How momentum measurement is defined in Pilot Wave interpretation?

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Discussion Overview

The discussion revolves around the definition of momentum measurement within the context of the pilot wave interpretation of quantum mechanics. Participants explore how this interpretation reconciles the behavior of particles, particularly in relation to the Born rule and standard quantum mechanics, while addressing the implications for momentum measurement.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests that in the pilot wave interpretation, a particle's measurements are defined by its wave function and position, implying a realistic explanation for observed randomness consistent with the Born rule.
  • The same participant questions how momentum can be defined realistically within this framework, particularly using the example of a hydrogen atom where the electron appears to remain stationary.
  • Another participant counters that while the pilot wave does not change with time, it guides the particle's motion, suggesting that the electron orbits the proton rather than remaining fixed.
  • A further point is made that measurement in Bohmian mechanics alters the wave function, indicating that one cannot use the pre-measurement wave function to understand measurement outcomes.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the pilot wave interpretation for momentum measurement. There is no consensus on how momentum is defined or whether the initial assumptions regarding the hydrogen atom are valid.

Contextual Notes

Participants acknowledge limitations in their understanding of how momentum can be reconciled with the pilot wave interpretation, particularly in relation to the behavior of particles and the effects of measurement on the wave function.

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

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