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i thought of a paradox that i'm not sure i can resolve for myself.

You have a 1-dim potential well of length L. You measure a particle to be within [tex]x=L/2\pm \sigma[/tex] with equal probability. Assume sigma is very tiny. After a short time [tex]\Delta t[/tex] the wavefunction has evolved to be non-zero even at [tex]x=L/3[/tex], say (with tiny probability). But if a measurement of the position of the particle actually yielded [tex]x=L/3\pm \sigma'[/tex], as unlikely it may be, wouldn't relativity be violated, in that the particle would have had to travel with velocity [tex] \frac{L/6}{\Delta t} [/tex], which for short enough [tex] \Delta t [/tex] might in fact be larger than the velocity of light?

My guess would be, that this is making too much of non-relativistic quantum mechanics and that it would all work out if instead of speaking about velocity v one talked about the momentum p, which might become as large as necessary to satisfy the uncertainty relation, without making the velocity larger than c (in the same way as the momentum of a constantly accelerated particle in relativity can become as large as necessary without the velocity increasing very much).

Is this the resolution? If yes, is it possible to make a more convincing argument for that?

If no, what is the resolution?

Thanks

Jeremy

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# Paradox seemingly violating relativity

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