local, deterministic hidden-variables theory that reproduces the predictions of QM, but it is not difficult to show that there is no local nondeterministic hidden-variables theory that works, either. If you allow for nonlocal interactions, then there is no constraint about whether it's random or deterministic.

 

[Demystifier]

Yes, a variant of Bell's theorem says that quantum mechanics is truly random as long as we cannot signal faster than light.

Even if it doesn't make sense from a fundamental microscopic point of view (as stevendaryl correctly recognized), it does make sense from an operational macroscopic point of view. The line of reasoning is the following: We cannot signal faster than light, therefore QM is operationally local, therefore an operational version of Bell theorem excludes operational determinism, therefore QM is operationally random.

What people (both physicists and philosophers) cannot reach a consensus about is whether the operational aspects are the only meaningful aspects one can talk about.

 

[phyzguy]

[this thread was forked from another thread, as it is an interesting topic in its own right]
Yes, a variant of Bell's theorem says that quantum mechanics is truly random as long as we cannot signal faster than light.
http://arxiv.org/abs/quant-ph/0508016
http://arxiv.org/abs/0911.2504

atyy: Thanks for pointing out this paper, which I found very interesting. Instead of talking about philosophical issues like non-locality and determinism, it focuses on operational issues, like the ability to signal faster than light (which they call signal locality), and the ability to predict the results of experiments (which they call predictability). These are experimentally measurable quantities which are ultimately not open to dispute. If the paper is correct, and it seemed so to me, Bell's inequalities say that we cannot live in a universe that has both signal locality and predictability. Since I think most of us agree that we cannot send signals faster than light (otherwise we violate causality), it means that we must conclude that our universe is inherently unpredictable.

Reading the earlier posts, I now realize that I'm just re-stating what Demystifier said. In answer to his last statement, I think that while we can talk about non-operational aspects, it may be that ultimately the only aspects we can agree on are the operational aspects.

 

[Matta Tanning]

I don't understand the bit in the introductory part of the paper where it says:
"models that maintain locality but violate determinism (standard operational quantum theory is an example)."
To my mind quantum mechanics is certainly non-local. Can someone explain what the authors mean?

Furthermore I feel that 'signalling' is far from indisputable. The violation of Bell's inequalities in nature indicate something non-local, going by Bell's definition of the word. However, if you want to start talking about signalling then who are the signallers? The operational aspects of quantum mechanics are precisely those that Bell rejects:

" Do we then have to fall back on ‘no signalling faster than light’ as the expression of the fundamental causal structure of contemporary theoretical physics? That is hard for me to accept. For one thing we have lost the idea that correlations can be explained, or at least this idea awaits reformulation. More importantly, the ‘no signalling…’ notion rests on concepts which are desperately vague, or vaguely applicable. The assertion that ‘we cannot signal faster than light’ immediately provokes the question:
Who do we think we are? We who can make ‘measurements’, we who can manipulate ‘external fields’, we who can ‘signal’ at all, even if not faster than light? Do we include chemists, or only physicists, plants, or only animals, pocket calculators, or only mainframe computers?" " - Bell, La Nouvelle Cuisine.

 

[atyy]

I don't understand the bit in the introductory part of the paper where it says:
"models that maintain locality but violate determinism (standard operational quantum theory is an example)."
To my mind quantum mechanics is certainly non-local. Can someone explain what the authors mean?

Quantum mechanics is "local", in the definition of the paper, because in an EPR experiment, the reduced density matrix of Bob does not depend on anything that Alice does, so all of Bob's probabilities are independent of Alice's measurement choices.

The paper defines another notion of locality called "local causality" by which quantum mechanics is nonlocal.

 

[RUTA]

... it is not difficult to show that there is no local nondeterministic hidden-variables theory that works, either.

Relational Blockworld http://www.ijqf.org/archives/2087 is a local, hidden-variable theory and I believe it is nondeterministic in the sense here. Do you disagree?

 

[bhobba]

Quantum mechanics is "local", in the definition of the paper,

I am a bit uneasy about this locality definition thing. Standard QM is non local in the same way classical mechanics is non local ie its based on the Galilean transformations. I know this aspect is often not emphasised (Landau being a notable exception) but it is still true. Locality is the issue of theories that use the Lorentz transformations ie QFT. In QFT locality is as per the cluster decomposition property:
http://en.wikipedia.org/wiki/Cluster_decomposition_theorem

It only applies to uncorrelated systems - which EPR type set-ups most certainly are not. What we need to be clear about is exactly what we mean by locality in correlated systems.

