Doubts about the electron magnetic moment.

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Discussion Overview

The discussion revolves around the electron's magnetic moment, specifically addressing the z-component's deviation from classical predictions due to relativistic effects. Participants explore the implications for the x and y components and the role of relativistic considerations in quantum mechanics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions why only the z-component of the electron's magnetic moment is discussed, suggesting that it may be assumed that the axis of rotation aligns with the z-axis, leading to zero x and y components.
  • Another participant agrees with the assumption that the z-axis is aligned with the spin, indicating that the x and y components are indeed zero.
  • A participant raises a question about the relevance of relativistic effects, expressing confusion about their necessity given the absence of high speeds.
  • A response clarifies that relativistic effects arise from the need to reconcile quantum mechanics with special relativity, with spin being a consequence of this reconciliation.
  • A later reply confirms that the different description of electrons in this context is related to the Dirac equation.

Areas of Agreement / Disagreement

Participants generally agree on the alignment of the z-axis with the electron's spin and the relevance of the Dirac equation in describing relativistic effects, but there remains some uncertainty regarding the implications for the x and y components and the necessity of relativistic considerations.

Contextual Notes

The discussion does not resolve the assumptions regarding the x and y components or the specific nature of relativistic effects in this context.

carllacan
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Hi.

According to this page and other sources I found the z-component of the electronic magnetic moment is greater than the classically calculated value due to relativistic effects. Which makes me wonder:

1) What about the x and y components? I am completely lost as to why only the z axis is mentioned. I'm thinking that it is assumed that the axis of rotation of the electronand therefore the moment are aligned in that direction and therefore the x and y comps are 0. Am I right?

2) How are relativistic effects sneaking in here? There isn't anything going really fast, which I thought (perhaps naively) was necessary for them to be relevant.

Thank you.
 
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1) What about the x and y components? I am completely lost as to why only the z axis is mentioned. I'm thinking that it is assumed that the axis of rotation of the electronand therefore the moment are aligned in that direction and therefore the x and y comps are 0. Am I right?
Right. The z axis is chosen to be aligned with the spin.
2) How are relativistic effects sneaking in here? There isn't anything going really fast, which I thought (perhaps naively) was necessary for them to be relevant.
To make quantum mechanics compatible with special relativity, you need a different description of electrons - and spin is one result of that different description.
 
Does that different description of electrons happen to be the Dirac equation?
 

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