# How does magnetic moment transform due to relativity?

• idea2000
In summary, textbooks model how an electric field of an electron changes when viewed from another frame of reference by showing that the electric fields appear to compress along the axis of motion. However, the electric and magnetic fields are not Lorentz invariant and depend on each other. In special relativity, the Lorentz invariant quantities mix them. The magnetic moment also gets compressed in these situations and its shape changes. For more information, please refer to the provided sources.
idea2000
Hi, I have seen textbooks model how an electric field of an electron changes when viewed from another frame of reference. In these models, the electric fields seems to "compress" along the axis of motion. What happens to the magnetic moment in these situations? Does the magnetic moment also get compressed? What is the new shape of the magnetic moment?

Thanks in advance for any help with this question.

The electric and magnetic field are not Lorentz invariant themselves...In special relativity, you can show that the Lorentz invariant quantities mix them (from the field-strength tensor $F_{\mu \nu}$... they depend on each other, and that's why they are the same coin from different sides...

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## 1. How does the magnetic moment change in a relativistic system?

The magnetic moment is a measure of the strength and direction of a magnetic field produced by a current loop or a moving charged particle. In a relativistic system, the magnetic moment can change due to the effects of time dilation and length contraction.

## 2. How does the magnetic moment transform in special relativity?

In special relativity, the magnetic moment transforms according to the Lorentz transformation equations. This takes into account the relative motion between the observer and the charged particle, as well as the orientation of the magnetic field.

## 3. Can the magnetic moment be affected by the speed of an object?

Yes, the magnetic moment is affected by the speed of an object due to the effects of special relativity. As an object's speed approaches the speed of light, its magnetic moment may increase or decrease depending on the direction of its motion and the orientation of the magnetic field.

## 4. How does the magnetic moment change in a strong gravitational field?

In a strong gravitational field, the magnetic moment may change due to the effects of general relativity. This can occur when a charged object moves through a region with a strong gravitational field, such as near a black hole.

## 5. Is the magnetic moment conserved in relativity?

In special relativity, the magnetic moment is not conserved as it can change due to the effects of time dilation and length contraction. However, in general relativity, the magnetic moment is conserved in the absence of external forces or fields.

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