What is physical significance of g factor?

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SUMMARY

The g-factor is a crucial dimensionless quantity in quantum mechanics that relates the magnetic moment of particles to their angular momentum. For orbital angular momentum, g equals 1; for electron spin, g equals 2; and for protons, the value is approximately 5.59. The g-factor was introduced by Lande to explain the Zeeman effect and is essential for understanding the discrepancies between classical and quantum mechanical models. Experimental measurements of g provide insights into quantum electrodynamics (QED) and the behavior of particles in magnetic fields.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of magnetic moments and angular momentum
  • Familiarity with the Zeeman effect
  • Basic knowledge of quantum electrodynamics (QED)
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  • Study the Zeeman effect in detail to understand its implications on the g-factor
  • Explore quantum electrodynamics (QED) corrections to the g-factor
  • Read "The Story of Spin" by Sin-Itiro Tomonaga for historical context
  • Investigate the relationship between gyromagnetic ratios and magnetic moments in various particles
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  • #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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