The theory of relativity usually encompasses two interrelated theories by

^{2}/c^{2}) were possible in principle, Maxwell thought they were too small to be detected with then-current technology.
The Michelson–Morley experiment was designed to detect second-order effects of the "aether wind"—the motion of the aether relative to the earth. Michelson designed an instrument called the

The Meaning of Relativity

Albert Einstein: Four lectures delivered at Princeton University, May 1921

How I created the theory of relativity

Albert Einstein, December 14, 1922; Physics Today August 1982

Relativity

Sidney Perkowitz Encyclopædia Britannica

Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born , widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the , but he also made important contributions to the develo ...

: special relativity
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

and general relativity
General relativity, also known as the general theory of relativity, is the of published by in 1915 and is the current description of gravitation in . General generalizes and refines , providing a unified description of gravity as a geome ...

, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity
Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate'' toward) one another. , gravity gives to s, and the causes the s of the oceans. The gravitational attracti ...

. General relativity explains the law of gravitation and its relation to other forces of nature. It applies to the cosmological
Cosmology (from Greek#REDIRECT Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece
Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...

and astrophysical realm, including astronomy.
The theory transformed theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, natural phenomena. This is in contrast to experimental phy ...

and astronomy
Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...

during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of s ...

. It introduced concepts including spacetime
In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and when events occur.
Until the 20th century, it was assumed that the three ...

as a unified entity of space
Space is the boundless extent in which and events have relative and . In , physical space is often conceived in three s, although modern s usually consider it, with , to be part of a boundless known as . The concept of space is considere ...

and time
Time is the continued of and that occurs in an apparently succession from the , through the , into the . It is a component quantity of various s used to events, to compare the duration of events or the intervals between them, and to of ...

, relativity of simultaneity
In physics, the relativity of simultaneity is the concept that ''distant simultaneity'' – whether two spatially separated events occur at the same Time in physics, time – is not absolute time and space, absolute, but depends on th ...

, kinematic
Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion
Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position
In physics, motion is the phenomenon in which an object changes its ...

and gravitational
Gravity (), or gravitation, is a natural phenomenon by which all things with mass
Mass is both a property
Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an ...

time dilation
In physics and Theory of relativity, relativity, time dilation is the difference in the elapsed Time in physics, time as measured by two clocks. It is either due to a relative velocity between them (special relativity, special relativistic "kine ...

, and length contraction
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length
Proper length or rest length is the length of an object in the object's rest frame.
The measurement of lengths is more compl ...

. In the field of physics, relativity improved the science of elementary particles
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include the fundamental fermions (quarks, leptons, antiquarks, and a ...

and their fundamental interactions, along with ushering in the nuclear age
The Atomic Age, also known as the Atomic Era, is the period of history following the detonation of the first nuclear weapon, The Gadget at the ''Trinity (nuclear test), Trinity'' test in New Mexico, on July 16, 1945, during World War II. Although ...

. With relativity, cosmology
Cosmology (from Greek#REDIRECT Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece
Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approx ...

and astrophysics
Astrophysics is a science that employs the methods and principles of physics in the study of astronomical objects and phenomena. Among the subjects studied are the Sun, other stars, galaxy, galaxies, extrasolar planets, the interstellar medium and ...

predicted extraordinary astronomical phenomena such as neutron stars
A neutron star is the of a massive , which had a total of between 10 and 25 es, possibly more if the star was especially -rich. Except for s, and some objects (e.g. s, s, and s), neutron stars are the smallest and densest currently known c ...

, , and gravitational waves
Gravitational waves are disturbances in the curvature of spacetime
In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and wh ...

.
Development and acceptance

Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born , widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the , but he also made important contributions to the develo ...

published the theory of special relativity
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

in 1905, building on many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz
Lorentz' theory of electrons. Formulas for the curl of the magnetic field (IV) and the electrical field E (V), ''La théorie electromagnétique de Maxwell et son application aux corps mouvants'', 1892, p. 452.
Hendrik Antoon Lorentz (; 18 Ju ...

, Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French
French (french: français(e), link=no) may refer to:
* Something of, from, or related to France
France (), officially the French Repu ...

and others. Max Planck
Max Karl Ernst Ludwig Planck, (; ; 23 April 1858 – 4 October 1947) was a German
German(s) may refer to:
Common uses
* of or related to Germany
* Germans, Germanic ethnic group, citizens of Germany or people of German ancestry
* For citi ...

