What frame of reference is used to measure particle momentum in QM?

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Discussion Overview

The discussion revolves around the concept of measuring particle momentum in quantum mechanics (QM) and the implications of frame of reference in this context. Participants explore theoretical scenarios, including the implications of uncertainty relations and the behavior of particles in extreme conditions such as near black holes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that while momentum can be defined in a laboratory frame, the uncertainty principle complicates the assignment of a specific frame of reference for particles, especially in a universe with very few particles.
  • Another participant introduces a speculative model involving black holes and Hawking radiation, discussing how particles might be created and destroyed in such scenarios, although this may not directly address the original question about momentum measurement.
  • A later reply discusses the mathematical representation of momentum in a time-independent frame, asserting that the momentum operator can be defined in this context, but does not clarify how this relates to the broader question of frame of reference.

Areas of Agreement / Disagreement

Participants express differing views on the implications of frame of reference in measuring momentum, with no consensus reached on how to reconcile these ideas with the uncertainty principle or the specific conditions of extreme environments.

Contextual Notes

The discussion includes assumptions about the applicability of classical mechanics to quantum scenarios and the limitations of defining frames of reference in quantum systems, particularly under conditions of low particle numbers.

kristobal hunta
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Doing some kinematical calculations we say that particle possesses momentum p. It is definite, so we choose momentum representation to describe the state of particle. However I am curious in what frame of reference we measure particle momentum.
We can not assign frame of reference to any physicial object due to the uncertainty relation. Surely we can introduce something averaged, imaginary point at which we fix the origin of our frame of reference. It will work almost perfectly for the case of laboratory frame of reference (uncertainty relation can be neglected for the macroscopic world) , I guess.
But what if we have universe where there is only 3 or 4 electrons?
 
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3 or 4 electrons

... I think the black hole that would create the baby universe would constatly give off new particles through Hawking Radiation.

In empty space PAIRS of particles are constantly being created and then destroyed BY EACH OTHER. The black hole that created the baby universe has an event horizen, which is just a simple circular ring around the hole. When something enters the event horizon it simply does not come back out, the gravitation is too strong. Well, these pairs of particles that normally destroy each other would not because (if close enough to the event horizon) one of the particles would escape the other. Therefor particles would constantly be created.

If I am off, please explain why...
 
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Problem+Solve=Reason said:
... I think the black hole that would create the baby universe would constatly give off new particles through Hawking Radiation.

In empty space PAIRS of particles are constantly being created and then destroyed BY EACH OTHER. The black hole that created the baby universe has an event horizen, which is just a simple circular ring around the hole. When something enters the event horizon it simply does not come back out, the gravitation is too strong. Well, these pairs of particles that normally destroy each other would not because (if close enough to the event horizon) one of the particles would escape the other. Therefor particles would constantly be created.

If I am off, please explain why...

well, probably black hole can create a new universe. i just never saw the solution for such scenario.
i just suggested a model where we have only a few electrons in the universe.

Let's make the question simpler: when we measure the momentum of particle by momentum operator, what is the frame of reference we use for it? (don't beat me for this question, so far i deal mainly with classical GR :smile:. I had QM before but pure math. Never thought about its interpretation)
 
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If I work in a frame with time independent coordinates, that is my rest frame, and I find a particle of momentum p, then the particle's wave function is exp(ixp) {up to a constant factor}. If x is a position coordinate in a frame S, then p= -id/dx (let hbar=1) is the momentum operator for the frame S -- what else could it be?. Recall, also, that the same question applies to the Hamilton-Jacobi approach to classical mechanics.
Regards,
Reilly Atkinson
 

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