Relativity and Special Relativity, the difference?

Special relativity has two postulates. The first (also known as the "Principle of Relativity") which Mistress Bekki expressed so well goes all the way back to Gallileo. "Relativity is the idea that the laws of physics do not change from one inertial reference frame and another." The second, which Ms. Bekki also said, but not so explicitly, is that the speed of light is the same for all observers, and it does not depend on the relative velocity of the observer and the light source.

General relativity keeps those two postulates, and adds a third called the Principle of Equivalence that says, acceleration due to gravity is indistinguishable from accelerated motion. To make that a little more clear, imagine an observer who is sealed inside a closed box, and who feels an acceleration pulling him toward the "floor" of the box. There is no experiment that the observer can do inside the box to determine whether the acceleration is due to the box sitting motionless on the surface of a massive planet or, due to the box being accelerated through space by a rocket motor.

All of the weird laws of special relativity (e.g., time dialation, and length contraction) are inevitable, mathematical consequences of the first two postulates, and all of the additional phenomena predicted by general relativity (e.g., gravitational lensing and black holes) are consequences of all three postulates.

Relativity is the idea that the laws of physics do not change from one inertial reference frame and another. Any experiment that you can do in your laboratory at home should work equally well in a train coach or the stateroom of a ship (provided the train/ship is just cruising along and not accelerating, bumping, rolling, or turning). This was known since before the time of Galileo. Newtonian mechanics incorporates relativity. Specifically, Newtonian mechanics work under the following transformation (called the Galilean transformation) from one reference frame (x,t) to another (x',t') moving at a speed v.

x -> x' - vt'

t -> t'

That's pretty straightforward. Everybody measures the same time and their positions are off by a reasonable, intuitive amount based on the relative motion. Everyone agrees on the time and distance between two events.

Now the trouble is that the laws of electricity and magnetism (discovered by various folks and compiled by Maxwell) are NOT invariant under this transformation. Some folks thought that the old concept of relativity does not apply to electricity and magnetism--that the laws of E&M only work with respect to an ether. Einstein, however, assumed that relativity SHOULD apply to E&M and that Newtonian mechanics must be flawed. He thereby developed special relativity and derived new transformation laws (which had already been figured out by Lorentz, so they have his name).

x -> gamma (x' - vt')

t -> gamma (t' - vx' / c^2)

Under these new laws, not everybody measures the same times and distances between events. That factor of gamma goes from one at slow speeds up towards infinity as you approach the speed of light. Moving clocks run slow and moving rulers are short!

To expand on Mistress Bekki's excellent answer:

In this case, the word "special" means that it only applies in special circumstances. The special circumstances are: the reference frame (the "lab" from which you make your measurement) must be stationary or moving in a straight line at a constant speed. This version of the theory did not consider what happens in cases where the reference frame is changing speed, changing direction or rotating.

The term "special" was NOT meant to distinuish Einstein's relativity from the older (Galilean) idea of relativity. "Special" was meant to distinguish it from Einstein's OTHER theory of relativity, which he developed a few years later, and which was called the "General" theory of relativity. The general theory deals with reference frames in any type of motion, not just "straight line, constant speed" motion.

In science and math, "special" means it applies in a limited set of circumstances; and "general" means it applies in all circumstances.

General theory of relativity = the geometric theory of gravitation

eg gravitational lensing, black holes e.t.c.

Special Theory of Relativity = the physical theory of measurement in inertial frames of reference.

eg. time dilation and length contraction