Justo wrote:minkwe wrote:Justo wrote:minkwe wrote:
If you disagree explain why. If you agree then we can proceed.
I disagree. Under the conditions you described, all we know is that
There are no reasons that justify the upper bound should be equal to 2.
Perhaps you did not understand it. For the first case which you agree to, we have 4 experiments each with no restrictions whatsoever, each measuring pairs of results and each calculating E(a,b) for their set of settings. For that experiment, you already agreed that their results will never exceed 4, which is the correct answer.
Now we move to a different scenario in which we again have 4 experimenters again with no restrictions except each is measuring just a single stream of N particles at one setting. From their results which we can place on an Nx4 spreadsheet, we can calculate E(a,b) for each of the setting pairs above. And for this scenario, their results will never exceed 2. Do you disagree with this? If you still disagree, I can show you the proof but I'm hoping it's so obvious that we don't have to waste time doing it.
Note when I say "will never exceed", I mean not even by experimental error. So Heinera's complaint is not only irrelevant it is unfounded. The results are mathematically bounded above by that value, not statistically. So it is impossible to exceed it under any circumstances. That is the meaning of upper bound.
Still I desagree that QM predics a bound of 2 under those conditions. I would agree that the hidden variables prediction is bounded by 2.
I'm not asking you about QM specifically and reference to hidden variables is actually irrelevant. Remember I said already that there are no restrictions on types of particles or how the data are generated. I'm asking generally about what the results of such an experiment can show. And I'm claiming that NOTHING (QM or not) can produce a result that exceeds 2 in that scenario. It is mathematically impossible.
If you disagree, can you give me a single row of a such a spreadsheet that exceeds 2. In other words give me 4 values corresponding to the settings that will produce a result above 2? You can use whatever method you like to obtain the 4 values, even QM. No restrictions there.