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What mechanism decides when an unstable nucleus decays? [...] Let me rephrase that question so: "Given some initial number of (otherwise equal) objects, and having measured the sequence of their subsequent decays (if any), what can we conclude about the mechanism, or "barrier", which had prevented them from each having decayed/disintegrated right ...

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Your question addresses a general principle in quantum mechanics. If we have an initial state $i$ and a final state $f$ then we can calculate the probability of a transition from $i$ to $f$, but this is only a probability - we cannot say when the transition will happen, only the probability that it will happen in some time interval. This isn't because we ...

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As far as we know, nuclear decay is truly random, that is, random in the quantum mechanical sense. That is, when you observe the system, there is a probability that you will see the decay products rather than the original nucleus, because the wave function of the system is a superposition of the parent nucleus state and the daughter nucleus state (+alpha ...

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From my perspective quantum mechanics is deterministic. It gives us a set of rules for calculating quantities that we can observe. The outcomes (probability distributions) are uniquely determined by the initial conditions. This has been borne out by experiment for sufficiently simple systems. Philosophically you might argue differently. Because quantum ...

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