, Hermann Minkowski
Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as ...

and others did subsequent work.
Einstein developed general relativity
General relativity, also known as the general theory of relativity, is the of published by in 1915 and is the current description of gravitation in . General generalizes and refines , providing a unified description of gravity as a geome ...

between 1907 and 1915, with contributions by many others after 1915. The final form of general relativity was published in 1916.
The term "theory of relativity" was based on the expression "relative theory" (german: Relativtheorie) used in 1906 by Planck, who emphasized how the theory uses the principle of relativity
In physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

. In the discussion section of the same paper, Alfred Bucherer
150px, Alfred Bucherer
Alfred Heinrich Bucherer (* 9 July 1863 in Cologne
Cologne ( ; german: Köln ; ksh, Kölle ) is the largest city of Germany, Germany's most populous States of Germany, state of North Rhine-Westphalia (NRW) and the List ...

used for the first time the expression "theory of relativity" (german: Relativitätstheorie).
By the 1920s, the physics community understood and accepted special relativity. It rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of atomic physics, nuclear physics
Nuclear physics is the field of physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ent ...

, and quantum mechanics
Quantum mechanics is a fundamental theory
A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...

.
By comparison, general relativity did not appear to be as useful, beyond making minor corrections to predictions of Newtonian gravitation theory. It seemed to offer little potential for experimental test, as most of its assertions were on an astronomical scale. Its mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...

seemed difficult and fully understandable only by a small number of people. Around 1960, general relativity became central to physics and astronomy. New mathematical techniques to apply to general relativity streamlined calculations and made its concepts more easily visualized. As astronomical phenomena
A phenomenon (; plural phenomena) is an observable fact or event. The term came into its modern philosophical
Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, existence, knowledge ...

were discovered, such as quasars
A quasar (; also known as a quasi-stellar object, abbreviated QSO) is an extremely luminous active galactic nucleus (AGN), powered by a supermassive black hole, with mass ranging from millions to tens of billions of solar masses, surrounded by a ...

(1963), the 3-kelvin microwave background radiation
The cosmic microwave background (CMB, CMBR), in Big Bang
The Big Bang theory
A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and ratio ...

(1965), pulsar
A pulsar (from ''pulsating radio source'') is a highly magnetized rotating neutron star
A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the s ...

s (1967), and the first candidates (1981), the theory explained their attributes, and measurement of them further confirmed the theory.
Special relativity

Special relativity is a theory of the structure ofspacetime
In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and when events occur.
Until the 20th century, it was assumed that the three ...

. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies
200px, Einstein in 1904 or 1905, about the time he wrote the ''Annus Mirabilis'' papers
The ''Annus mirabilis'' papers (from Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European l ...

" (for the contributions of many other physicists see History of special relativity
The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz
Lorentz' theory of electrons. Formulas for the curl of the magnetic field (IV) and the electr ...

). Special relativity is based on two postulates which are contradictory in classical mechanics:
# The laws of physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

are the same for all observers in any inertial frame of reference
In classical physics and special relativity, an inertial frame of reference is a frame of reference that is not undergoing acceleration. In an inertial frame of reference, a physical object with zero net force acting on it moves with a const ...

relative to one another (principle of relativity
In physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

).
# The speed of light
The speed of light in vacuum
A vacuum is a space
Space is the boundless three-dimensional
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...

in a vacuum
A vacuum is a space
Space is the boundless three-dimensional
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter
A parameter (from the Ancient Gr ...

is the same for all observers, regardless of their relative motion or of the motion of the light
Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

source.
The resultant theory copes with experiment better than classical mechanics. For instance, postulate 2 explains the results of the Michelson–Morley experiment
The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether
upright=1.25, The luminiferous aether: it was hypothesised that the Earth moves through a "medium" of aether that carries light
Luminiferous aet ...

. Moreover, the theory has many surprising and counterintuitive consequences. Some of these are:
* Relativity of simultaneity
In physics, the relativity of simultaneity is the concept that ''distant simultaneity'' – whether two spatially separated events occur at the same Time in physics, time – is not absolute time and space, absolute, but depends on th ...

: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
* Time dilation
In physics and Theory of relativity, relativity, time dilation is the difference in the elapsed Time in physics, time as measured by two clocks. It is either due to a relative velocity between them (special relativity, special relativistic "kine ...

: Moving clock
A clock or a timepiece is a device used to measure and indicate time
Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past ...

s are measured to tick more slowly than an observer's "stationary" clock.
* Length contraction
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length
Proper length or rest length is the length of an object in the object's rest frame.
The measurement of lengths is more compl ...

