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In classical mechanics, one can keep track of individual particles. For example, if you have two particles in a system, you can color these particles red and blue and follow them. Notice this, for classical mechanics, dynamical variables are $(q_i,p_i)$ with $i=1,2$. There is nothing classical mechanics that prevents you from specifying more variables e.g ...

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When you say "improves the reliability", well that is not clear at all, because you have reduced your sample size and possibly introduced an (unknown) bias. Median filtering is typically used where you do not fully understand the noise properties of your sample and where there may be cases of results that are way out from the expected result because of rare ...

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Yes, it is a statistical average in the sense that the measured half life will approach a single value of a true half life if you do lots of measurements. In other words, if you did the experiment many, many times you would find that on average you had 4 particles left after a half-life had passed. For any individual experiment, the results would vary. ...

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Half life is, by definition, the amount of time until half of an infinitely large sample would decay. That's precisely equivalent (according to the frequentist interpretation of probability, if that matters to you) to the time until an individual particle's probability of decay reaches one half. The half life is a theoretical quantity that doesn't depend on ...

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