Special Relativity
Relativistic Electrodynamics
Remember special relativity and its frames of references8? Where an event’s history depends on who we ask?
Well, it happened. Special relativity reminds us that according to an observer, something could be at rest or moving depending on that observer’s own motion. An observer could perceive himself as being stationary in his own frame of reference, but he could still be whizzing through space at incredible speeds, but view space as the moving entity. That’s all well and dandy, but when a phenomenon, such as the formation of a magnetic field, depends on the motion of something, then we’ll probably start scratching our heads a little. Whose frame of reference do we use?
A while back we learned how relativity alters fundamental notions such as time, energy, and momentum, and how no matter what, the laws of physics are the same in each frame of reference, though relating them to each other takes some skill. After all, Newtonian mechanics got quite the addition when Einstein came along.
That’s all fine and dandy, but how do the fundamental notions of electromagnetism change, then, when taking into account special relativity?
They don’t.
Even Albert Einstein thought a lot about this: one of his famous papers is called On the Electrodynamics of Moving Bodies. Relativity says light is always traveling at speed c. What Maxwell’s equations say is that an electromagnetic wave in one frame of reference should still be an electromagnetic wave in another frame. Not only that, but all electromagnetic waves are traveling at speed 
. Always. No matter the frame of reference or speed of an observer: the speed of light is an absolute constant.
Even electromagnetic induction relies on the relative motion of a magnet and a wire. It doesn’t matter which one is moving, as long as one of them does. This suggests no relativistic correction is needed for electromagnetic phenomena.
This may be true, but there’s still a catch: although all components of electromagnetic fields obey Maxwell’s equations, which do not ever change, the electric and magnetic fields themselves can change depending on the observer. This may seem bizarre, but as we recall that a point charge creates an electric field while a current produces a magnetic field, we may start to catch the drift.
Picture an observer sitting in the rest frame of a point charge and then start to move relative to it. In essence, according to the observer, there’s now a magnetic field present as well. What does it mean for the laws of electromagnetism to stay absolute? Simply that the electromagnetic field will break up consequentially in electric and magnetic components that are different for each observer.
Pretty neat, huh?
Brace yourself for a mind-blowing exploration of concept in Thoughts and Study.