In principle limitations of hidden variable theories

[mjpam]

"In principle" limitations of hidden variable theories

I think the whole issue of determinism is really over-hyped as well. People forget to distinguish between "determinism" and "predictability". The fact that a theory is deterministic doesn't mean that it's predictable - even in principle, because the theory can limit (even in principle) what you can find out about the initial conditions of the system. deBB being an example of this.

Does this mean that the "hidden variable" is the factor the knowledge of which is limited in principle?

What I am wondering about is to what extent such factor can be said to exist if they cannot be know in principle.

I'm sorry if the question is ill-formed but, at this point, I'm not sure how to phrase it exactly. Hopefully, some attempts at answers to what people think I mean will help me pose my question better.

 

[mjpam]

Is my question too poorly posed for a meaningful answer?

 

[Pio2001]

Does this mean that the "hidden variable" is the factor the knowledge of which is limited in principle?

I don't know about interpretations where there is a factor that exists, but cannot be known, even in theory.

I've heard about speculations about information and entropy : some events may not be observable because recording their information would violate the second principle of thermodynamics.

 

[MrHigh]

hidden variable theory is not always present. one can show that in some situations there isn't a hidden variable that contain the sense of the lack of information. One example of that is the bell theorem (http://en.wikipedia.org/wiki/Bell's_theorem). In there you can see a lot of detalis... but i think you might get interisting is the starting point of the theorem:

"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."

 

[Demystifier]

hidden variable theory is not always present. one can show that in some situations there isn't a hidden variable that contain the sense of the lack of information. One example of that is the bell theorem (http://en.wikipedia.org/wiki/Bell's_theorem). In there you can see a lot of detalis... but i think you might get interisting is the starting point of the theorem:

"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."

Why so many people miss that crucial word "local", even when they correctly quote it?

 

[DrChinese]

"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."

This should make it clear that a deterministic theory - which also respects locality - cannot coexist with QM. This is in direct contradiction to the quote by alxm. Clearly, whether you can know the initial conditions or not is irrelevant. There are no hidden variable value sets that explain Bell test results.

 

[MrHigh]

This should make it clear that a deterministic theory - which also respects locality - cannot coexist with QM. This is in direct contradiction to the quote by alxm. Clearly, whether you can know the initial conditions or not is irrelevant. There are no hidden variable value sets that explain Bell test results.

thanks to make clear what i tried to say.

 

[mjpam]

I think I may have conflating things that shouldn't have been conflated. Namely, the wave mechanics of the transactional interpretation with hidden variables.

 

[Hurkyl]

This should make it clear that a deterministic theory

Hidden variable != Deterministic

 

[Demystifier]

Hidden variable != Deterministic

There are actually TWO quite different DEFINITIONS of hidden variables:
1) Deterministic causes of apparently random quantum events.
2) Objective properties (that correspond to observed phenomena) which exist even without measurements.

The Bell theorem actually excludes nonlocal hidden variables of the type 2. The type 2 hidden variables do not need to be deterministic. For example, if you think that a wave function is an objectively existing entity which randomly collapses when a measurement is performed, then this is also a nonlocal nondeterministic hidden variable theory. For that reason, to make this point more explicit, it is frequently said that Bell theorem actually excludes LOCAL REALITY (rather than local "hidden variables").

 

[DrChinese]

Hidden variable != Deterministic

I would say by definition they are not the same. Otherwise, the words would be synonymous, and they are not.

However, when you look at what alxm is saying, you can see that determinism is excluded even when there are prior states whose values are unknown. That is simply because there are no prior states which local-deterministically lead to Bell Test results.

I would agree with Demystifier's designation of 2 different styles of defining HVs and his saying that strictly Bell addresses type 2. However, I think it becomes clear pretty quickly that the same line of reasoning excludes type 1 as well. How do I know? Because no rule set respecting locality can be constructed for his type 1 that yields results consistent with QM. So you just come back to my original statement anyway. Which is that alxm is not correct to assert that local determinism is viable.

 

[Demystifier]

The Bell theorem actually excludes nonlocal hidden variables of the type 2.

Now I have noted a misprint, so let me correct myself. The correct statement, of course, is:
The Bell theorem actually excludes local hidden variables of the type 2.

 

[Pio2001]

I think I may have conflating things that shouldn't have been conflated. Namely, the wave mechanics of the transactional interpretation with hidden variables.

They are not incompatible. Especially since the transactional interpretation is non-local.

 

[mjpam]

They are not incompatible. Especially since the transactional interpretation is non-local.

OK, but my OP was more about whether forward-in-time and backward-in-time waves are observable independently of one another. I don't really have a stake in which interpretation of quantum mechanics is correct, but I was wondering if certain interpretations posit phenomena that are in principle not observable.