Theory of Relativity

The theory of relativity, or simply relativity, refers specifically to two theories: Albert Einstein's special relativity and general relativity. [1]

Special relativity
Albert Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" introduced the special theory of relativity. Special relativity considers that observers in inertial reference frames, which are in uniform motion relative to one another, cannot perform any experiment to determine which one of them is "stationary". This is actually Galileo's principle of relativity; Einstein's contribution was to explicitly include electromagnetism within this principle, which required that the Galilean transformations be replaced by the Lorentz transformations. The resultant theory has many surprising consequences. In particular, it requires that the speed of light in a vacuum be the same for all these observers, regardless of their motion, or the motion of the source of the light, since the invariance of the speed of light is a consequence of Maxwell's equations of electromagnetism. [1]

Einstein's theory of special relativity results from two statements [4]:

1. The speed of light is the same for all observers, no matter what their relative speeds.

The first postulate -- the speed of light will be seen to be the same relative to any observer, independent of the motion of the observer -- is the crucial idea that led Einstein to formulate his theory. It means we can define a quantity c, the speed of light, which is a fundamental constant of nature.

2.The laws of physics are the same in any inertial (that is, non-accelerated) frame of reference. This means that the laws of physics observed by a hypothetical observer traveling with a relativistic particle must be the same as those observed by an observer who is stationary in the laboratory.

This second postulate is really a basic though unspoken assumption in all of science -- the idea that we can formulate rules of nature which do not depend on our particular observing situation. This does not mean that things behave in the same way on the earth and in space, e.g. an observer at the surface of the earth is affected by the earth's gravity, but it does mean that the effect of a force on an object is the same independent of what causes the force and also of where the object is or what its speed is.

General relativity
General relativity was developed by Einstein in the years 1907 - 1915. General relativity replaces the global Lorentz symmetry of special relativity with a local Lorentz symmetry in the presence of matter. The presence of matter "curves" spacetime, and this curvature affects the path of free particles (and even the path of light). General relativity uses the mathematics of differential geometry and tensors in order to describe gravitation as an effect of the geometry of spacetime. This theory is based on the general principle of relativity, which requires all observers to experience the same laws of physics, not just those moving with uniform speed, hence its name. [1]

[1] http://en.wikipedia.org/wiki/Theory_of_relativity
[2] http://en.wikipedia.org/wiki/Special_theory_of_relativity
[3] http://en.wikipedia.org/wiki/General_relativity
[4] http://www2.slac.stanford.edu/vvc/theory/relativity.html