Is the freedom-of-choice loophole valid in quantum entanglement experiments?

[little1406]

TL;DR Summary

Why do we have to rotate the polarizers at all? If we set one at 45 degrees w.r.t. the other, doesn’t the >50% coincidences prove quantum non-locality.

The freedom-of-choice loophole to explain the results of quantum entanglement experiments says that somehow a non-random manipulation of the two polarizer angles could reproduce the prediction of Bell’s inequality without quantum non-locality. But it strikes me that the experiment could be conducted with polarizers fixed at 45 degrees w.r.t. each other. Classically we expect exactly 50% coincidences but quantum entanglement of the particles will produce >50% coincidences. If this is true, then doesn’t that invalidate the freedom-of-choice loophole??

(my apologies if this seems stupid. It took me years to really grasp what’s surprising about the results of these experiments.)

 

[PeroK]

I think the loophole requires that nature's local variables conspire (in each and every experiment) to produce the same results as QM. If QM says 75% and the experiment gives 75%, then the counterargument is that it just so happens that the particles were configured that way. Just so that the rules of QM appear to be obeyed.

Personally, I don't understand how anyone can take this seriously, but apparently some people do.

 

[nicholas_eng]

If one assumes that the universe is deterministic (i.e. the configuration of the universe is a single one), then all of the results of all experiments are determinate. That means that all future measurements have a single, definite outcome. Being humans, we have the limitation of only remembering the past, so we can't possibly know/remember the outcome of experiments until they are in our past. But that doesn't mean that measurements performed in our future won't have single, definite outcomes. That is a pretty uncontroversial version of "determinism", which is hard to refute.

A "stronger" version of determinism claims that all future outcomes/configurations should depend ONLY on the past, such that complete knowledge about the configuration (of a system, or the universe) in an initial time $t_0$ implies in complete knowledge for any $t > t_0$. This version of determinism is much harder to defend, and it's safe to say that it has been refuted by the (inescapably) probabilistic nature of quantum mechanics.

When Bell (and also the authors of every major no-go theorem) assume "freedom of choice", they are tacitly excluding determinism. But not the "strong" already-refuted determinism of my second paragraph. They are excluding the uncontroversial determinism of the first paragraph. Because if the universe has a definite configuration, then the experimentalist (which is a part of the universe) also has a definite configuration, and the measuring apparatus also has a definite configuration, etc. As long as this version of determinism remains unrefuted, there will be a "freedom of choice loophole", because if the universe does work in this deterministic way, you can't assume "freedom of choice".

Alas, for science in general, it is imperative to look at the past in a different way than you look at the future. One of the major roles of physics is to make predictions after all. Predictions about the future. So a fundamental part of physics is thinking about the future as something open, "not set in stone", that we have to find out; and the actions of the experimentalists as the "controllable" parameters to find things out. The assumption of freedom of choice is an important one in that sense, and I think Bell's theorem is one of the most impressive and beautiful results in physics.