Can an experimental test of entanglement ever be considered complete?
Cat said:
The problem here seems to be that Bell's inequality depends on being able to set your detectors independently and also on being able to measure your particles separately. It is not at all clear that the detector settings can be regarded as independent, and it is most certainly not true that the particles are measured separately.[/url].
Cat
I do not agree with this statement, and I don't think it is represented in Bell's Theorem. I realize that locality is represented in the Theorem, I am not questioning that.
1. Suppose we set the polarizers at 22.5 degrees for one hour, and measure many event correlations. I am not concerned that the polarizer at A sent a message to the polarizer at B. I believe this is a red herring that confuses the locality issue. The observed correlation will be .8536 (ideal case of course) and we can be happy with that value as being valid in agreement with the predictions of the QM formalism.
What underlying mechanism accomplishes this is totally irrelevant to this experimental result, just as the mechanism of the double slit is not relevant to that result. In each case, the Heisenberg Uncertainty Principle is respected. That's QM!
2. If (during its measurement) the particle at A sends a message to the particle at B via a non-local communication channel which is invisible to us, then that could explain the observed results (non-local realistic). This is true whether the measuring apparatus is space-like separated or not! This is where the assumption of locality fits into the Theorem. In other words:
if you are postulating a non-local theory containing hidden variables, then Bell's Theorem does not apply at all.
3. On the other hand, the mathematical formalism of Bell's Theorem incorporates an explicit requirement for realistic (hidden variable) theories to which 2. does not apply - i.e. local realistic theories only. That requirement is the existence of a C to go along with polarizer angle settings A and B, the hypothetical other measurement that could have been performed. This leads to bounds on values that any such LR (LHV) theory can yield.
And this has absolutely nothing to do with the measuring apparatus settings at A and B. It's all about throwing C into the equation. If there is no C, it's not realistic in the first place!
Bell's Theorem essentially says that the eight permutations below add to a total probabilty of 1:
[1] A+ B+ C+ (and the likelihood of this is >=0)
[2] A+ B+ C- (and the likelihood of this is >=0)
[3] A+ B- C+ (and the likelihood of this is >=0)
[4] A+ B- C- (and the likelihood of this is >=0)
[5] A- B+ C+ (and the likelihood of this is >=0)
[6] A- B+ C- (and the likelihood of this is >=0)
[7] A- B- C+ (and the likelihood of this is >=0)
[8] A- B- C- (and the likelihood of this is >=0)
...But that there are no such predictive values for A, B, C that match QM's predictions. You don't need to do an experiment to reach this conclusion. Without moving from my armchair, I can see that all LR theories respecting Bell make radically different predictions than QM. Therefore experiments that support QM also rule out LR.
After all, the purported local counter-explanations are essentially "un-realistic" in the first place; we are told to expect MORE correlations than unentangled random chance should allow! It is the reverse that should happen.
4. It makes no sense to say that the experiment was contaminated so that entanglement "appears to occur" even though there is no actual entanglement.
That isn't really science. If it is there, where is it? What causes it? Measure it! Explain it! Why haven't we ever noticed it before? Why doesn't it show up in experiments designed to look for it? Test results don't vary when heretofor unknown local causes are eliminated as a factor, and they don't vary when sampling is eliminated as a factor. If these were really loopholes, tests would have identified this. But instead, every Bell test shows the same results, LR is ruled out by 5/10/20/30+ standard deviations.
Perhaps someone should write a paper entitled "Can an experimental test of entanglement ever be considered complete?"