Question

We are introduced to the magnetic field as a way to keep track of the force that arises from lenght contraction in special relativity. A moving distribution of charge becomes more dense in the right frame. So in a way, the magnetic field is just the E-field. However, when I glance over the physics of permanent magnets, it is said that their magnetic field arises from the integral sum of their electrons with aligned spin(which generates a magnetic moment).Spin is quantized fundamental property of elementary particles, analoguous(but not the same as) angular momentum of rotation.(Point like particles don't rotate).So what is the magnetic field? How do these two views are reconciled?

Answer 1

You are very right about what you said, and everybody has this confusion. But the picture becomes clear when we study Quantum field theory.

An important point to know is that the field is electromagnetic and not simply just electric or magnetic. It sometimes shows as electric field or magnetic field. But it is incorrect to say that magnetic field is just a case of electric field or vice-versa.

You can say we defined the field poorly, or we didn't had enough knowledge back then.

Things will be more clear when you see Maxwell's equations in 4-vector notation where time is not a parameter but a coordinate.

The Gauss and the Ampère law written as

and, the Faraday's law and the Gauss law of magnetism as

Where,

F is the electromagnetic field tensor (electromagnetic field term)

J is the 4- current (charge density and current density written together)

is partial derivative with respect to the coordinates (x,y,z,t)

is just a sign factor.

You don't need to get deep into this. Just compare these two equations to the regular Maxwell's equations in differential form. Notice that there is a single entity F that describes both phenomenon (electric and magnetic).

Feel free to ask if you have any confusion.