Passion at a distance of 30 sigma?

Richard Gill,
University Utrecht, Netherlands

Exploring the hidden assumptions of Einstein, Podolsky and Rosen (1935) and adding a brilliant new twist of his own, Bell (1964) proved that local realism and quantum mechanics are imcompatible. The purpose of the Aspect et al. (1982) experiment was to prove that the real world chooses the side of quantum mechanics. Most agree that they succeeded. Now, Bell's theorem talks about probabilities (or correlations, or expectation values), while in the real world we look at relative frequencies (or averages) based on a finite number of repetitions of a random trial. Moreover, the repetitions in the Aspect experiment come from one location over a period of time, not from millions of different locations simultaneously. This means that there is potentially a memory loophole, and a finite statistics loophole, alongside the more well-known loopholes to application of Bell's theorem (detector efficiency, ..). The key feature of the Aspect experiment, implemented so far only by Weihs et al. (1988), is that polarizer settings are repeatedly chosen at random. I will show that this randomization effectevily closes both the now loopholes described above. The main tool will be the martingale Bernstein inequality, saying that large deviations of sums of a special kind of dependent variables are no bigger than in the case of independence. The main ideas go back to some more landmark papers of 1935 from the fields of statistics and probability respectively, perhaps not so well-known among physicists: Fisher's (1935) book on the design of experiments, and Levy's (1935) paper on martingales.