This paper has been a 'busy' page on the web since it was put there in 1995. The attention was to assist high school and university students to a mathematically sound view of the concept of special relativity which is often difficult to grasp and often misunderstood when approached more 'lyrically'.
Based on two simple assumptions, it follows a logical path to strange results which have been time and time again verified by observation and experiment.
This explanation is complete and mathematical, but only at high school level, it does not require calculus or complex algebra or calculations, merely a bit of trigonometry to get started.
The popularity of the special theory of relativity stems from extraordinary predictions about time, distance, mass, Energy and the nature of space. What follows attempts to connect the concepts of time dilation with the equivalence of mass and energy and the concept of four dimensions. Relativity isn't a fact, it is a set of ideas which can be used to interpret the results of experiments and observations and to make predictions in a consistent way, so far it has done so with great accuracy.
NOTE: Throughout this essay an assumption that NO ACCELERATION is going on is implicit, consideration of relativistic effects due to acceleration (or vice versa) are the realm of General relativity and Mach's Principle (which has nothing to do with the speed of sound).
There are two principles:
1. The speed of light, in empty space, is the same c independent of the motion of its source.
2. A principle best stated in several forms:
Electrodynamic and mechanical effects do not have properties that require the concept of an absolute state of rest.
The speed of an object cannot be determined IN ANY WAY without external reference. This is hard to prove since EVERY WAY of detecting motion should be checked and we don't know them all!
No object is absolutely stationary (this is well known to the highway patrol).
The concept of absolute (non-accelerating) motion is invalid.