Thanks
Bill

 

[atyy]

I am a bit uneasy about this locality definition thing. Standard QM is non local in the same way classical mechanics is non local ie its based on the Galilean transformations. I know this aspect is often not emphasised (Landau being a notable exception) but it is still true. Locality is the issue of theories that use the Lorentz transformations ie QFT. In QFT locality is as per the cluster decomposition property:
http://en.wikipedia.org/wiki/Cluster_decomposition_theorem

It only applies to uncorrelated systems - which EPR type set-ups most certainly are not. What we need to be clear about is exactly what we mean by locality in correlated systems.

QFT is a type of QM.

 

[stevendaryl]

Relational Blockworld http://www.ijqf.org/archives/2087 is a local, hidden-variable theory and I believe it is nondeterministic in the sense here. Do you disagree?

You're right, and I was wrong. I believe that RBW is superdeterministic, which is another way out of Bell's proof.

 

[bhobba]

QFT is a type of QM.

Of course it is. But standard QM is based on the Galilean transformations so is inherently non local eg Schroedinger's equation follows from it and conversely it obeys the Galilean transformations. Locality must be discussed in the context of QFT and the cluster decomposition property. This is not usually pointed out in papers, but is true.

Thanks
Bill

 

[atyy]

Of course it is. But standard QM is based on the Galilean transformations so is inherently non local eg Schroedinger's equation follows from it and conversely it obeys the Galilean transformations. Locality must be discussed in the context of QFT and the cluster decomposition property. This is not usually pointed out in papers, but is true.

It is not true. The Bell inequalities are derived without assuming QM. Relativistic QFT violates the Bell inequalities, so it is not does not satisfy local causality.

 

[bhobba]

It is not true. The Bell inequalities are derived without assuming QM.

The Galilean transformations are non local because time is absolute. Schrödinger's equation obeys the Galilean transformations, and, interestingly, as detailed in Chapter 3 of Ballentine (and pretty well known at a more advanced level) the converse is true. QM + the Galilean transformations leads to Schrodingers equation. Non locality is built right into the foundations of ordinary QM. Locality is only an issue in QFT.

Its the violation of Bells inequalities from experiment that is the issue - it shows QM can't be interpreted as local realism. But standard QM is non local anyway. That's all I am saying. If you want locality to actually be an issue you need to go to QFT and its concept of locality that doesn't apply to correlated systems.

Thanks
Bill

 

[RUTA]

You're right, and I was wrong. I believe that RBW is superdeterministic, which is another way out of Bell's proof.

Superdeterminism means there is a mechanism that dictates the outcomes and settings using info at the source only. RBW doesn't do that, so it's not superdeterministic.

 

[RUTA]

You're right, and I was wrong. I believe that RBW is superdeterministic, which is another way out of Bell's proof.

Superdeterminism means there is a mechanism that dictates the outcomes and settings using info at the source only. RBW doesn't do that, so it's not superdeterministic.

 

[RUTA]

You're right, and I was wrong. I believe that RBW is superdeterministic, which is another way out of Bell's proof.

Superdeterminism means there is some mechanism that dictates the device settings and outcomes using info at the source only. RBW does not do that, so it is not superdeterministic.

 

[stevendaryl]

Superdeterminism means there is some mechanism that dictates the device settings and outcomes using info at the source only. RBW does not do that, so it is not superdeterministic.

I once asked for a better description of what, exactly, RBW is, and I didn't get any answer. The papers by the original authors are completely unsatisfying. I can't completely understand what they're proposing.

I understand that the poincare generators give rise to commutation relations like those in QM, but I don't understand what it means to claim that the QM commutation relations are literally due to relativity.

 

[RUTA]

I once asked for a better description of what, exactly, RBW is, and I didn't get any answer. The papers by the original authors are completely unsatisfying. I can't completely understand what they're proposing.
I understand that the poincare generators give rise to commutation relations like those in QM, but I don't understand what it means to claim that the QM commutation relations are literally due to relativity.

Sorry, I didn't see that post or I would've responded of course. Forget the early stuff about Poincare generators from Bohr et al., we've replaced that formalism with our own. Just read the intro of the IJQF paper (7 pp) and let me know if you've any questions. Probably better send questions via private correspondence.

 

[stevendaryl]

Sorry, I didn't see that post or I would've responded of course. Forget the early stuff about Poincare generators from Bohr et al., we've replaced that formalism with our own. Just read the intro of the IJQF paper (7 pp) and let me know if you've any questions. Probably better send questions via private correspondence.

Is there a preprint avalable on arxiv?

 

[RUTA]

Is there a preprint avalable on arxiv?

I didn't post it on the arXiv because it's freely available from IJQF where it's under review. The link is at the bottom of the abstract. Try this http://www.ijqf.org/wps/wp-content/uploads/2015/03/Stuckey-et-al-2015.pdf

 

[stevendaryl]

Thanks!