Graduate How momentum measurement is defined in Pilot Wave interpretation?

[MichPod]

Considering pilot wave interpretation, a singular particle measurements are fully defined (?) by knowing its wave function (a pilot wave) and the position of the "particle" (some hypotetical point particle riding on the wave). This should provide some sort of "realistic" explanation of how a random coordinate may be observed/measured which disribution is in accordance with the Born rule. Yet I fail to see how the momentum of the particle may be defined which will be in accordance with stanard "copenhagen" QM and which will be "realistic". What does pilot wave interpretations say of the momentum measurement?

To take the case to extreme, let's consider a Hydrogen atom with the electron in the ground state. According to the pilot wave interpretation, the electron "particle" will not move (!), staying still at some fixed distance and direction from the proton. Then, for each such position of the "electron particle" is it possible to prescribe a momentum which will be consistent with normal QM? I fill like it is hardly possible for the same reason it is impossible to brush a hairy sphere.

 

[MichPod]

After thinking a bit more... my idea with hydrogen atom is probably wrong, it does not disprove pilot wave interpretation.

 

[PeterDonis]

According to the pilot wave interpretation, the electron "particle" will not move (!), staying still at some fixed distance and direction from the proton.

No, it won't. The pilot wave doesn't change with time, but that doesn't mean the particle position doesn't change with time. The pilot wave guides the motion of the particle; in this case it causes it to orbit the proton.

 

[Demystifier]

What does pilot wave interpretations say of the momentum measurement?

The most important thing to realize is that measurement (of momentum or anything else) in Bohmian mechanics (as well as in standard QM) significantly changes the wave function. So you cannot understand the results of measurement by using the wave function that is valid in the absence of measurement.