Theory of relativity
The Theory of Relativity is a geometrical theory of gravitation, stating that the speed of light and laws of physics are constant for all observers, regardless of their velocities relative to eachother.
The theory of relativity was first proposed based on mathematical theory (derived from a series of thought experiments by Einstein) rather than observation. The theory rests on two postulates that are themselves difficult to test, and then derives mathematically what the physical consequences should be (and hence experimentally testable predictions). Einstein's thought experiments pondered what would happen if the speed of light was constant in all frames of reference, and all laws of physics were the same in every (inertial) frame of reference no matter where it is or how fast it is traveling. This theory improves on Isaac Newton's theory of gravitation by disposing with the idea of a universal, mutually agreeable scale of time (i.e. a universal clock that all times can refer to) and space (i.e. a universal sheet of "graph paper", which location refers to). In general terms, relativity predicts that space-time can be curved by massive bodies, so that (for example) near a black hole the sum of the angles in a triangle is not exactly 180 degrees, time passes more rapidly away from a black hole than near it (for a distant observer) and other apparent violations of geometry and common sense.
Relativity is important for massive or fast-moving bodies: at low mass and low speed, it can be accurately approximated by classical mechanics (such as Isaac Newton's laws of motion). At the two extremes, modelling the behaviour of electrons requires that relativistic effects be taken into account (the chemically significant phenomenon of electron spin arises from relativity), and the course light passing through a region containing many massive bodies such as galaxies will be distorted (classical mechanics, in which light travels with infinite speed in straight lines, does not predict this). These are both experimentally confirmed (electron spin was known before relativity arose, and telescopic observations confirm that galactic clusters distort the paths of the light passing through them).
One of the mathematical consequences of the theory - the well known equivalance between energy and matter, E=mc^2 - predicted the release of energy in nuclear reactions, explaining the source of the sun's fusion energy and spurring the development of fissile weapons (the atomic bomb). Another was the effect of high-relative-speed ("relativistic") travel on the passage of time: from this relativity was able to explain, and accurately predict, the anomalous orbit of the planet Mercury (travelling at high speed very close to the sun).
British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir Arthur Eddington, an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse. Upon his return to England declared that his observations proven the theory of relativity. In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data was inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the Hubble Space Telescope.
Like most significant scientific discoveries, relativity has been widely adopted as a social analogy, but the comparison has little factual basis (the common quip about placing a hand on a hot stove has nothing to do with Einstein's theory). For example the idea of moral relativity exists independent of (and substantially predates) the theory of relativity.
Many ongoing questions in physics arise from relativity. For example there is much debate on the curvature of the universe as a whole - while it locally curves inwards at planets and stars, it is not obvious that it curves inwards overall. It may by flat, or curve outwards (a counterintuitive situation in which the universe is hyperbolic). Also, while concepts from relativity have been integrated into quantum mechanics, the two are still incompatible. Development of a quantum theory of gravity (the "theory of everything") is arguably the most important research effort in physics today, one of the most notable examples being string theory.
