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As an example of how far things have come post Bell/Aspect, here is a just announced experimental test which limits any future expectations one might have on "completing" QM:
An experimental test of all theories with predictive power beyond quantum theory, Terence E. Stuart, Joshua A. Slater, Roger Colbeck, Renato Renner, Wolfgang Tittel (2011)
Abstract:
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"According to quantum theory, the outcomes of future measurements cannot (in general) be predicted with certainty. In some cases, even with a complete physical description of the system to be measured and the measurement apparatus, the outcomes of certain measurements are completely random. This raises the question, originating in the paper by Einstein, Podolsky and Rosen, of whether quantum mechanics is the optimal way to predict measurement outcomes. Established arguments and experimental tests exclude a few specific alternative models. Here, we provide a complete answer to the above question, refuting any alternative theory with significantly more predictive power than quantum theory. More precisely, we perform various measurements on distant entangled photons, and, under the assumption that these measurements are chosen freely, we give an upper bound on how well any alternative theory could predict their outcomes. In particular, in the case where quantum mechanics predicts two equally likely outcomes, our results are incompatible with any theory in which the probability of a prediction is increased by more than ~0.19. Hence, we can immediately refute any already considered or yet-to-be-proposed alternative model with more predictive power than this. "
Conclusion:
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"In conclusion, under the assumption that measurements can be chosen freely, no theory can predict measurement outcomes substantially better than quantum mechanics. In other words, any already considered or yet-to-be-proposed theory that makes signicantly better predictions would either be incompatible with the experimental observations presented herein, or be incompatible with our assumption that the measurement parameters can be chosen freely. While the former is true, for example, for local hidden variable theories (as already pointed out by Bell [2]) or for the Leggett model [4], the de Broglie-Bohm theory [29, 30] is an example of the second type|the theory cannot incorporate measurement parameters that satisfy our free choice assumption."
This is not a Bell test, and uses different logic to achieve their conclusions. They claim that dBB type theories are incompatible with freely chosen measurement parameters. Enjoy!
-DrC
An experimental test of all theories with predictive power beyond quantum theory, Terence E. Stuart, Joshua A. Slater, Roger Colbeck, Renato Renner, Wolfgang Tittel (2011)
Abstract:
=======
"According to quantum theory, the outcomes of future measurements cannot (in general) be predicted with certainty. In some cases, even with a complete physical description of the system to be measured and the measurement apparatus, the outcomes of certain measurements are completely random. This raises the question, originating in the paper by Einstein, Podolsky and Rosen, of whether quantum mechanics is the optimal way to predict measurement outcomes. Established arguments and experimental tests exclude a few specific alternative models. Here, we provide a complete answer to the above question, refuting any alternative theory with significantly more predictive power than quantum theory. More precisely, we perform various measurements on distant entangled photons, and, under the assumption that these measurements are chosen freely, we give an upper bound on how well any alternative theory could predict their outcomes. In particular, in the case where quantum mechanics predicts two equally likely outcomes, our results are incompatible with any theory in which the probability of a prediction is increased by more than ~0.19. Hence, we can immediately refute any already considered or yet-to-be-proposed alternative model with more predictive power than this. "
Conclusion:
=========
"In conclusion, under the assumption that measurements can be chosen freely, no theory can predict measurement outcomes substantially better than quantum mechanics. In other words, any already considered or yet-to-be-proposed theory that makes signicantly better predictions would either be incompatible with the experimental observations presented herein, or be incompatible with our assumption that the measurement parameters can be chosen freely. While the former is true, for example, for local hidden variable theories (as already pointed out by Bell [2]) or for the Leggett model [4], the de Broglie-Bohm theory [29, 30] is an example of the second type|the theory cannot incorporate measurement parameters that satisfy our free choice assumption."
This is not a Bell test, and uses different logic to achieve their conclusions. They claim that dBB type theories are incompatible with freely chosen measurement parameters. Enjoy!
-DrC