[effie]

> there are no hidden variables such that a particle really took only one path to a point and we just don’t know which one it was.

We don't know that. It is a statement of your belief in such interpretation of quantum theory.

But I wasn't suggesting hidden variables predict which path will be taken - that is a different idea. I admit my description was somewhat confusing. My point is that retrodiction of trajectory is much easier than prediction of trajectory, because of records of the past. In other words, past is constrained by existing records of the past, while future is not constrained by records of the future, because those do not exist yet.

This retrodicted past is still loaded with uncertainty stemming from the records having uncertainty, and is speculative and not experimentally testable, of course.

> It really did go through all of them. All the ones that are consistent with the current state of the system.

This is also a speculative statement that is experimentally untestable. And I agree it is consistent with quantum theory, if we add "...and consistent with records of the past". So both stances are just an interpretation of what is going on, there is no experimentally testable idea here.

[fallingfrog]

>We don't know that. It is a statement of your belief in such interpretation of quantum theory.

No, Bell’s Theorem conclusively proved it.

From Wikipedia: “To date, Bell tests have consistently found that physical systems obey quantum mechanics and violate Bell inequalities; which is to say that the results of these experiments are incompatible with any local hidden-variable theory.”

[effie]

Bell's Theorem does not prove that. It is a theorem itself, so this theorem has been proven using quantum theory and other assumptions in Bell's paper.

In the quote, notice "Bell tests...have consistently found" and the word local. So not the Theorem, but the "Bell test" experiments' results, when interpreted using theorems like the Bell theorem and similar, show nature manifests non-local behaviour. They do not prove your belief that hidden variables do not exist.

More details on this:

http://www.scholarpedia.org/article/Bell%27s_theorem#Missing...

Also, I recommend using more reliables sources than Wikipedia to argue a point about physics. It is not a reliable source, even though it is useful for discovery and occasionaly is correct.