I recently read a little about the Bell test (I'm not a physicist, but reasonably well educated) and I started wondering if there is a way to express the level of non-determinism as a single number given specific conditions. I'm just interested how the values would look like.

I can imagine there is a lot of variables involved. For example I can imagine that it's temperature dependent (but I don't know) and I'm pretty certain it depends on the scale. The larger the physical system the more deterministic it probably is.

I wonder if there is a way to define some common conditions under which one can calculate something like "particles behave with 71% determinism and 29% pure randomness"

Thanks in advance

Edit: I mean the part of randomness that stays even if all hidden variables were known / the purely random part that will stay if I have all information about the system I can get.


1 Answer 1


In classical physics there is so called deterministic chaos, a level of unpredictability caused by an uncertainty of initial conditions. For this case there is a number called the Lyapunov exponent that measures the rate of exponential divergence of two solutions with small differences in initial conditions. This number is the measure of unpredictability in classical mechanics.

  • $\begingroup$ I heard of deterministic chaos in machine learning, but I'm looking more for the random part which could not be predicted even if all hidden variables were known. $\endgroup$
    – evolution
    Apr 5, 2016 at 18:38

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