: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
* Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.
** The effect of gravity can only travel through space at the speed of light, not faster or instantaneously.
* Mass–energy equivalence
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

: , energy and mass are equivalent and transmutable.
* Relativistic mass
The word ''mass'' has two meanings in special relativity: ''invariant mass'' (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the ''relativistic mass'' is dependent on the velocity ...

, idea used by some researchers.
The defining feature of special relativity is the replacement of the Galilean transformation
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Spa ...

s of classical mechanics by the Lorentz transformation
In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the ...

s. (See Maxwell's equations
Maxwell's equations are a set of coupled partial differential equation
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), ...

of electromagnetism
Electromagnetism is a branch of physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in ...

.)
General relativity

General relativity is a theory of gravitation developed by Einstein in the years 1907–1915. The development of general relativity began with theequivalence principle
In the theory
A theory is a rational
Rationality is the quality or state of being rational – that is, being based on or agreeable to reason
Reason is the capacity of consciously making sense of things, applying logic
Logic (fr ...

, under which the states of accelerated motion and being at rest in a gravitational field
In physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

(for example, when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall #REDIRECT Free fall #REDIRECT Free fall
In Newtonian physics, free fall is any motion of a body where gravity
Gravity (), or gravitation, is a list of natural phenomena, natural phenomenon by which all things with mass or energy—inc ...

is : an object in free fall is falling because that is how objects move when there is no force
In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

being exerted on them, instead of this being due to the force of gravity
Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate'' toward) one another. , gravity gives to s, and the causes the s of the oceans. The gravitational attracti ...

as is the case in classical mechanics. This is incompatible with classical mechanics and special relativity
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

because in those theories inertially moving objects cannot accelerate with respect to each other, but objects in free fall do so. To resolve this difficulty Einstein first proposed that spacetime is curved
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight.
Intuitively, a curve may be thought of as the trace left by a moving point (geo ...

. In 1915, he devised the Einstein field equations
In the general theory of relativity
General relativity, also known as the general theory of relativity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the curren ...

which relate the curvature of spacetime with the mass, energy, and any momentum within it.
Some of the consequences of general relativity are:
* Gravitational time dilation: Clocks run slower in deeper gravitational wells.
* Precession
Precession is a change in the orientation
Orientation may refer to:
Positioning in physical space
* Map orientation, the relationship between directions on a map and compass directions
* Orientation (housing), the position of a building with re ...

: Orbits precess in a way unexpected in Newton's theory of gravity. (This has been observed in the orbit of Mercury
Mercury usually refers to:
* Mercury (planet)
Mercury is the smallest planet in the Solar System and the closest to the Sun. Its orbit around the Sun takes 87.97 Earth days, the shortest of all the Sun's planets. It is named after the Roman g ...

and in binary pulsar
A binary pulsar is a pulsar
Animation of a rotating pulsar. The sphere in the middle represents the neutron star, the curves indicate the magnetic field lines and the protruding cones represent the emission zones.
A pulsar (from ''pulse'' and ' ...

s).
* Light deflection: Rays of light
Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

bend in the presence of a gravitational field.
* Frame-dragging
Frame-dragging is an effect on spacetime
In physics, spacetime is any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional manifold. Minkowski diag ...

: Rotating masses "drag along" the spacetime
In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and when events occur.
Until the 20th century, it was assumed that the three ...

around them.
* Metric expansion of space
The expansion of the universe is the increase in distance
Distance is a numerical measurement
'
Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or ...

: the universe is expanding, and the far parts of it are moving away from us faster than the speed of light.
Technically, general relativity is a theory of gravitation
Gravity (), or gravitation, is a natural phenomenon
Types of natural phenomena include:
Weather, fog, thunder, tornadoes; biological processes, decomposition, germination
seedlings, three days after germination.
Germination is t ...

whose defining feature is its use of the Einstein field equations
In the general theory of relativity
General relativity, also known as the general theory of relativity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the curren ...

