A local deterministic theory that violates Bell's inequaities

[kote]

You need to give physicists at least some measure of respect for their intelligence. If they see something that is logically inconsistent, they would have addressed it. As of now, it appears that YOUR understanding of QM that is inconsistent, and you're confusing that, with QM itself.

Zz, while I totally agree with you, I do find it interesting that physicists have in the past (and still recently) decided that throwing out classical logic is an acceptable solution. See von Neumann and the whole idea of quantum logic, which goes back to 1932. The "negative probability" explanation makes a similar leap. Post-modernism and naturalism seem to (unfortunately) have had quite the effect on physics. From http://plato.stanford.edu/entries/qt-quantlog/:

At its core, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. ​

And quoting von Neumann:

Whereas logicians have usually assumed that properties … of negation were the ones least able to withstand a critical analysis, the study of mechanics points to the distributive identities … as the weakest link in the algebra of logic. [1937, p. 839]​

The idea of quantum logic or of logic being up for empirical revision make discussions of interpretations and Bell's Theorem etc more complicated. I wish we could just go back to assuming the primacy of logic and math as the framework through which we must interpret our experiments and physical theories. I guess when the physics gets weird enough, even the foundations of physics start to be questioned.

 

[Halcyon-on]

Kote, I point out that if we were able to describe QM in terms our old classical logic, this would means that we have finally understood QM. I mean that we would explain it in terms of extension of classical system, like relativistic waves, conservation of the energy, the least action principle and so on. Thus explain QM in terms of classical logic would be an important goal.

But there is something that I don't really understand from the description that you give about quantum logic. It doesn't convince me and I try to explain why. QM logic should be something valid only at quantum scale and this logic should be approximated with the classical logic at human scale. So this logic depends on a scale parameter (h). But logic should be something valid at every scale, it should be scale independent, there should be a truth table that is always valid, no matter the scale. In the truth table there cannot be a dimensional parameter that fixes the scale. Am I right?

 

[DrChinese]

2.What evidence do you have that they have never been in causal contact? Did they not originate from the big-bang singularity?

3. Are you sure that GR does apply for them? For example, two objects that were not in causal contact should not attract at all. Likewise, two charged particles should not display Coulombian interaction. I doubt that such a case has been observed.

4. First I'd like you to answer my previous question: Let's consider a system that is completely described by GR. Is it possible to separate this system into 2 or more independent subsystems or not?

I am not interested in the history of that system, only in the fact that it is correctly described by GR.

Maybe, but then this system isn't correctly described by GR (two massive objects would not attract at all), do you agree?

2. This is simply the standard inflationary scenario (which of course may not be correct). Whether or not there was an initial pure "singularity" (at t=0) is still open for discussion as obviously it leads to infinite density etc. under GR.

3. Regardless of above, there are certainly giant sections of the universe that are no longer in causal contact via GR. In fact, pick any 2 random points in the universe and they are likely no longer in causal contact. That is because they are receding from each other faster than c and their recession speed is accelerating.

4. I have to say that I am not certain whether there is any element of mutual attraction for objects that are no longer in each other's future light cones. I would assume not.

I am not sure if the "causal contact" issue is spoiling our discussion of superdeterminism. That was not my intent. But I was trying to address your point as accurately as am able. I would agree that everything in the Milky Way is in causal contact (with c as a limiting factor of course) - and again we are ignoring Bohmian type issues here to make it clearer.

Does that help?

 

[ueit]

2. This is simply the standard inflationary scenario (which of course may not be correct). Whether or not there was an initial pure "singularity" (at t=0) is still open for discussion as obviously it leads to infinite density etc. under GR.

3. Regardless of above, there are certainly giant sections of the universe that are no longer in causal contact via GR. In fact, pick any 2 random points in the universe and they are likely no longer in causal contact. That is because they are receding from each other faster than c and their recession speed is accelerating.

4. I have to say that I am not certain whether there is any element of mutual attraction for objects that are no longer in each other's future light cones. I would assume not.

I am not sure if the "causal contact" issue is spoiling our discussion of superdeterminism. That was not my intent. But I was trying to address your point as accurately as am able. I would agree that everything in the Milky Way is in causal contact (with c as a limiting factor of course) - and again we are ignoring Bohmian type issues here to make it clearer.

Does that help?

It seems to me that you make a great effort not to answer my simple question (can a system that is completely described by GR be split in more independent subsystems?). You have chosen to discuss systems that are not described by GR, in fact they can be interpreted as a failure of the theory. Expansion is supposed to be caused by "dark energy" but nobody knows its nature. GR does not explain the big-bang itself, neither the inflation. So, could we just discuss a system that is in the domain if GR? A galaxy would be fine (if we ignore magnetic fields, radiation and such). So, do you think that two subsystems, say two star systems in our galaxy, could have independent evolution according to GR?

 

[DrChinese]

So, do you think that two subsystems, say two star systems in our galaxy, could have independent evolution according to GR?

As I said, I would agree that they would not (again ignoring other forces). So yes, there would be one deterministic system regardless of separation.

