Orbital Path Length Contraction: Explained by Relativity

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Discussion Overview

The discussion revolves around the concept of length contraction in the context of high-speed particles, specifically electrons in orbit. Participants explore how relativistic effects might influence the orbital path and the associated wavelength relationships, referencing both classical and quantum mechanical frameworks.

Discussion Character

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

Main Points Raised

  • One participant questions whether the orbital path of a high-speed particle, such as an electron, is length contracted and how this relates to the equation nλ=2πr.
  • Another participant notes that nλ=2πr originates from Bohr's model, which has been superseded by quantum mechanics, suggesting that relativistic quantum mechanics can adequately describe electron orbitals around heavy nuclei.
  • A different viewpoint emphasizes that length contraction is frame-dependent and argues that since measurements are not being made in the electron's frame, there is no need to apply length contraction in this context.
  • One participant reiterates the initial question about length contraction and suggests that both the orbital path and wavelengths are length contracted, proposing a modified relationship for distance traveled around the path.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of length contraction to the orbital paths of electrons, with some asserting its relevance and others arguing against it. The discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

There are limitations in the assumptions made regarding the applicability of classical equations in a relativistic context, as well as the dependence on the chosen frame of reference for measurements.

Who May Find This Useful

This discussion may be of interest to those studying relativistic effects in quantum mechanics, particularly in relation to electron behavior in high-speed scenarios.

neilparker62
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Hi

Just wondering about the orbital path of a high speed particle - eg electron in orbit. Is it length contracted? Then how do we manage nλ=2.π.r ?

Neil
 
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nλ=2πr comes from Bohr's model, this has been replaced by quantum mechanics about 90 years ago.
With relativistic quantum mechanics, it is no problem to find orbitals for electrons even around heavy nuclei, where relativistic effects are important. It is problematic to switch to the view of the electron (because it does not have a fixed velocity).
 
Length contraction is a description of a difference in an observation between two different frames of reference. We're not doing any measurements in a frame of reference moving along with the electron, so there is no reason to convert to or from that frame.
 
neilparker62 said:
Hi

Just wondering about the orbital path of a high speed particle - eg electron in orbit. Is it length contracted? Then how do we manage nλ=2.π.r ?

Neil

Orbital path is length contracted, and wavelengths are length contracted. So we don't have a radius, and we have many different lambdas.

So we write: d = n * sum of lambdas, where d is distance traveled when going around the path once.

d changes smoothly when speed changes smoothly.(I assumed this was a question about a high speed hydrogen atom)
 
Last edited:

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