When we hear about Einstein and the special relativity (or the special theory of relativity, to use the real name), we think of the famous equation, and weird things like the twin paradox. While those things are all true and important, the problem SR tries to solve is a completely different one. It is an attempt to defend a basic principle in physics.
The basic principle of relativity is that the laws of physics do not change when you move without acceleration. In other words, motion at a constant velocity is indistinguishable from being stationary, which is why you may have had this illusion while in a stationary train on a platform that you are moving, when the train next to you starts moving. Whatever experiments you can do will not tell you whether you are standing still or moving.
If you think about it, it has to be this way. If there were only two objects in the universe, it wouldn’t make any sense to say which one is moving. Only relative motion has physical significance. Associated with each moving object is a coordinate system, or a frame of reference, called an inertial frame. All inertial frames are equivalent, which is considered a symmetry in physics and is called the principle of relativity.
The symmetry of indistinguishability of inertial frames (the principle of relativity) in motion is true of electricity and magnetism as well. By the way, I don’t know what the corresponding conserved quantity is, but I suspect it is the length of space or space-time vectors, depending on whether you use pre-Einstein (Galilean) or post-Einstein (Lorentz) relativity. A coil moving next to magnet generates electricity. The amount of electricity generated depends only on the relative velocity, doesn’t matter whether you move the coil or the magnet. So the principle of equivalence of inertial frames holds for electricity and magnetism as well. Electromagnetism is described in Maxwell’s equations (relating space and time variations in electric and magnetic fields to currents and charges) should be “covariant” – meaning, it should change in the same was as the coordinates transform. Otherwise, microwave ovens would work differently on an airplane.
One solution to Maxwell’s equations is EM waves (light) moving at its speed. The covariance of these equations means that the speed of light has to be the same constant when measured in any inertial frame. Based on this observation, Einstein postulated that the constancy of the speed of light is a basic law of nature. Once you accept this postulate, we have to accept that it does not change when measured in different inertial frames. In order for this speed to be a constant, space and time will have to change instead. We will delve into this constancy, both in terms of physics and philosophy, in the next section.