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Let us suppose that inherent randomness (atleast partially) in the universe exists. By this, I mean that certain things especially in the micro world are not predictable even if on the macro scale, things can seem much more predictable in a practical sense.

As an example, let’s suppose that it is impossible to come up with a theory to explain why a particular atom decays at a specific time.

Could it then still be the case that the atom could not have decayed at another time? In other words, could the atom’s decay at that time be inevitable even if there was no law possible to explain why it decayed at that time?

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  • Insofar as necessity is glossed as involving "all possible worlds," the role of "all" there seems to dispose us towards characterizing necessity as proceeding from general laws to particular cases. However, other theories of modality might allow for particular necessitation directly, and there doesn't a priori seem to be anything too incoherent about, "X necessitates Y," even when X and Y are framed primarily in local/specific terms. Perhaps divine causation can even be characterized like so (i.e. God specifically necessitates things, not per some outside "law"). Oct 19, 2023 at 16:40
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    If they are necessary/inevitable then they are determined. That we cannot predict them or that they are not determined "by a law" is another matter. For example, omnipotent God does not have to set up "laws" to govern events, he can simply lay them out in a random sequence and make it happen.
    – Conifold
    Oct 19, 2023 at 19:58
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    It might be worth contemplating what actually is the difference between predetermined randomness and un-predetermined randomness, because if you can't put your finger on that, the question about whether it is predetermined becomes rather meaningless. Oct 19, 2023 at 20:08

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If we assume presentism or growing block universe then I don't think this is possible because even the universe doesn't "know" if it will decay at that time.

However, in a block universe we have all spacetime paths existing at the same time, in which case it is inevitable that that particular atom decayed but that there is insufficient information to any observer at that time to know that it will.

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To focus on your example about the decay of an atom:

IMO the answer to your last question is yes. But the "yes" has no weight. Many things are possible. But they remain pure speculation as long as no one comes up with a corresponding law.

According to the Copenhagen interpretation of quantum mechanics there is no law which governs the decay of a single given atom. Not only, that we do not know a law, the Copenhagen interpretation considers quantum mechanics to be a complete(!) theory concerning the laws of radioactive decay. And these laws only make statistical predictions about the outcome of experiments with single particles.

This conclusion did not convince all physicists of the time, e.g. it was the subject of several longlasting discussions between Bohr (Copenhagen) and Einstein. Neither one could convince the other.

Afterwards there were several approaches to find "hidden parameters" which determine the single event. But also this field triggered a long discussion without convincing the other party.

The fundamental parameter of the law of radioactive decay is the half-life, the duration T during which half of all atoms from a sample of radiactive atoms decay. Independently how long you wait to start the observation, the probability that half of all remaining atoms decay during the next period T is always the same, namely one. Hence radiactive atoms are not aging.

Keywords: Copenhagen interpretation, Bell's Theorem

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