All of special relativity proceeds from two basic ideas. The first is that Maxwell's equations, which seem to be superb descriptions of electromagnetism, yield a wave equation with a speed of 3x10^8 m/s for the propagation of electromagnetic waves, which we now recognize as light. Now, the wave equation for any phenomenon always tells you the propagation speed, and that speed is always understood to be relative to the medium in which the wave disturbance travels - water, string, air. With light, however, no medium is necessary. The implications of this are so profound that for years physicists refused to believe it; they continued to try to find the "aether", a medium possessed of increasingly tenuous properties. It had no mass, no charge, no taste or smell. It just couldn't be found, which was too bad, because it would certainly define an interesting reference frame for the universe.

Einstein escaped this morass by accepting the nonexistence of the aether, and endorsing an old standard, that is, that all inertial reference frames are equally good. That's the second basic idea.

From those two basic ideas come all the peculiar-looking stuff of special relativity: length contraction, time dilation, nothing going faster than c, the mass-energy relation. For this course, what you really need to know is that mass can be converted into other forms of energy, following the rule E=mc^2. You also need to know that the classical definition of kinetic energy is a good approximation to the true (relativistic) definition as long as v<<c or, equivalently, KE<<mc^2.

It's also important to know that momentum remains an important (and conserved!) quantity, except that it turns out that the classical definition of momentum, p=mv, is just the low-speed approximation to the true momentum, p=gamma mv, where gamma is 1 over the square root of 1-(v/c)^2. This gamma turns up all over the place. The total energy of a particle is E=gamma mc^2. This total energy consists of the kinetic energy plus the rest energy, which is mc^2. You can easily show that the square of the total energy equals the square of the rest energy plus the square of the quantity (pc); go ahead and do so.