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So my physics teacher assigned us an article about how special relativity causes magnetism in a wire with a current, even with the low drift velocities of electrons in a current. It seemed that the basis of the article was that magnetism is just relativistic electricity, so I was wondering how a permanent magnet worked? It makes sense to me that a moving charged particle attracts unmoving particles of the opposite charge, but how do the orbits of electrons in a magnet cause it to have a magnetic field?

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For an explanation on why Special Relativity implies magnetism, try to find Schwartz's book on Electrodynamics. Permanent magnets are related to spin alingment. – jinawee May 15 '13 at 16:42
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duplicate of physics.stackexchange.com/q/63009/4552 – Ben Crowell May 15 '13 at 19:03
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Related: physics.stackexchange.com/q/65335 but I'd say not a duplicate, nor is the other suggested duplicate quite the same. The emphasis here, unlike in the other questions, is on permanent magnets, which requires a bit of quantum mechanics to explain properly. – Chris White May 23 '13 at 2:55
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There are two phenomena in your question.

(1) Let us first understand how magnetic field can be considered to "arise" because of relativity. Imagine a frame of reference in which a charge $Q$ is at rest. If another charge $q$ is brought in its vicinity, it will experience only an electrostatic force. Now get on to another inertial frame of reference moving at a velocity $\vec{v}$ with respect to the first one. In this frame of reference, you will observe both the charges moving. The static charges of the old reference frame now appear as charges and currents. The electrostatic field of the previous frame now appears as an electrostatic field of different magnitude and a magnetic field. Since physics is the same in all inertial frames of reference, we are inclined to believe that $\vec{E}$ and $\vec{B}$ are manifestations of a single electromagnetic field.

This is a very "hand-waving" kind of an explanation. You may want to refer to Rober Resnick's "Special Theory of Relativity" or Melvin Schwartz's "Principles of Electrodynamics" for greater mathematical details.

(2) The first point tries to explain how magnetism due to a current can be considered to be a relativistic effect. Now let us consider magnetism due to electrons. Apart from charge and mass, electrons also have an intrinsic magnetic moment that can be explained only through relativistic quantum mechanics. Thus, magnetism of a bar magnet is also a relativistic effect. Please note that magnetism in a bar magnet is because of the electron's spin and not orbital motion.

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Thank you, interesting how it has to do with spin and not orbitals or anything, but Schwartz's book sounds like a good start. – Zach Johnson May 15 '13 at 17:35
    
Very interesting explanation. – Inquisitive Feb 4 '15 at 22:58

It is a mistake to think that special relativity (SR) causes magnetism. The article you're reading is arguing that

  • (A) "If electricity exists, and SR is true, then magnetism has to exist".

This statement is true, I admit it. But it's equally true that

  • (B) "If magnetism exists, and SR is true, then electricity has to exist".

In reality, electricity and magnetism are equally fundamental parts of physics. Special relativity unites electricity and magnetism into electromagnetism, in exactly the same way that it unites space and time into spacetime. Time does not cause space, space does not cause time, and SR causes neither space nor time. SR merely reveals the relatedness of space and time. Similarly, electricity does not cause magnetism, magnetism does not cause electricity, and SR causes neither electricity nor magnetism. SR merely reveals the relatedness of electricity and magnetism.

A lot of people come across (A) in their high school or intro college physics classes, and wind up misunderstanding it as the fundamental reason that magnetism exists. Why is that? And why do textbooks almost never point out (B)?

The reason is simply that nobody questions why electricity exists--electrical attraction and repulsion seem perfectly natural--whereas magnetism seems more mysterious. In other words, this asymmetry between electricity and magnetism has nothing to do with physics, and everything to do with our inborn preconceptions and intuitions.

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Actually, the asymmetry has everything to do with physics, given that there are only electric and not magnetic charges in nature. Moreover, lots of the apparent symmetry between electricity and magnetism is an artifact of a 3+1 spacetime -- magnetism would not be expressible as a vector field in any other number of dimensions. – Chris White Jan 29 at 17:21
    
I didn't say that electricity and magnetism were "symmetric" in the sense that you're using the term. (Please re-read my answer, I was discussing asymmetry of pedagogical emphasis.) Any 6-year-old can tell them apart. I only said that the relationship between electricity and magnetism is not cause-and-effect: They are equally fundamental parts of physics. – Steve B Jan 29 at 19:57
    
@ChrisWhite -- For what it's worth, most serious theoretical physicists believe that magnetic monopoles exist in the universe, but that they're very very rare. I don't think it matters for the issue under discussion though. – Steve B Jan 29 at 19:58

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