It is generally thought (see Special Relativity, A. P. French) that the magnetism we detect form an electric field, is related to relative motion with respect to that field. Specifiically a moving current generates a magnetic field.
Does that also apply to the magnetic field generated in electromagnetism. Specifically does the magnetic field derive from the motion of the electric field.
Dear Andrew,
The answer is no. For instance a magnet is material (in a ferromagnetic phase) that has a magnetization M different than zero due to the atomic magnetic moments given by the spin, orbit and spin-orbit coupings which don't follow the Lorentz transformations.
Dear Andrew,
Let me to explain it a little deeper. There are two kind of magnetism: in vacuum and in matter. The magnetism in vacuum is associated to the magnetic field which can change given electromagnetic field for a given observer in relative motion, i.e. magnetic field and electric one. In the same form the electric field transforms in electromagnetism under a relative motion. The most extreme case is the application of an electric field to a metal. In such a case the electric field E in vacuum is zero, but the motion of the relative charges (electrons respect to positive ions) gives only a magnetic field. Lorentz transformations allows us to control the kind of electromagnetic field that we have and its group has two invariants which keep constant the quantity of "electricity" or "magnetism" for each observer moving at relative motion.
Another very different source of magnetism is the magnetization M in a material, which cannot be transformed in its partner in electricity, the electric polarization P. The origin of M is fundamentally the magnetic moment associated to fermions as protons, electrons or neutrons in the atom. But even if the atom has this magnetic moment this dosen't garantees to have magnetization M. It is necessary to form an inner lattice field as Weiss field which is very strong at allows to align the spins below a certain critical temperature. For M different zero we have ferromagnetism and a critical temperature known as Curie temperature, but even if we have a global M=0 this doesn't prevent us to have other kind of magnetic order as antiferromagnetism below a critical temperature called Neel temperature.There are more different kind of magnetic order.
In summary, the answer to your question is that the magnetism is not only obtained by the motion with respect to one electric field, due to have spins in matter which have associated an inner magnetic moment.
@Daniel
So if the speed of light is a constant then the magnetic field generated by the photon should also be a constant
Dear Andrew,
Sure! No doubt about that. The problem is that a photon is always made by a magnetic and electric field: both are necessary. Thus the whole magnetic field, that is assumed to be formed by photons, must have an special form of phtons and also different than the ones of the electric field. Some time ago I have made such a question trying to glue the point of view of QED and Classical Electrodynamics, but I didn't obtain a convincing answer so far.
Yes, that is always the velocity of every phonon in vacuum. But there is a subtlety if you think that the electric or magnetic fields alone (electrostatics or magnetostatics) don't follow a wave equation but a Laplace's one. Thus from a pure classical point of view the velocity of a pure electric or magnetic field is infinite, which enters in difficulties with relativity and also with the idea that the those fields are made of photons.
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