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Let's suppose I'm in the lab and I claim that I can predict more than QM can, specifically, I can predict exactly at which moment in time a particle decays. You don't believe me (naturally) so I set up the experiment, provide a piece of paper with a time written on it, and start the clock. At the time I have written down, the particle decays.

Exactly which of the six postulates of QM would this violate? As far as I can tell, it violates none of them so long as the results from multiple identical trials of this experiment reproduce the correct particle decay time distribution.

(And yes, I'm aware of this paper http://arxiv.org/abs/1005.5173, but I would prefer a simpler explanation.)

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"I claim I can predict how this coin will land. It will be heads." *Tosses coin. It comes up heads.* . "See? I can beat statistics. I don't need to repeat this experiment, I have made my point." What would you do if the particle had not decayed at the time you said? Blame experimental error? That's what I do when my coin demo fails... –  Floris Aug 19 at 19:21
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You read my post far too literally. Or you're pretending to read it too literally. –  Nick Aug 19 at 22:48
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I'm sorry - I thought that was how science works. –  Floris Aug 19 at 22:59
    
There are six postulates of QM? –  Bubble 2 days ago
    
@Nick I love this question! But the QM wiki link doesn't seem to list 6 clearly defined postulates, can you enumerate them here or point to a more definitive source? –  CuriousKev 2 days ago

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If in the Stern-Gerlach experiment we prepare an ensemble of particles in a superposition of spin up and spin down with respect to the z-axis and you could predict in every instance if we would obtain either spin up or spin down with respect to this axis but still reproduce the statistics corresponding to that superposition, there would at first sight be no real problem. However, according to quantum mechanics I could use the unitary operator on the state you provided before we measured the state and find out that we didn't actually start off in the superposition which leads to the contradiction in presuming we actually prepared the superposition in the first place. Then before we measured I could decide to measure along, for example, the x-axis and get results inconsistent with the preparation of a superposition.

For the case of the radioactive decay it is a bit less clear to me, but I would say that you could possibly determine the time-dependence of the metastable state.

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"I would say that you could possibly determine the time-dependence of the metastable state" ... isn't the whole point of this question that you can't do this? Imagine a hydrogen atom prepared in an excited state, can one predict when it decays from this metastable state? The linked paper seems to state definitively no. –  CuriousKev 2 days ago
    
That is exactly what I mean, but the question states that I were to be given the exact time of decay, in which case I would be able to use that information to do a unitary transformation to get a more defined initial state of the metastable state before it has decayed. –  Jasper 2 days ago

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