 

[Faizan]

Thanks for that




_______________---
Dark Green Onyx | http://www.pakistan-black-and-gold-marble.faizanmarbles.com/

 

[ThomasT]

How might the assumption of locality be modeled then, because this is the problem: how do you formally represent locality in a way that doesn't include statistical independence?

Locality means that the evolution of a system only depends on the physical variables in its proximity. Earth's trajectory only depends on the local space curvature. This does not mean that Earth's motion and Pluto's motion are independent. They are not, because the two objects are also part of the same star system so they evolve around its center. SD has nothing to do with locality or the lack of it.

I don't think you addressed the question of how to formally explicate the assumption of locality. We both seem to believe that the assumption that the evolution of our universe is constrained by local causality is the most reasonable at this time.

Bell's locality assumption isn't that separated systems evolve independently (because, obviously, observational contexts can be expanded to define ever larger nonseparable systems), but rather that (given deterministic evolution and a transmission speed limit, c) spacelike separated events can't causally affect each other within certain time intervals.

In order to model this, Bell represented the joint (entangled) state in factorable form. The problem with this is that this also represents statistical independence, which is not relevant to locality. Statistical dependence is necessitated by the experimental designs and procedures associated with the observation of quantum entanglement.

QM circumvents this problem insofar as it is a statistical theory and correctly represents the statistically nonseparable state, which neither affirms nor denies the assumption of locality. The variables involved in accurately predicting the rate of coincidental detection aren't hidden.

't Hooft's approach is to circumvent the lhv problem formalized by Bell by explicating locality in a rather less direct form than that proposed by Bell.

Superdeterminism, as far as I can tell, just refers to universe scale determinism.

And the term, free-will, is just an expression of our ignorance.

 

[ueit]

As I said, I would agree that they would not (again ignoring other forces). So yes, there would be one deterministic system regardless of separation.

So, do you agree that any HVT that shares this property with GR (that it doesn't allow a separation of a system into independent subsystems) would not satisfy the statistical independence assumption used in Bell's theorem?

 

[ueit]

I don't think you addressed the question of how to formally explicate the assumption of locality. We both seem to believe that the assumption that the evolution of our universe is constrained by local causality is the most reasonable at this time.

Bell's locality assumption isn't that separated systems evolve independently (because, obviously, observational contexts can be expanded to define ever larger nonseparable systems), but rather that (given deterministic evolution and a transmission speed limit, c) spacelike separated events can't causally affect each other within certain time intervals.

In order to model this, Bell represented the joint (entangled) state in factorable form. The problem with this is that this also represents statistical independence, which is not relevant to locality. Statistical dependence is necessitated by the experimental designs and procedures associated with the observation of quantum entanglement.

QM circumvents this problem insofar as it is a statistical theory and correctly represents the statistically nonseparable state, which neither affirms nor denies the assumption of locality. The variables involved in accurately predicting the rate of coincidental detection aren't hidden.

't Hooft's approach is to circumvent the lhv problem formalized by Bell by explicating locality in a rather less direct form than that proposed by Bell.

Superdeterminism, as far as I can tell, just refers to universe scale determinism.

And the term, free-will, is just an expression of our ignorance.

If a theory is local or not can be seen by looking at its mathematical formulation. 't Hooft's proposed theory (cellular automata) is obviously local because each cell is only affected by adjacent cells. I still do not understand what you mean by "formally explicate the assumption of locality".

The statistical independence assumption is in fact the assumption that the emission and detection events do not have a common past cause, they are not synchronized by a hidden mechanism. It has nothing to do with locality and I do not see why the negation of this assumption (statistical independence) should have any implications in regards to local causality.

 

[DrChinese]

The statistical independence assumption is in fact the assumption that the emission and detection events do not have a common past cause, they are not synchronized by a hidden mechanism.

I think it is the detector settings and NOT the emission event that are to have independence. Common emission is assumed and is present in all experimental setups except in a few exotic cases (i.e. entanglement of photons that have never interacted in the past).

 

[PTM19]

No local realistic physical theory can provide the same predictions as QM.

Bell does not rule out local realism, a theory can allow effects propagating faster then c and still be local.

1. Why do ONLY entangled particle pairs display this behavior? I would expect it to appear everywhere!

It is possible that only when you have a pair the effect is clear and easy to observe, with multitude of entanglement the effect may cancel out.

 

[DrChinese]

1. Bell does not rule out local realism, a theory can allow effects propagating faster then c and still be local.

2. It is possible that only when you have a pair the effect is clear and easy to observe, with multitude of entanglement the effect may cancel out.

Welcome to PhysicsForums, PTM19!

1. I guess most would say that by definition, anytime you have a deterministic effect propagating faster than c it is non-local.

2. Not concerned about the case where the entanglement is diffused due to a large number of particles. If superdeterminism were true, why aren't EVERY pair of particles entangled? Why is it ONLY the pairs QM predicts that are entangled? (I.e. the ones that come out of a PDC crystal.) Because QM certainly doesn't have anything like superdeterminism present in it.