Agree re (5), as I indicated in earlier post. But, No. Not because of experimental results (I'm not sure where that idea comes from, but will look and correct it). They are true because of my theory. This truth is "proven" when I show that "the mess" in (5) reduces to the simplicity of (6). That's when I claim my theory is vindicated because it agrees 100% with QM.

Perhaps it was not clear what I was saying. Everything in (5a)-(5d) is independent of experiment, EXCEPT for the last equality in each one where you say that all the other things are equal to [imath]\cos^2[/imath] of something. Only that last equality depends on experiment (or, if you prefer to think of it this way, on QM theory which is supported by experiment). The particular fact that [imath]\cos^2[/imath] is involved cannot be derived from your theory up to that point, because so far you have created a system of hidden variables and a system of equivalence classes, but nothing to actually say how they are related. Naturally, that part has to come from QM theory and experiments.

Are you misspeaking here? The ECs are scattered right throughout (5); (6) shows that my use of everyone of them in (5) is consistent with QM.

I don't believe I am misspeaking. I must refer you to the pizza parlor example that I have presented below, which explains why equations (5) can show equation (6) without actually being consistent with QM.

Bell's theorem refuted wrote:Now: This a serious charge -- in many many fields. So thanks for raising it. BUT am I guilty?

I am assuming the validity of local realistic hidden-variables. Bell did the same. I show that they yield results consistent with experiment. Bell did not show this.

Is not my approach OK for theoretical physics? Don't we make hypotheses (my assumptions) and show that experiment confirms them?

What Bell actually did was: he assumed the existence of local hidden variables, and then followed a chain of reasoning until he came to a result that contradicted experiments.

Now, what you have done is: you assumed the existence of local hidden variables, and then followed a chain of reasoning until you came to a result that does not contradict experiments.

Superficially, these seem to be similar logical "moves," but they are actually completely different.

Let me illustrate Bell's reasoning first:

1. Assume, for purposes of contradiction, that local realism is true.

2. (Theorem). IF local realism is true, THEN all experimental results must conform to Bell's Inequality.

3. Therefore (from 1 and 2), all experimental results must confirm to Bell's inequality.

4. There exist experimental results that do not conform to Bell's inequality.

5. 3 and 4 are contradictory.

6. Therefore, our assumption (1) must have been false. That is, local realism is false.

Now here is (as closely as I can reconstruct it) your reasoning:

1. Assume that local realism is true.

2. IF local realism is true, THEN we can create these equivalence classes of hidden variables.

3. IF these equivalence classes of hidden variables exist, THEN they must satisfy equations (5a) through (5d) (this is because of the experimental data).

Now, here is where the reasoning stops making sense to me. One possible way to continue from here would be to construct equivalence classes that actually DO satisfy the equations (5a) through (5d). (However, you will not be able to do this. It is impossible.) If you could do that, then you would have created a hypothesis that is confirmed by experiment; namely, that the behavior of the particles is described by hidden variables in those equivalence classes. However, as you have not created any such equivalence classes (and you won't be able to, because it is impossible), you don't actually have a hypothesis.

Let me explain why with an example. I heard this from a quantum physicist.

Here is the setup. In my city there is a certain pizza parlor with three kinds of pizzas (pepperoni, cheese, and mushroom). They have a very small oven -- in fact, the oven can only hold up to 2 pizzas. I have observed that if I go into the pizza parlor and order a pizza, fully 3/4 of the time a worker immediately goes over to the oven, opens it, and (without showing me the contents) takes out a pizza of the type I ordered. (This observation plays the role of experiment; or, alternatively, of existing QM theory.) What is going on here?

Well, I have a theory which we will call the

hidden variable theory of the pizza oven. The theory says that the pizza oven has a "hidden variable"; namely, the pizzas inside the oven. In my theory, this hidden variable can fall into one of 6 mutually exclusive equivalence classes (PP, PM, PC, MM, MC, CC). Which equivalence class is governed by processes unknown to me.

I also have experimental evidence. The evidence says that the probability of mushrooms is 3/4. In the hidden variable theory, this means that P(PM or MM or MC) = 3/4. Similarly, the probability of pepperoni is 3/4. That is, P(PP or PM or PC) = 3/4. Finally, P(PC or MC or CC) = 3/4. Now, these three equations I have just given are the equivalent of your equations (5a) through (5d). In my pizza parlor example, there are only 3 different measurements that can be performed, whereas in your case there were more. This is why your equations were slightly more complicated than the ones I have here.

From these equations I can easily conclude that P(I get the pizza I ordered) = 3/4, beautifully matching the experimental (or QM-theoretical) predictions. This is the equivalent of your equation (6).

From this, should I conclude that I have confirmed (or at least, failed to falsify) the hidden variable theory of the pizza oven? No! In fact, the hidden variable theory of the pizza oven is bogus. If I add my three probability equations together, I find that[math]P(PP) + P(MM) + P(CC) + 2(P(PM) + P(MC) + P(PC)) = {9 \over 4},[/math] or, after some algebra,

[math]P(PP) + P(MM) + P(CC) + P(PM) + P(MC) + P(PC) = {9 \over 8} + {1 \over 2}(P(PP) + P(MM) + P(CC)).[/math] But the left-hand-side of that equation is, in my model, 1. So 1 is equal to 9/8 plus something positive, which is a contradiction. In other words, the hidden variable theory of the pizzas is WRONG, despite the fact that I was able to "deduce" the experimental results from my theory just as you were.