I think I understand the fundamental result about the Bell inequality. From my statistician’s perspective, however, I really mind only about the (statistical) distribution of the outcomes of random generators. Which means a sequence that stands testing by die-hard filters like Marsaglia’s battery. This is the only reason I have been posting entries against “true” randomness claims. Once again, those criticisms are only pertaining to the fit to a distribution. Complete unpredictability and causality vs. non-causality escape my realm and I have no statistician’s opinion to express!

]]>In particular, when you consider radioactive decay, the process appears random from a statistical point of view, but you cannot rule out the existence of a hidden variable whose knowledge would make the process deterministic. The violation of a so-called “Bell inequality”, however, is incompatible with any such (local) hidden variable model for your process, meaning that no amount of knowledge could ever allow you to predict with certainty the outcome of your experiment. This is the kind of “randomness” considered by Pironio et al.

I’m curious: do these kinds of consideration make any sense to a statistician? ]]>

This sounds like very old-fashioned (Laplacian) determinism… Anyway, I agree that we are not talking of the same think when we consider randomness! Probabilistic phenomena are found in other parts of physics, like radio-active decomposition, and while they can be explained at a certain level, hence are “predictable”, they remain random in the probabilistic sense that they can be characterised by a probability distribution (e.g., Poisson). To call a single number random thus does not make sense in this perspective.

]]>The idea is that one can prove that a random process was “truly” random (but possibly biased) in the sense that the outcome of the experiment could not have been known (even by God) before the experiment was performed.

In my opinion, it’s quite an amazing feature of Nature that such a claim can be proven.

You could argue that flipping a coin does the same thing, namely that you cannot predict beforehad the outcome, but in principle you could (if you were able to model precisely enough your coin, the way you threw it, etc). In fact, the same applies for any usual random process: with enough computational power, you would be in principle able to predict its outcome.

In this paper, the authors show that, even in principle, the outcome of the experiment based on a violation of a Bell inequality is not predetermined.

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