In quantum mechanics, the probability, say, that a radioactive atom will decay is well defined. By the Born Rule, it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude.
But if, say, these things were unpredictable and happening for no reason, why does the Born’s rule exist in the first place? Why is it the square of the amplitude and not 1/4 or 1/8?
Secondly, why does the way this work stay constant? If for example, a radioactive atom’s decay point is truly happening for no reason, why doesn’t it just suddenly start decaying with different probabilities? It is easy to imagine this to happen, atleast in a logical sense.
But because this does not happen, does it not still indicate some level of order? If there is order, where does this come from without determinism?
I am aware that “randomness” can create order through the law of large numbers but that originally interpreted randomness as a mere function of ignorance going back to Laplace’s time. This doesn’t fully explain how or why indeterminism can lead to specific probability functions over others and why they generate particular kinds of order over others. If this can’t be explained, how are we so sure that the universe is indeterministic in the first place?