Hi Alexander,

don't you believe the classical equations on electrodynamics?

I havn't yet measured directly the magnetic field for example of electrons in vacuum. But from own experiments I have learned that for example moving electrons in vaccum strictly obey the Maxwell equations, such as electrons in x-ray tubes during focussing and deflection as well as other charged particles in accelerator and storage rings. There is not hint at all on a violation of thoses laws.  

Dear Gerhard,

The magnetic moment of a particle can be induced by an external source. It is necessary to measure own magnetic field of a moving charge using non-invasive method (without external magnetic field) to write more truly theory.

All approved theories must have direct experimental proofs.

So Alexander,

then let's wait for a colleague who has really measured that magnetic field.

It seems no one made such an experiment.

Gerhard, would you like to make this? I have no required equipment. It needs, for example, powerful electron gun and Hall probe in electrostatic screen (foil) to measure the magnetic field near electron beam. Interesting result may be obtained.

Hi Alexander,

sorry but I am retired now. I have no access  now anymore on experimental equipment.

 Two years ago I had access to a nice vacuum system provided with an electron gun and a lot of flanges and electrical feedtroughs for attaching a Hall probe. Sorry.

Understandably, no problem.

The second part of your question might create an impression that magnetic field should be present/observable near the electric charge in its own reference frame, i.e. the one in which the said charge is at rest.  This is generally false, at least when we think about electrified dust particle.  However, a single electron has a spin, or in other words a magnetic moment, which, in turn, is a source of magnetic field. Yet in isotropic vacuum it is impossible to tell what could be the orientation of such a field.

In other aspects I have to agree with opinion of Gerhard Martens.

The magnetic field is characteristic of the "quantum" medium. It is like a vortex in a gase from a source. So, it is or not- regardless reference frame. What is a spin? Do not you think that an electron may have complex internal structure? One its part may rotate and the other ones may be in rest or have some complex movements. The electron structure is some wave packet at first approximation. An electron shows its "spin" when external magnetic field is applied. And what if there is no external field? Look at macroscopic magnetic dipoles. All of them may be ordered / disordered by the magnetic field or for other reasons.