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:
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:
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:
where m_{0} is the rest mass of the body.
(The term √( 1 - v^{2}/c^{2} ) 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
which is precisely equal to the "energy of existence", m_{0}c^{2}, and the Newtonian kinetic energy, m_{0}v^{2}/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 implication 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 carrying mass or information can move faster than this speed. As an object's velocity approaches the speed of light, the amount of energy required to accelerate it approaches infinity, making it impossible 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.
The name "tachyon" has been used for hypothetical particles which would move faster than the speed of light, but to date evidence of the actual existence of tachyons has not been produced.
There are a handful of people opposed to relativity on various grounds who have proposed various alternatives, mainly [ether theories]?.
See also general relativity.