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I read "The Quantum Universe (Cox & Forshaw)" that a particle can be measured at a given position at a given time, and in another galaxy one second later. The probability of such event may be small but still non zero. As he explains, this would be due to the fact that the wave function propagate in the universe instantly, as opposed to a water wave that propagate at a finite speed.

This is striking me because from what I remember from quantum physics, the wave function does propagate at a finite speed. So if a particle is detected somewhere at time $t$, the wave function collapse and starts spreading at time $t$.

Am I missing something here?

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  • $\begingroup$ What exactly do you mean by "measure" here? Because I would argue that anyone would have an hard time traveling in a second to another galaxy to carry out the second measurement $\endgroup$ – glS Mar 24 '16 at 15:42
  • $\begingroup$ I don't see how does that really matter... I am considering the probability that the particle is measured in some position by however. Thanks anyway, I edited for more clarity. $\endgroup$ – David Mar 24 '16 at 16:00
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    $\begingroup$ If you measure a particle in one place you can't be measuring it in another place. What you are probably referring to is what happens in the case of entangled states. If two particles (say, two photons) are in an entangled state, and they are a galaxy apart (or wherever else), then measuring one of the photons instantaneously makes the wavefunction of the entangled state collapse, thus affecting the other photon no matter the distance (though it should be always remembered that this property cannot be used for FTL communication) $\endgroup$ – glS Mar 24 '16 at 16:01
  • $\begingroup$ Thanks glS. No I am not referring to entanglement. Really the same particle $\endgroup$ – David Mar 24 '16 at 16:02
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    $\begingroup$ It does not make sense to say that for a single particle. While a single particle can simultaneously be at two different places, once you detect it in one place you cannot "measure" it at another place, because you already collapsed its wavefunction and the particle is now only at one place $\endgroup$ – glS Mar 24 '16 at 16:04
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This is a statement that you hear in discussions of the path integral formulation of quantum mechanics, first developed by Feynman. For a non-relativistic theory there is no speed-of-light constraint and so there's no reason for the probability to teleport to another galaxy to vanish.

In a relativistic theory, it is a result, not a postulate, that the amplitude for a particle to leave its light cone is zero.

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