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Suppose one measures the position, then momentum, then position of a particle, and that all these measurements are done in quick succession of one another (ie. arbitrarily close to zero-time as possible). After the momentum measurement, the particles position is very uncertain. Therefore, the second measurement of the particles position can be quite different from the first. But does this not violate causality, since the particle can move a great distance in practically no time?

Qmechanic
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Denn
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  • Either you can't make measurements infinitely quickly, or you can't measure the momentum very certainly, which decreases the uncertainty of position brought by moment measurement. – Luessiaw Jul 26 '23 at 06:27
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    This question and answers might help you see how complicated causality is when quantum mechanics is involved ( the HUP) https://physics.stackexchange.com/questions/346780/does-relativistic-quantum-mechanics-rqm-really-violate-causality – anna v Jul 26 '23 at 09:11
  • This may be related to the Mott problem - (how do a trajectory emerges from wave functions?). The culprit is that the whole detection context must be considered. See the original paper. – Stéphane Rollandin Jul 26 '23 at 14:15
  • Related: https://physics.stackexchange.com/q/762398/226902 and https://physics.stackexchange.com/q/561760/226902 – Quillo Jul 26 '23 at 15:42

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The HUP applies to simultaneous measurements (of $x$ and $p$). What you propose are consecutive measurements.

A nice discussion of the distinction is given in

Raymer, M. G. "Uncertainty principle for joint measurement of noncommuting variables." American Journal of Physics 62.11 (1994): 986-993.

ZeroTheHero
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