That there is no finite algorithm behind, which would decide when which atom will explode.
We can test algorithms which we use to predict which atom would explode and when. The variables are part of the theory, not of the atoms. Absence of hidden variables effectively means that there is no regularity such that we could infer a law that would predict the state of an arbitrary system at time t1 with certainty* from observations made at time t0 < t1. Nevertheless any selected atom* is either going to explode or isn’t at a given time, and we can observe which was the case afterwards. Bayesianism doesn’t prohibit updating our beliefs about events after those events happened, in fact it doesn’t say anything at all about time. The “inherent randomness” of radioactive decay doesn’t make the uncertainty non-Bayesian in any meaningful way.
That said, I am afraid we may start to argue over the silly problem of future contingents and over definitions in general. The right question to ask now is: why do you want to distinguish truly random numbers from apparently random ones? The answer to the question about the quality of quantum randomness may depend on that purpose.
*) Although I know that certainty is impossible to achieve and atoms are indistinguishable, I have chosen to formulate the sentences the way I did for sake of brevity.
We can test algorithms which we use to predict which atom would explode and when. The variables are part of the theory, not of the atoms. Absence of hidden variables effectively means that there is no regularity such that we could infer a law that would predict the state of an arbitrary system at time t1 with certainty* from observations made at time t0 < t1. Nevertheless any selected atom* is either going to explode or isn’t at a given time, and we can observe which was the case afterwards. Bayesianism doesn’t prohibit updating our beliefs about events after those events happened, in fact it doesn’t say anything at all about time. The “inherent randomness” of radioactive decay doesn’t make the uncertainty non-Bayesian in any meaningful way.
That said, I am afraid we may start to argue over the silly problem of future contingents and over definitions in general. The right question to ask now is: why do you want to distinguish truly random numbers from apparently random ones? The answer to the question about the quality of quantum randomness may depend on that purpose.
*) Although I know that certainty is impossible to achieve and atoms are indistinguishable, I have chosen to formulate the sentences the way I did for sake of brevity.