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?


1 Answer 1


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.


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