What is physical significance of g factor?

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Discussion Overview

The discussion revolves around the physical significance of the g factor in quantum mechanics, particularly in relation to magnetic moments and angular momentum. Participants explore its historical introduction, its role in various models, and its implications in both classical and quantum contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note that the g factor is essential for understanding the magnetic moment of particles, with specific values for orbital angular momentum (g=1), electron spin (g=2), and proton (g=3.56 or 5.59 according to different sources).
  • One participant mentions that the g factor was introduced by Goudsmit and Uhlenbeck to explain electron behavior in magnetic fields, while another corrects this to Lande's introduction related to the Zeeman effect.
  • There is a discussion about the dimensionality of the g factor versus the gyromagnetic ratio, with some arguing that the g factor is dimensionless and useful for comparing different particles.
  • Participants explore the historical context, suggesting that the g factor was initially a convenience or "fudge factor" that later found theoretical justification.
  • Some participants express uncertainty about the interpretation of g as a relativistic effect, with differing views on whether spin can be understood without relativity.
  • There are claims that the relationship between angular momentum and magnetic moment can be modeled classically, but quantum corrections are necessary for precise values of g.
  • One participant raises a question about the relationship between different angular momentum components and the g factor, indicating confusion about the formulas involved.

Areas of Agreement / Disagreement

Participants express a range of views on the significance and interpretation of the g factor, with no clear consensus on its implications or the necessity of relativity in understanding spin. Some points are contested, particularly regarding the historical introduction and the interpretation of g as a relativistic effect.

Contextual Notes

There are unresolved questions about the assumptions underlying the definitions of g and its relationship to the gyromagnetic ratio. Additionally, the discussion includes varying interpretations of the mathematical relationships involving angular momentum and magnetic moments.

  • #31
Speaking of some size of electron means we can see it without perturbing it. In fact any interaction (scattering) from an electron is inelastic because it is coupled permanently to the quantized EMF. Electron and the quantized EMF form a compound system in which the electron charge is smeared quantum mechanically, mathematically similarly to atomic orbitals. The elastic picture is a cloud of rather big size (depending on the external field).We cannot speak of electron itself but only in some "bound" state determined with the proper quantized EMF and the external field.
 
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  • #32
When ever an electron is found it is a full electron and the g- factor applied when in spin-orbit coupled state.
Electron-Positron collisions are being conducted shows ther is some size for these particles.

We should find an answer with a broader perspective to Dirac’s (1/2) spin. A point particle approach is fine mathematically, but a qualitative approach is needed for clarity and visibility. Thought try a semi classical approach.
Is it not right then to take classical radius based on my prevous reply and that
The (electron mass – me), h and “C” brought in the famous TRIO unit lengths- Compton wavelength, Bohr Radius and the classical radius of electron (re) that has been left out but solves so many problems.
May be there is a need to find a right interpretation for the experimented results
 
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  • #33
granpa said:
.

I know that the field resulting from the polarization of the virtual particles is weak. so is the difference from 2.
[For the electron,] g = 2.002 319 3043617(15)

What is more interesting is that the g factor for the muon (also a lepton), is larger:
g=2.002 331 8414

See http://en.wikipedia.org/wiki/G-factor

Bob S
 
  • #34
Bob S said:
What is more interesting is that the g factor for the muon (also a lepton), is larger:
g=2.002 331 8414

See http://en.wikipedia.org/wiki/G-factor

Bob S
fascinating. thank you.
 
  • #35
granpa said:
fascinating. thank you.

You are right
Dirac’s spin appears to be limited two degree of freedom “spin up” and “spin down” and its correlation to spin angular moment magnitude and the component half spin along Z-axis seems incorrect since it fails for composite particles also.
For photons it should then be unidirectional “spin 1”. Am I correct?
 
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  • #36
Both the muon and electron are (supposed to be) point structureless leptons. Therefore, the g factor due to internal QM should be the same. The g factor should then be
g = 2( 1 + α/2π) = 2.002322819454
including only the external vertex correction.

The electron g factor is 0.000 003 515 lower, and

the muon g factor is 0.000 009 021 higher.

These disparities are due to external radiative corrections. The muon is higher than the electron primarily because the electron-positron vacuum polarization (2 Feynman bubbles) correction is much higher in the muon case than in the electron case.
Bob S

signs corrected 11/19/09
 
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