[Quark2005]

Quantum theory posits there is no distinction between atoms. Could be wrong, but QM has not been wrong yet.

My 2¢ (if anyone still cares):

Not exactly true. QM theory posits there is no distinction between particles with the same quantum numbers. For example, two free electrons in a positive spin state are truly indistinguishable.

Nuclei are a bit more complex. There can be several spin states (and thus energy levels & quantum numbers) of the protons & neutrons, for example (although still a limited number of states). This can (and will) affect decay rates; but you would have to isolate and identify which atoms had which spin states (by separation with a magnetic field, for example) to get this information. Problem is, such an apparatus would have the effect of changing some of the quantum numbers (some of the spins would "realign" with the magnetic field). There would thus be some "smearing" of the original identity of the nuclei caused by the mere fact that you are trying to isolate them - an effect that is totally unavoidable. This blurry zone is statistical in nature; one can only be sure within a statistical certainty of which original particles they are looking at. With lone neutrons (the simplest decaying "nucleus"), you have no certainty at all; with plutonium nuclei, where there are many more quantum numbers to work with, you can (in theory) separate them with less alteration to the initial identities.

If you consider large molecules, there are so many possible quantum states that you start to approach the limit of a classical (i.e. normal) system; they are almost certain to retain their "original" identity upon observation. Nuclei sort of ride that "middle zone" of being truly indistinguishable and distinguishable; they can be properly said to have a limited number of distinguishable states which can be observed on an individual basis with a limited certainty.

(Hope I got all this right; I'm a much newer player to this game than Physicist et.al. QM can really give you a headache.)

[js1138]

So returning to the original question, will two nuclei having the same spin state decay at the same time? Is there any property of an atom that predicts decay time?

[Physicist]

That's all fine. The way I think about atoms is that, while indentical particles will mix their wavefunctions, you can in practice "mark" one of a pair of otherwise identical atoms by adding or subtracting a neutron or electron. (Easier to visualize than a spin state.) Throw the two of them into a box together and their wavefunctions almost won't mix. I say "almost" because there's a finite probability the spare neutron or electron can "tunnel" from one atom to the other.

[spunkets]

"For example, two free electrons in a positive spin state are truly indistinguishable."

If they're in a free state, they can be distinguished. Consider Milliken's experiment and spacial separation. In systems, distinguishability depends on spin, as you were describing. A beam energy of electrons(Fermions) with net spin, is higher than a random spin beam. A polarized photon(Boson) beam has the same energy as an unpolarized one. That's the idea in your post.

On these threads it's common to find the belief that random processes have no cause, or that random is a cause. In this subthread, the former was the topic. Random refers to the process itself, is evidenced by the outcome and at any point in the process. If all processes in Nature weren't random, the probability of a real photon "hv" being absorbed by an harmonic oscillator would be zilch, because the linewith was zero and every trial would fail. ie. the tolerance is too tight.