Summary: We develop the basics of special relativity. Key is determining the allowable coordinate changes. This will let us show in the next chapter not just how but why magnetism and electricity must be linked.

Special Theory of Relativity

The physics and mathematics of Maxwell's equations in the last chapter were worked out during the 1800s. In these equations, there is no real description for why electricity and magnetism should be related. Instead, the more practical description of the how is treated. Then, in 1905, came Albert Einstein's “On the Electrodynamics of Moving Bodies” [19], the paper that introduced the world to the Special Theory of Relativity. This paper showed the why of Maxwell's equations (while doing far more).

The Special Theory of Relativity rests on two assumptions, neither at first glance having much to do with electromagnestism.

Assumption I:Physics must be the same in all frames of reference moving at constant velocities with respect to each other.

Assumption II:The speed of light in a vacuum is the same in all frames of reference that move at constant velocities with respect to each other.

The first assumption is quite believable, saying in essence that how you choose your coordinates should not affect the underlying physics of what you are observing. It leads to an interesting problem, though, of how to translate from one coordinate system to another. It is the second assumption that will drastically restrict how we are allowed to change coordinate systems.

It is also this second assumption that is, at first glance, completely crazy. In the last chapter we saw that this craziness is already hidden in Maxwell's equations. Assumption II is an empirical statement, one that can be tested. In all experiments ever done (and there have been many), Assumption II holds. The speed of light is a constant.

But Einstein in 1905 had not done any of these experiments. How did he ever come up with such an idea?