uncool

My apologies - I mistook your enthusiasm for that of the newly-"initiated". Good on you for keeping up that enthusiasm! I would say that even in the OP, the thread should clearly have been at the level of Newton's laws, and simple integration. I think that there already as a problem just with intrinsic vs extrinsic properties, as I plan to explain.

Unified Field: how much of standard physics do you accept? Do you accept Newton's laws? Newtonian gravity (as a nonrelativistic approximation)?

Mordred - I'm guessing that you just recently learned a lot of relativity, and really liked it. Which is good, but it's not the level appropriate for this conversation. This should be possible to discuss just using Newton's laws and Newtonian gravity - and probably very little in the way of integration.

Planck's "number" isn't really a number. It has units; your question is analogous to asking "Is 1 meter rational?"

Ok.

It is not that you must agree with the premises. It is that you must understand them in the first place. It is that if you wish to reject what experts are saying, you need to know what they are saying in the first place.

I wouldn't be happy yet. Here's the thing: your rejection of those assumptions is precisely where a mathematical understanding of the physics comes in. Understanding the difference between those two integrals is precisely where you must learn the mathematics behind both classical and quantum mechanics.

No, you hadn't, because there is a difference between rejecting the theorem and rejecting the application of its assumptions. I do not mean it as a critique. I mean it as an attempt to make your position clearer. Now that it is clear you reject the application of the assumptions of Bell's theorem - namely, the integrals - your position is far clearer.

It seems to me that you have not because you have not followed your own argument to its natural conclusion. Your argument seems to be entirely related to rejecting the conclusion of Bell's theorem to your experiment; if you accept the mathematical validity of Bell's theorem, then you must reject the application of the assumptions of Bell's theorem to your experiment.

I strongly disagree; this is an attempt at precision, something that you - of all people here - should welcome. It is an attempt to get at the heart of what you think the problem is - the precise place where you think philosophy and the current descriptions of quantum theory (including entanglement) disagree.

I see no general claims in that question. "something that runs counter to that" could mean a counterexample. To be more explicit: you seem to be saying that you think your example fails to be described mathematically by the systems described in Bell's theorem. Correct?

Then we are back to where I started. Namely: You seem to be asking for a justification for the assumption - why, philosophically, should a classical theory require such a mathematical description - and seem to think you have something that runs counter to that. Correct?

I never said that it did. In fact, that was the point of one of the first questions I asked you. Then we have gotten exactly to the point of the question I asked you. You seem to agree (or at least, are refusing to dispute) the mathematical correctness of the theorem - but instead, whether the mathematical assumptions of the theorem match physical reality (or alternatively, what is meant by a "classical (local) theory"). Which is exactly what I asked with my integral question.

I am not asking you to analyze its mathematical structure. I am asking you only whether you accept the mathematical proof in it. Either the proof is valid, or it is not; whether that proof is being applied to a specific example or not is irrelevant. So I ask you again: do you accept that the proof is valid? Edit: As a note, you are free to have an answer along the lines of "I don't know whether the proof is valid; I think there is a problem with the conclusion for this example, and I don't know whether that problem appears in the assumptions or in the proof."

So to be clear: do you accept the mathematical proof of Bell's theorem? Your problem is with the assumptions of the theorem, not with the proof itself?

That's not how theorems work. If there is a special case where the theorem doesn't work, then it's not a theorem (assuming the consistency of mathematics as a whole). There are two possibilities. Either 1) you doubt the proof of the theorem, or 2) you doubt that the hypotheses of the theorem apply. Do you know which one?

What, exactly, do you mean by "reject [Bell's theorem]"? Do you accept that the theorem - the mathematical theorem - has been proven? I was guessing that you were doubting the relationship between the mathematics and the physics, because if you accept both the mathematics and the relationship between the mathematics and the physics, then the only consistent possibility is to accept the physics.

To clarify a little bit: in the proof of Bell's no-go theorem, the following assumption is made: A classical (local hidden variable) theory is required to measure the expectation value of a random variable X according to [math]\int X(\lambda) p(\lambda) d \lambda[/math], according to some (hidden) probability measure p. On the other hand, a quantum theory is required to measure the expectation value of a random variable X according to [math]\int \langle \phi | X | \phi\rangle[/math], according to Bohr's rules. The theorem is then that there is a limit to the outcomes from any classical theory that doesn't appear for a quantum theory, as defined there, and therefore (since our experiments match Bohr's rules) that a quantum theory is necessary (or rather, a classical theory is insufficient). You seem to be asking for a justification for the assumption - why, philosophically, should a classical theory require such a mathematical description - and seem to think you have something that runs counter to that. Correct?

Here is part of the problem. You are making statements that could have multiple meanings in the theory, some of which are correct, some are not. Do you mean that both photons have a definite state (that is simply unknown), each time the experiment is run? Because if so, this is false, and in fact is exactly hat Bell's Theorem disproves.

How does this explain the correlations whatsoever?

Why not?

I do not believe that the version matters for my question. Does superdeterminism address your concerns?

Dalo, I am curious. Have you heard of superdeterminism?

There is one further main point, and that main point is the center of Bell's theorem. That difference is, approximately, that for a classical (non-quantum) theory, that certain probabilities must add in certain ways.

As you yourself said: "saying it is not enough. You have to show it. " If you don't have any understanding of linear algebra, you will not understand the way that waves can add together, and therefore what it is that a polarizer is doing.