Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I know this topic has been discussed quite a bit -- and in particular it's been done in this thread and this thread. But there are still some things I want to talk about in order to (hopefully) clarify my own thoughts.

One of the threads discusses this Ballentine article in which Ballentine presents an argument against the statement that the HUP requires that simultaneous measurements of conjugate variables have a lower bound in uncertainty. I find Ballentine's argument convincing, but in one of the threads, Demystifier makes a convincing argument that Balletine's experiment requires identifying the probability of the momentum with the probability of the position measurement [itex] |\langle y | \psi \rangle|^2 [/itex] when it is experimentally the case the the momentum is identified with the Fourier transform [itex] |\langle p_y | \psi \rangle|^2[/itex] of the coordinate space wavefunction. My first question then is: where does Balletine's experiment fail?

Additionally, I see a lot of people make the argument that the HUP does not say anything about simultaneous measurements of conjugate variables, but that it is rather a statement about a given prepared state (which describes an ensemble of particles). I understand the argument and find it convincing since it doesn't make sense to talk about deviations for a single particle. But then what about the obvious manifestation of the HUP in single particle systems where simultaneous eigenfunctions of position and momentum cannot exist? Indeed, doesn't this suggest that the HUP *does* imply that, for a given particle, its position and momentum cannot be simultaneously identified up to arbitrary accuracy -- that there *is* a lower bound?

Many thanks,

jmcelve

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# The HUP, simultaneous measurements, and eigenfunctions

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