Using the term "determinism" un the philosophicall sense (not in a matemáticas sense) ....Is the decay of an atom a deterministic event?

I'm not sure what the difference between the philosophical and the mathematical sense of "determinism" is supposed to be, but I think that the answer will be the same in any case. And that answer is: it depends on how you think quantum theory should be understood.

On what we might describe broadly as the "orthodox interpretation" of quantum theory, the answer is no: the decay is not a deterministic event. Roughly put, this means that the state of the world before the decay doesn't determine whether the atom will decay. There are some complications here about relativity and about so-called entangled states, but we can leave them aside. On this way of looking at quantum theory, sometimes the "wave function" or "quantum state" changes unpredictably and discontinuously, and these changes are genuine chance events. Radioactive decay is a special case.

According to Bohmian mechanics, the most important of the so-called "hidden variable" views, quantum systems are thoroughly deterministic. What happens in the quantum world is completely fixed by the underlying configuration of particles and by the theory's equations. Radioactive decay will be unpredictable from our perspective, since the way the equations work implies that we will never be able to assemble the information we'd need to make the predictions. Nonetheless, there's no chance in the process; the configuration of the particles and the laws of nature settle whether and when decays will take place.

There's yet a third alternative: the "Many Worlds" or Everettian interpretation. This view is also deterministic. What makes it striking is that if it's correct, the universe is continually branching. If we observe a radioactive decay, there's another branch of the universe on which no decay happened. That branch is every bit as real as ours, but we don't have any access to it. The argument for the branching isn't direct observation of the branches; it's that according to the Everettians, the detailed version of the view makes the best overall sense of quantum theory.

There are other interpretations that we haven't mentioned, and what I've called the "orthodox interpretation" is shorthand for several quite different views, though all agree in understanding quantum mechanics indeterministically. There are yet other interpretations that we haven't described, but the point remains: there isn't any simple matter-of-fact answer to your question. Quantum mechanics is a theory that we know how to apply with exquisite precision. What exactly the world is like if quantum theory is true, however, is another matter and a controversial one at that.

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