Incompleteness of Bell's Theorems

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It seems rather dubious to come to any conclusion of Bell's Theorem regarding Non-Locality without a complete description of quantum spacetime. The fundamental tenet of Non-Locality is that 'distant' physically isolated systems are correlated. However, distance is only well-defined in terms of a Metric Space. I argue that if we do not have a complete description of quantum spacetime then we do not have a suitable metric space to come to the conclusion that these physical systems are indeed 'distant'. This necessitates that quantum spacetime must have more structure than Minkowski spacetime. The apparent paradox associate with Bell's Theorems emerges from the implicit assumptions of the underlying topology of spacetime. Indeed it is possible that the correlation of these physical systems is fundamentally dictated by a much more rich topology on the planck scale.
 

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  • #2
Nugatory
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The apparent paradox associate with Bell's Theorems emerges from the implicit assumptions....
Where in Bell's proof of his theorem do you see such an assumption being used?
 
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Where in Bell's proof of his theorem do you see such an assumption being used?
I have no qualms with the proof itself but the conclusions drawn from it.
 
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Bell proved that either correlations can happen for no reason or there exists superluminal signals, which would violate causality. We have not experimentally found these superluminal signals and therefore until we do we assume that correlations can happen for no reason. My quarrel is that there is an implicit assumption of how information propagates in spacetime that is required to come to these conclusions. This implicit assumption is precisely the structure of quantum spacetime. For all we know this structure could be an entire network of quantum wormholes in which no superluminal signal is required.
 
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atyy
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This necessitates that quantum spacetime must have more structure than Minkowski spacetime. The apparent paradox associate with Bell's Theorems emerges from the implicit assumptions of the underlying topology of spacetime.
Bell's notion of local causality does indeed assume a background classical Minkowski spacetime, or at least a background classical pseudo-Riemannian spacetime of known topology. The application of the Bell inequalities to infer that there is no theory obeying relativistic causality that can explain the correlations predicted by quantum mechanics is not affected by the possibility you raise, since we can define the predictions of quantum mechanics on such a spacetime. On the other hand, the application of the Bell inequalities to real experiments to infer that Nature itself is nonlocal may be affected by such considerations, where it is only one of many loopholes.
 
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DrChinese
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I have no qualms with the proof itself but the conclusions drawn from it.
The usual conclusion is: No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

What's problematic about that? If there are hidden variables, they cannot be local to the quantum object. Even with your hypothesis of spacetime, any hidden variables would not be considered local. Local meaning that only "nearby" (relative to c) influences can impact the outcome.

Also: please be aware that the state of the art in Bell tests has come a long way. It is possible to entangle particles that a) have never existed in each others' light cones; b) have never even existed at the same time; and c) are entangled AFTER they no longer exist. All of these situations are consistent with standard QM but inconsistent with many traditional views of either locality or realism.

So make of it what you will, we don't have a complete description of spacetime (maybe) or we don't have a complete description of "something" (not sure what). We simply know a "classical" perspective won't cut it. :-) That has to be good for something!
 
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The problem is the notion of what is considered "nearby" to the quantum object. The measure we use is a minkowski metric, which assumes that quantum spacetime is described by the same metric. I appreciate where Bell's tests have taken us insofar as we are capable of entangling particles that have never previously interacted. Although I do not see the meaningfulness of saying two particles that no longer exist can be entangled. What I am trying to say is that non-locality should be a consequence of the structure of quantum spacetime.
 

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