General relativity

General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. It unifies special relativity and Sir Isaac Newton's law of universal gravitation with the insight that gravitational force can be regarded as the manifestation of the curvature of space and time, with this curvature being produced by the mass-energy and momentum content of the matter in space-time. General relativity is distinguished from other metric theories of gravitation by its use of the Einstein field equations to relate space-time content and space-time curvature.

General relativity is currently the most successful gravitational theory, being almost universally accepted and well supported by observations. The first success of general relativity was in explaining the anomalous perihelion precession of Mercury. Then in 1919, Sir Arthur Eddington announced that observations of stars near the eclipsed Sun confirmed general relativity's prediction that massive objects bend light. Since then, many other observations and experiments have confirmed many of the predictions of general relativity, including gravitational time dilation, the gravitational redshift of light, signal delay, and gravitational radiation. In addition, numerous observations are interpreted as confirming one of general relativity's most mysterious and exotic predictions, the existence of black holes.

In the mathematics of general relativity, the Einstein field equations become a set of simultaneous differential equations which are solved to produce metric tensors of space-time. These metric tensors describe the shape of the space-time, and are used to obtain the predictions of general relativity. The connections of the metric tensors specify the geodesic paths that objects follow when traveling inertially. Important solutions of the Einstein field equations include the Schwarzschild solution (for the space-time surrounding a spherically symmetric uncharged and non-rotating massive object), the Reissner-Nordström solution (for a charged spherically symmetric massive object), and the Kerr metric (for a rotating massive object).

In spite of its overwhelming success, there is discomfort with general relativity in the scientific community due to its being incompatible with quantum mechanics and the reachable singularities of black holes (at which the math of general relativity breaks down). Because of this, numerous other theories have been proposed as alternatives to general relativity. An early and still-popular class of modifications is Brans-Dicke theory, which, although not solving the problems of singularities and quantum gravity, appeared to have observational support in the 1960s. However, those observations have since been refuted and modern measurements indicate that any Brans-Dicke type of deviation from general relativity must be very small if it exists at all.

Special relativity

The special theory of relativity was proposed in 1905 by Albert Einstein in his article "On the Electrodynamics of Moving Bodies".Earlier, Galileo's principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest; a person on the deck of a ship may be at rest in his opinion, but someone observing from the shore would say that he was moving. Einstein's theory combines Galilean relativity with the postulate that all observers will always measure the speed of light to be the same no matter what their state of uniform linear motion is.

This theory has a variety of surprising consequences that seem to violate common sense, but that have been verified experimentally. Special relativity overthrows Newtonian notions of absolute space and time by stating that distance and time depend on the observer, and that time and space are perceived differently, depending on the observer. It yields the equivalence of matter and energy, as expressed in the mass-energy equivalence formula E = mc², where c is the speed of light in a vacuum. Special relativity agrees with Newtonian mechanics in their common realm of applicability, in experiments in which all velocities are small compared to the speed of light.

The theory was called "special" because it applies the principle of relativity only to inertial frames. Einstein developed general relativity to apply the principle generally, that is, to any frame, and that theory includes the effects of gravity. Special relativity doesn't account for gravity, but it can deal with accelerations.

Although special relativity makes some quantities relative, such as time, that we would have imagined to be absolute based on everyday experience, it also makes absolute some others that we would have thought were relative. In particular, it states that the speed of light is the same for all observers, even if they are in motion relative to one another. Special relativity reveals that c is not just the velocity of a certain phenomenon - light - but rather a fundamental feature of the way space and time are tied together. In particular, special relativity states that it is impossible for any material object to accelerate to light speed.