Magnetic field seen by electron in thomas precession

In summary: In Thomas precession, one writesdL/dt (lab frame) = dL/dt (rotating frame) + omega X LanddL/dt (rotating frame) = gamma*L x (B-v X E/c)where ω is the Larmor precession frequency in one case and the Thomas precession frequency in the other. The only reason they look different is because in the Larmor case they rewrite ω as a fictitious B field, and in the Thomas case they leave it as ω.
  • #1
rays
12
0
According to Larmor's theorem, the magnetic field seen by a rotating frame is changed. In a frame that rotates at the Larmor frequency, the magnetic field appears nonexistent.

In the treatment of thomas precession, the magnetic field in the instantaneous resting frame (which is rotating to an observer in the laboratory frame) is as if the frame is not rotating. Why?
 
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  • #2
According to Larmor's theorem, the magnetic field seen by a rotating frame is changed. In a frame that rotates at the Larmor frequency, the magnetic field appears nonexistent.
This is a misunderstanding. The E and B fields change under a velocity boost, but are unaffected by a rotation. A rotating frame causes a Coriolis force, and at the Larmor frequency the Coriolis force is just sufficient to balance the (unchanged) B field.
 
  • #3
Bill_K,

Thank you! I understand that the actual B field is not changed during Larmor precession.

However, the equaiton of motion in the rotating frame should read

dL(angular momentum)/dt = gamma*L x (B-B') while B' is the fictitious magnetic field.

In Thomas precession, one writes

dL/dt (lab frame) = dL/dt (rotating frame) + omega X L

and

dL/dt (rotating frame) = gamma*L x (B - v X E/c)

The fictitious B field is missing in (B-vXE/c). Still don't understand why.
 
  • #4
rays, There's nothing mysterious going on. In both cases, (dL/dt)rot = (dL/dt)nonrot - ω x L, where ω is the Larmor precession frequency in one case and the Thomas precession frequency in the other. The only reason they look different is because in the Larmor case they rewrite ω as a fictitious B field, and in the Thomas case they leave it as ω.
 
  • #5
Thanks again.

In the rotating frame of thomas precession, the B field from the non rotating frame in its entirety is used to describe the motion in the rotating frame.

This seems in contradiction to the treatment of other scenarios. For example, in nuclear magnetic resonance, when one decribes the motion of nuclear spins in the Larmor rotating frame the static B field does not enter into the equation of motion.

Souldn't one use a B field in the rotating frame of the thomas precession that is different from the actual B field (in non rotating frame)? If one does that, then

dL/dt(rot) = magnetic moment X (B-a*omeag)

dL/dt(nonrot) = dL/dt(rot) + omeag X L = magnetic moment X B

The correction term from a*omega disapears from the energy calculation which is performed in the nonrotating frame.

rays
 

1. What is Thomas precession?

Thomas precession is a relativistic effect that occurs when a charged particle, such as an electron, moves through a magnetic field. It causes a small additional rotation of the particle's spin, resulting in a change in the direction of the magnetic moment.

2. How does a magnetic field affect an electron in Thomas precession?

A magnetic field interacts with the spin of an electron, causing it to precess or rotate around the direction of the field. This is known as Larmor precession. In addition, the relativistic effects of Thomas precession cause the electron's spin to also precess around its own axis, resulting in a more complex motion.

3. What is the significance of Thomas precession in quantum mechanics?

Thomas precession is an important concept in quantum mechanics as it helps explain the behavior of particles with spin, such as electrons, in the presence of magnetic fields. It also plays a crucial role in the understanding of the fine structure of atomic spectra.

4. How is the magnetic field seen by an electron affected by Thomas precession?

The magnetic field seen by an electron is affected by Thomas precession in that it causes the direction of the field to appear to change from the electron's perspective. This is due to the relativistic effects of the electron's motion and its spin.

5. What factors influence the strength of Thomas precession?

The strength of Thomas precession is influenced by several factors, including the strength of the external magnetic field, the speed of the electron, and the angle between the direction of the electron's motion and the direction of the magnetic field. Additionally, the mass and charge of the electron also play a role in the strength of Thomas precession.

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