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I know there are similar questions, but I don't think they address exactly this question.

Radioactive decay is a truly random process, according to physics. We believe that there is no hidden particle or cause that we have not discovered yet that governs particle decay. On the contrary, computer generated "random" numbers follow a deterministic rule, and are not truly random.

If one did not know the rules behind computer generated "random" numbers, may believe they are truly random, since it may be very hard to understand the rule.

How can be sure that there are no yet undiscovered physical laws that would explain away the supposed randomness of the radioactive decay?

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    $\begingroup$ We are not sure, but it's probable. Quite highly probable. Because, it follows the rules of quantum mechanics, and by definition, it is purely probabilistic. You can throw out probability if you believe in hidden variable theories, but I guess they still haven't made much of an impact. $\endgroup$ – Yuzuriha Inori Mar 24 '18 at 14:57
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    $\begingroup$ You'll find on the internet advice to not use various classes of PRNGs for certain purposes. That's because those purposes are effectively tests that can expose the pattern in that class of PRNGs. For example, throwing random points in two-dimensions (i.e. ordered pairs) will expose correlations between successive numbers in linear congruent generators. $\endgroup$ – dmckee Mar 24 '18 at 21:37
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The theoretically derived statistical distribution for the radioactive decay, using the formalism of Quantum Mechanics (QM), which is intrinsically probabilistic, agrees well with empirical results.

So, first we have to acknowledge that QM is able to explain the radioactive decay observations, just as it is able to explain every other phenomena at the micro level.

If you now seek a deterministic law underlying radioactive decay, then it suggests that there should also be a deterministic explanation for all other phenomena for which quantum mechanics has been successful.

But attempts to construct such local "hidden variable" theories have not been successful in reproducing all the successes of QM, and a large class of them have already been ruled out by experiments (testing Bell type inequalities).

In summary, QM, with its intrinsic uncertainty, is still the best theory we have of the micro world. Is QM the last word? Maybe not. Maybe one day we will find a deeper underlying theory, but it would likely be even further removed from our classical intuition.

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