A quantum particle at rest viewed from a merry-go-round.

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Discussion Overview

The discussion revolves around the transformation of the wavefunction of a quantum particle at rest when viewed from different reference frames, specifically focusing on inertial versus non-inertial frames, such as that of a merry-go-round. Participants explore the implications of rotation and velocity on the particle's properties, including momentum and angular momentum, as well as the visual representation of wavefunctions in these contexts.

Discussion Character

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

Main Points Raised

  • One participant references Feynman's Lectures on Physics to discuss the transformation of the wavefunction of a particle at rest when observed from a moving frame, suggesting a change in momentum.
  • Another participant questions how the wavefunction transforms when viewed from a rotating frame, proposing that the particle may now have angular momentum.
  • There is a suggestion that being on a merry-go-round constitutes a non-inertial reference frame, which may affect the perception of angular momentum, particularly in relation to falling rain.
  • One participant introduces the concept of Thomas Precession, indicating that relativity may add complexity to the situation of observing angular momentum from a rotating frame.
  • There is a playful exchange regarding the difficulty of the question posed, with one participant expressing frustration and another acknowledging the pedagogical nature of the inquiry.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the implications of rotation on the wavefunction and whether it leads to angular momentum. There is no consensus on the transformations or the effects of non-inertial frames, and the discussion remains unresolved.

Contextual Notes

Participants do not fully explore the mathematical details of the transformations or the specific conditions under which the wavefunctions are analyzed. The discussion includes assumptions about the nature of reference frames and the effects of rotation that are not explicitly defined.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, relativity, or the effects of non-inertial reference frames on physical systems.

Spinnor
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Feynman's Lectures on Physics has an interesting graphic in volume 3, page 7_3, "Fig. 7-1. Relativistic transformation of the amplitude of a particle at rest in the x-t systems.", see scan below. Say ψ is the wavefunction of a particle at rest in 3D space, ψ = exp[-iEt], hbar = 1.

If I now move with some velocity v the particle at rest now has some momentum so ψ --> ψ' = exp[-i(-mv.r' - Et')]?

If on the other hand, instead of going some velocity v, I instead rotate say on a merry-go-round how will ψ transform? Will I say the particle now has angular momentum?

Related question? What does a large field of simultaneous clocks look like from the reference frame of someone riding a merry-go round?

From the three points of view,at rest, moving, and rotating, what do the hyperplanes ψ = constant look like? Feynman's graphic gives clue for the first two? Does rotation cause the hyperplanes to curve or are they "flat"?

Does this problem have anything to do with the "magic" of boosts and rotations forming a group? Boosting around some point results in some rotation?

Thanks for any hints or help!
 

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If on the other hand, instead of going some velocity v, I instead rotate say on a merry-go-round how will ψ transform? Will I say the particle now has angular momentum?
You mean, if the observer is in a non-inertial reference frame?

Hint: What normally happens in this case?
 
Simon Bridge said:
You mean, if the observer is in a non-inertial reference frame?

Hint: What normally happens in this case?

If I'm on a spinning merry-go-round with no roof and it's raining vertically I would say from my frame of reference the rain has angular momentum? The further from the center the greater the momentum? Relativity adds an additional "twist" because of Thomas Precession?
 
Hint: What normally happens in this case?
I give up -- what?
 
Bill_K said:
I give up -- what?
Bill_K the Science Advisor ... is trying to trip me up :)
It's a pedagogical gambit Bill - admittedly I've been neglecting this thread... but since you are here, perhaps you'd like to try answering the question?
 

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