The theory of relativity is traditionally broken into two parts, special and general relativity. Special relativity provides a framework for translating physical events and laws into forms appropriate for any frame of reference. General relativity addresses the problem of accelerated motion and gravity.
Special Theory of Relativity :
A key problem for Newtonian physics was the need for absolute space and time when referring to events or interactions. In particular, the problems of light propagation required an medium, an aether, for the light waves to exist within. The Michelson-Morley experiment showed that there was not absolute space and that inertial frames were relative only to themselves.
Einstein realized that there is a logical contradiction with respect to Newtonian physics and electromagnetism with respect to what a light ray ``looks like'' when the observer is moving at the speed of light. The solution is that only massless photons can move at the speed of light, and that matter must remain below the speed of light regardless of how much acceleration is applied.
The key point to special relativity is that the speed of light (c=299,790 km per sec) is constant in all frames of reference. What this means can be best demonstrated by the following scenario:
In Newtonian mechanics, quantities such as speed and distance may be transformed from one frame of reference to another, provided that the frames are in uniform motion (i.e. not accelerating).
Under special relativity, there is a natural upper limit to velocity, the speed of light. And the speed of light the same in all directions with respect to any frame.
There are two important consequences of the speed of light limit; Lorentz contraction and time dilation. Lorentz contraction states than an object moving near the speed of light appears shorter to an observer at rest.
Similarly, time is compressed in frames of reference that travel at velocities near the speed of light, as compared to rest frames. This effect is called time dilation.
Time dilation leads to the famous Twins ``Paradox'', which is not a paradox but rather a simple fact of special relativity. Since clocks run slower in frames of reference at high velocity, then one can imagine a scenario were twins age at different rates when separated at birth due to a trip to the stars.
The effects of relativity are dramatic, but only when speeds approach the speed of light. At normal, everyday speeds the changes to clocks and rulers are too small to be measured. However, near extreme objects, such as black holes and neutron stars relativity dominates over Newtonian physics.
Special relativity describes changes in size and time through the use of Lorentz transformations. For an event that lasts to seconds in your frame, the same event will appear to last t in a frame that is moving with velocity v such that:
where c is the speed of light.
Spacetime:
Special relativity demonstrated that there is a relationship between spatial coordinates and temporal coordinates. That we can no longer reference spatial points without some reference to when. Einstein introduced a new concept, that there is an inherent connection between geometry of the Universe and its temporal properties. The result is a four dimensional (three of space, one of time) continuum called spacetime which can best be demonstrated through the use of Minkowski diagrams and world lines.
Spacetime makes sense from special relativity since it was shown that spatial coordinates (Lorentz contraction) and temporal coordinates (time dilation) vary between frames of reference.
Einstein also discovered that there is a relationship between mass, gravity and spacetime. Mass distorts spacetime, causing it to curve.
Gravity can be described as motion caused in curved spacetime .
Equivalence Principle :
The equivalence principle was Einstein's ``Newton's apple'' insight to gravitation. His thought experiment was the following, imagine two elevators, one at rest of the Earth's surface, one accelerating in space. To an observer inside the elevator (no windows) there is no physical experiment that he/she could perform to differentiate between the two scenarios.
An immediate consequence of the equivalence principle is that gravity bends light. To visualize why this is true imagine a photon crossing the elevator accelerating into space. As the photon crosses the elevator, the floor is accelerated upward and the photon appears to fall downward. The same must be true in a gravitational field by the equivalence principle.
The principle of equivalence renders the gravitational field fundamentally different from all other force fields encountered in nature. The new theory of gravitation, the general theory of relativity, adopts this characteristic of the gravitational field as its foundation.
General Relativity :
The second part of relativity is general theory of relativity and lies on two empirical findings that he elevated to the status of basic postulates. The first postulate is the relativity principle: local physics is governed by the theory of special relativity. The second postulate is the equivalence principle: there is no way for an observer to distinguish locally between gravity and acceleration.
The primary result from general relativity is that gravitation is a purely geometric consequence of the properties of spacetime. In this sense, general relativity is a field theory, relating Newton's law of gravity to the field nature of spacetime.
There were two classical test of general relativity, the first was that light should be deflected by passing close to a massive body. The first opportunity occurred during a total eclipse of the Sun in 1919.
Measurements of stellar positions near the darkened solar limb proved Einstein was right. Direct confirmation of gravitational lensing was obtained by the Hubble Space Telescope last year.
The second test is that general relativity predicts a time dilation in a gravitational field, so that, relative to someone outside of the field, clocks (or atomic processes) go slowly. This was confirmed with atomic clocks flying airplanes in the mid-1970's.
The general theory of relativity is constructed so that its results are approximately the same as those of Newton's theories as long as the velocities of all bodies interacting with each other gravitationally are small compared with the speed of light--i.e., as long as the gravitational fields involved are weak. The latter requirement may be stated roughly in terms of the escape velocity. A gravitational field is considered strong if the escape velocity approaches the speed of light, weak if it is much smaller. All gravitational fields encountered in the solar system are weak in this sense.
A low speeds and weak gravitational fields, general and special relativity reduce to Newtonian physics.
