Wikipedia: Theory of relativity

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The theory of relativity, first published in 1905 by Albert Einstein, describes the physics of motion. Prior to then, most physicists believed that the classical mechanics first devised by Isaac Newton described such concepts of velocity and force for all observers (or frames of reference). However, it had been noted, by [Hendrik Lorentz]? amongst others, that Maxwells equations, which govern electromagnetism did not behave in accordance with Newton's laws when the frame of reference is changed (i.e. when you consider the same physical problem from the point of view of two observers moving relative to each other. It is this notion of transforming the laws of physics between observers moving relative to one another that gives the theory its name). Lorentz showed how a correction term, known as the Lorentz transformation brought Maxwell's laws back in sync with Newton's.

Newton's laws, seemingly violated in electromagnetism, consider time to be invariant (unchanging) between the observers. Einstein's first great breakthrough, which came with the publication of his Special Theory of Relativity, was to show that if one applied the Lorentz transformation to all Newtonian mechanics, the resulting system had several interesting properties:

Electromagnetism was no longer a special case that required Lorentz' "fudge" for consistency.
When the velocities involved are much less than speed of light, the resulting laws simplify to Newton's laws.
Time is no longer invariant between frames, but the speed of light is.

The first two properties were very appealing, since any new theory had to fit existing data, and existing data said that Newton's laws were very accurate. The third conclusion was originally highly contentious, as it overthrew many well understood and seemingly obvious notions, such as the concept of simultaneity.

The Special Theory also had far reaching consequences: first, it stated that all motion was relative, that there is no universal notion of "stationary". Previously it had been believed that the universe travelled through a substance known as "ether" (absolute space), against which speeds could be measured. Einstein's rejection of the ether was in accordance with the famous [Michelson-Morley experiment]? which had singularly failed to detect it.

Perhaps most far reachingly, it also showed that energy and mass, previously considered separate, were equivalent, and related by the most famous expression from the theory:

E = mc²

where E is the energy, m is the mass and c is the speed of light. If the body is moving with speed v relative to the observer, this can be written as:

E = m₀c² / √( 1 - v²/c² )

where m₀ is the rest mass of the body.

(The term √( 1 - v²/c² ) occurs frequently in relativity, and comes from the Lorentz equations. It is worth noting that if v is much less than c this can be written as

E ~= m₀c² + m₀v² / 2

which is precisely equal to the "energy of existence", m₀c², and the Newtonian kinetic energy, m₀v²/2. This is just one example of how the two theories coincide when velocities are small.)

At very high speeds, the denominator in the energy equation (2) approaches a value of zero as the velocity approaches c. Thus, at the speed of light, the energy would be infinite, and precludes things that have mass from moving any faster.

The most practical result of this theory is that it puts an upper limit to the laws (see Law of nature) of Classical Mechanics and gravity formed by Isaac Newton at the speed of light. Nothing can move faster than this speed. As an object accelerates, approaching the speed of light, its mass will increase making it infinitely hard to reach the speed of light. Only particles with no mass, such as photons, can actually achieve this speed, which is approximately 300,000 kilometers per second or 186,300 miles per second.

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