Changes

'''Relativity''' refers to two closely-related mathematical theories in [[physics]]:

'''Relativity''' refers to two closely-related mathematical theories in [[physics]]:

*'''Special relativity''' (SR) is a theory which describes the laws of motion for non-accelerating bodies traveling at a significant fraction of the [[speed of light]].  As speeds approach zero, Special Relativity tends towards equivalence with [[Newton's Laws of Motion]].  Special Relativity was almost solely developed by [[Albert Einstein]], but had minor contributions from [[Hendrik Lorentz]], [[Henri Poincaré]], and Hermann Minkowski<ref>"German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical physics, and the theory of relativity." [http://www.britannica.com/eb/article-9052860/Hermann-Minkowski Hermann Minkowski -- Britannica Online Encyclopedia]</ref><ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Minkowski.html Hermann Minkowski, Biography]</ref>.

*'''Special relativity''' (SR) is a theory which describes the laws of motion for non-accelerating bodies traveling at a significant fraction of the [[speed of light]].  As speeds approach zero, Special Relativity tends towards equivalence with [[Newton's Laws of Motion]].  Special Relativity was developed by [[Hendrik Lorentz]], [[Henri Poincaré]], and Hermann Minkowski<ref>"German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical physics, and the theory of relativity." [http://www.britannica.com/eb/article-9052860/Hermann-Minkowski Hermann Minkowski -- Britannica Online Encyclopedia]</ref><ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Minkowski.html Hermann Minkowski, Biography]</ref>, and [[Albert Einstein]].

*'''General Relativity''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity.  This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as an extension of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.

*'''General Relativity''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity.  This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as an extension of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.

== Special Relativity ==

== Special Relativity ==

Special Relativity is usually explained in terms of two assumptions (postulates):

Lorentz and Poincare developed Special Relativity as way of understanding how Maxwell's equations for electromagnetism could be valid in different frames of reference. Einstein famously published an explanation of Poincare's theory in terms of two assumptions (postulates):

# ''The [[speed of light]] is constant for all (inertial) observers, regardless of their velocities relative to each other.''

# ''The [[speed of light]] is constant for all (inertial) observers, regardless of their velocities relative to each other.''

Special Relativity (SR) was initially developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], working on problems in electrodynamics and the [[Michelson-Morley experiment]], which had not found any sign of [[aether (science)|luminiferous aether]], which was believed to be the substance which carried electromagnetic waves. Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)

Special Relativity (SR) was initially developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], working on problems in electrodynamics and the [[Michelson-Morley experiment]], which had not found any sign of [[aether (science)|luminiferous aether]], which was believed to be the substance which carried electromagnetic waves. Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)

At low speeds (relative to light-speed), the Einstein-Lorentz relativity equations are equivalent to Newton's equations. The famous equation attributed to Einstein, ''E=mc²'', describes the relationship between energy and the rest mass of a body.

At low speeds (relative to light-speed), the Lorentz-Poincare relativity equations are equivalent to Newton's equations. The famous equation ''E=mc²'', describes the relationship between energy and the rest mass of a body.

Under relativity, particles at low mass and low speed can be accurately approximated by [[classical mechanics]] (such as [[Isaac Newton]]'s laws of motion). At the two extremes, modeling the behavior 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 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).

Under relativity, particles at low mass and low speed can be accurately approximated by [[classical mechanics]] (such as [[Isaac Newton]]'s laws of motion). At the two extremes, modeling the behavior 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 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).

== General Relativity ==

== General Relativity ==

General Relativity is a theory of gravity that is compatible with Special Relativity.  The theory was inspired by a thought experiment developed by Einstein involving two elevators.  The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g.  Einstein realized that any physical experiment carried out in the elevators would give the same result.  This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable.  General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.   

General Relativity is a theory of gravity that is compatible with Special Relativity.  Einstein explains a thought experiment involving two elevators.  The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g.  Einstein realized that any physical experiment carried out in the elevators would give the same result.  This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable.  General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.   

General Relativity is a mathematical extension of Special Relativity. GR views space-time as a 4-dimensional [[manifold]], which looks locally like [[Minkowski space]], and which acquires [[curvature]] due to the presence of massive bodies. Thus, near massive bodies, the geometry of space-time differs to a large degree from [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. Just as in classical physics, objects travel along [[geodesic]]s in the absence of external forces. Importantly though, near a massive body, geodesics are no longer straight lines. It is this phenomenon of objects traveling along geodesics in a curved spacetime that accounts for gravity.

General Relativity is a mathematical extension of Special Relativity. GR views space-time as a 4-dimensional [[manifold]], which looks locally like [[Minkowski space]], and which acquires [[curvature]] due to the presence of massive bodies. Thus, near massive bodies, the geometry of space-time differs to a large degree from [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. Just as in classical physics, objects travel along [[geodesic]]s in the absence of external forces. Importantly though, near a massive body, geodesics are no longer straight lines. It is this phenomenon of objects traveling along geodesics in a curved spacetime that accounts for gravity.