# B Polarized Electron in a Rotating Reference Frame

#### Dale

Mentor
So does this mean it would require a constant supply of energy to cause the electron to continuously change the vector of its magnetic moment?
No, just a constant magnetic field.

#### metastable

No, just a constant magnetic field.
So stationary (relative to the craft) permanent magnets on board the spinning craft could accomplish the task of causing the electron's magnetic moment vector to change continuously without a constant source of power (while the electron is still on board)?

#### Nugatory

Mentor
So does this mean it would require a constant supply of energy to cause the electron to continuously change the vector of its magnetic moment?
No. When you set the system up (move the object into position, move magnets into position, whatever, ...) you had to push on something, thereby adding energy to the system. Once that's done, the system is in a steady state, neither gaining nor losing energy.

Something similar happens when we put a satellite in orbit: We need the energy of the rocket engines to set things up, but once we have the satellite in the right place and travelling at the right speed it will orbit the earth more or less forever without further energy inputs.

#### Dale

Mentor
So stationary (relative to the craft) permanent magnets on board the spinning craft could accomplish the task of causing the electron's magnetic moment vector to change continuously without a constant source of power (while the electron is still on board)?
You would want the permanent magnet to be stationary in an inertial frame so as to avoid inducing any E-fields. But yes, it could be done without a source of constant power. It might even be possible to design a device that would not induce any E-fields while co-rotating, but I can't think of the details.

#### metastable

You would want the permanent magnet to be stationary in an inertial frame so as to avoid inducing any E-fields. But yes, it could be done without a source of constant power.
I struggle to envision such an arrangement. I imagine a permanent magnet stationary in an inertial frame, and an electron nearby with a constantly changing magnetic moment vector, over time even if somehow both objects could be made to stay in proximity of each other, won't the electron also exert a torque on the permanent magnet, causing it to begin to rotate in the inertial frame. Would it not require energy input to maintain the orientation of the permanent magnet as stationary in an inertial frame over a long timescale with the electron's magnetic moment vector constantly changing nearby?

#### Dale

Mentor
won't the electron also exert a torque on the permanent magnet, causing it to begin to rotate ... over a long timescale
The torque is constantly changing direction as the electron precesses. Every $\pi$ seconds the torque is applied in the opposite direction and undoes whatever minuscule angular acceleration may have happened $\pi$ seconds before. As long as it doesn't affect the magnet over a time scale of 2$\pi$ seconds then it will not affect it over long timescales either.

#### metastable

The torque is constantly changing direction as the electron precesses. Every ππ\pi seconds the torque is applied in the opposite direction and undoes whatever minuscule angular acceleration may have happened ππ\pi seconds before. As long as it doesn't affect the magnet over a time scale of 2ππ\pi seconds then it will not affect it over long timescales either.
So to attempt summarize what I think I've learned:

In the absence of an outside magnetic field, the electron cannot precess.

Still feeling unsettled because I can't help but think even if the permanent magnet had no charge, it would require an outside force to counteract the gravitational attraction to keep the system undisturbed over a long timescale.

#### Dale

Mentor
If something that negligible unsettles you then there is little anyone else can do for you. I can’t think of a more negligible effect here.

Are you still interested in rotating reference frames or is your interest now changed to long time scales? I had thought that your interest was in rotating reference frames, and others thought it was in electrons, and now I am unsure.

#### metastable

Are you still interested in rotating reference frames or is your interest now changed to long time scales? I had thought that your interest was in rotating reference frames, and others thought it was in electrons, and now I am unsure.
Is there a method that will cause the vector of the electron's magnetic moment to stop precessing & continuously point in a desired direction? Suppose I observe a distant galaxy and I want each measurement I perform of the electron's magnetic moment vector to show that it is substantially parallel with the vector pointing towards that galaxy from my present position within some small margin of error. What forces and methods would I rely on to orient the vector of the electron's magnetic moment in this desired vector?

#### Dale

Mentor
Is there a method that will cause the vector of the electron's magnetic moment to stop precessing & continuously point in a desired direction?
Not that I know of. But why not just use a classical gyroscope instead?

#### Nugatory

Mentor
Is there a method that will cause the vector of the electron's magnetic moment to stop precessing & continuously point in a desired direction?
No, if you’re thinking about an electron and quantum mechanical spin (and look at post #17 above again). Yes, if you’re thinking about a classical charged rotating object like a gyroscope.

#### metastable

No, if you’re thinking about an electron and quantum mechanical spin (and look at post #17 above again).
I'm confused... does that mean that for non-precessing electrons, the vector of the magnetic moment can only take one of 2 values-- up or down.... or does it mean the vector could be measured to point in any direction, but I have no way to alter this direction according to my wishes?

#### Dale

Mentor
This is going nowhere. Please make a choice:

If you want to learn about quantum mechanical spin and precession of electrons in a magnetic field, open a thread about that in the QM forum. Do not include any complications about rotating reference frames.

If you want to learn about rotating reference frames, choose a classical example and open a new thread about that here. Do not include any complications about quantum mechanical objects like electrons.

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