Low quantum numbers, high energy, and distance scales.

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Discussion Overview

The discussion revolves around the relationship between quantum numbers, energy scales, and distance scales in various physical processes. It explores how high energies are typically associated with small wavelengths and distance scales, while also considering the implications of low quantum numbers in ordinary quantum mechanics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes the association of high energies with small wavelengths and small distance scales, questioning the "rules" governing these associations beyond the de Broglie wavelength equation.
  • Another participant points out that binary black holes possess large overall energy but generally not high energies per particle, suggesting that the number of particles is also a factor in these processes.
  • A participant mentions that LHC collisions occur at tiny scales, indicating that the size of the accelerator does not influence the energy scale of the collisions.
  • In the context of neutron star mergers, it is proposed that high energies per particle can be present, which may complicate the relationship between energy and distance scales.
  • One participant suggests a method to determine the relevance of quantum mechanics by examining pairs of relevant coordinates that multiply to an action, comparing this to the Planck constant.
  • A later reply seeks clarification on how to demonstrate the relevance of quantum mechanics in specific systems.
  • Another participant states that the approach to demonstrating quantum relevance depends on the specific system being analyzed.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between energy and distance scales, with no consensus reached on the "rules" governing these associations. The discussion remains unresolved regarding the implications of quantum mechanics in various contexts.

Contextual Notes

Limitations include the dependence on specific definitions of energy and distance scales, as well as the unresolved nature of how to practically apply the proposed method for determining quantum relevance.

TomServo
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I understand how we associate high energies with small wavelengths and thus small distance scales, but we also tend to associate small distance scales with ordinary quantum mechanics, and hence low quantum numbers (low energy). Also, many high-energy processes are active across large distance scales, such as binary black hole mergers, neutron star mergers, the LHC, etc.

So what, really, are the "rules" (beyond the de Broglie wavelength equation) for associating large/small distance scales with large/small energy scales?
 
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Binary black holes have a large overall energy but not large energies per particle, in general there are also not many particles around.
LHC collisions are tiny, the size of the accelerator does not matter here.
For processes in neutron star mergers you can have high energies per particle.

To see if quantum mechanics is relevant, find pairs of relevant coordinates that multiply to an action (same units as the Planck constant). If it is small compared to the Planck constant quantum mechanics will be relevant, otherwise probably not.
 
mfb said:
To see if quantum mechanics is relevant, find pairs of relevant coordinates that multiply to an action (same units as the Planck constant). If it is small compared to the Planck constant quantum mechanics will be relevant, otherwise probably not.

Okay, that's interesting, but how would I show that?
 
That depends on your system.
 

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