. The solutions of the field equations are metric tensors
METRIC (Mapping EvapoTranspiration at high Resolution with Internalized Calibration) is a computer model developed by the University of Idaho, that uses Landsat satellite data to compute and map evapotranspiration (ET). METRIC calculates ET as a re ...

which define the topology
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...

of the spacetime and how objects move inertially.
Experimental evidence

Einstein stated that the theory of relativity belongs to a class of "principle-theories". As such, it employs an analytic method, which means that the elements of this theory are not based on hypothesis but on empirical discovery. By observing natural processes, we understand their general characteristics, devise mathematical models to describe what we observed, and by analytical means we deduce the necessary conditions that have to be satisfied. Measurement of separate events must satisfy these conditions and match the theory's conclusions.Tests of special relativity

Relativity is afalsifiable
In the philosophy of science, a theory is falsifiable if it is contradicted by ''possible observations''—i.e., by any observations that can be described in the language of the theory, which must have a conventional empirical interpretation. ...

theory: It makes predictions that can be tested by experiment. In the case of special relativity, these include the principle of relativity, the constancy of the speed of light, and time dilation. The predictions of special relativity have been confirmed in numerous tests since Einstein published his paper in 1905, but three experiments conducted between 1881 and 1938 were critical to its validation. These are the Michelson–Morley experiment
The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether
upright=1.25, The luminiferous aether: it was hypothesised that the Earth moves through a "medium" of aether that carries light
Luminiferous aet ...

, the Kennedy–Thorndike experiment
The Kennedy–Thorndike experiment, first conducted in 1932 by Roy J. Kennedy and Edward M. Thorndike, is a modified form of the Michelson–Morley experiment
The Michelson–Morley experiment was an attempt to detect the existence of the lumini ...

, and the Ives–Stilwell experiment
The Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler effect, Doppler shift of light. The result was in agreement with the formula for the relativistic Doppler effect, transverse Doppler effect and was ...

. Einstein derived the Lorentz transformation
In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the ...

s from first principles in 1905, but these three experiments allow the transformations to be induced from experimental evidence.
Maxwell's equations
Maxwell's equations are a set of coupled partial differential equation
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), ...

—the foundation of classical electromagnetism—describe light as a wave that moves with a characteristic velocity. The modern view is that light needs no medium of transmission, but Maxwell and his contemporaries were convinced that light waves were propagated in a medium, analogous to sound propagating in air, and ripples propagating on the surface of a pond. This hypothetical medium was called the luminiferous aether
Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium
Medium may refer to:
Science and technology
Aviation
*Medium bomber, a class of war plane
*Tecma Medium, a French hang glider design
Communic ...

, at rest relative to the "fixed stars" and through which the Earth moves. Fresnel's partial ether dragging hypothesis ruled out the measurement of first-order (v/c) effects, and although observations of second-order effects (vMichelson interferometer 300px, Figure 1. A basic Michelson interferometer, not including the optical source and detector.
The Michelson interferometer is a common configuration for optical interferometry and was invented by Albert Abraham Michelson. Using a beam splitter, ...

to accomplish this. The apparatus was more than accurate enough to detect the expected effects, but he obtained a null result when the first experiment was conducted in 1881, and again in 1887. Although the failure to detect an aether wind was a disappointment, the results were accepted by the scientific community. In an attempt to salvage the aether paradigm, FitzGerald and Lorentz independently created an ''ad hoc'' hypothesis in which the length of material bodies changes according to their motion through the aether. This was the origin of FitzGerald–Lorentz contraction, and their hypothesis had no theoretical basis. The interpretation of the null result of the Michelson–Morley experiment is that the round-trip travel time for light is isotropic
Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, "equal") and ''tropos'' (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by ...

(independent of direction), but the result alone is not enough to discount the theory of the aether or validate the predictions of special relativity.
While the Michelson–Morley experiment showed that the velocity of light is isotropic, it said nothing about how the magnitude of the velocity changed (if at all) in different inertial frame
In classical physics and special relativity, an inertial frame of reference is a frame of reference that is not undergoing acceleration. In an inertial frame of reference, a physical object with zero net force acting on it moves with a const ...

s. The Kennedy–Thorndike experiment was designed to do that, and was first performed in 1932 by Roy Kennedy and Edward Thorndike. They obtained a null result, and concluded that "there is no effect ... unless the velocity of the solar system in space is no more than about half that of the earth in its orbit". That possibility was thought to be too coincidental to provide an acceptable explanation, so from the null result of their experiment it was concluded that the round-trip time for light is the same in all inertial reference frames.
The Ives–Stilwell experiment was carried out by Herbert Ives and G.R. Stilwell first in 1938 and with better accuracy in 1941. It was designed to test the transverse Doppler effect
Figure 1. A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left.
The relativistic Doppler effect is the change in frequency
...

the redshift
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

of light from a moving source in a direction perpendicular to its velocity—which had been predicted by Einstein in 1905. The strategy was to compare observed Doppler shifts with what was predicted by classical theory, and look for a Lorentz factor
The Lorentz factor or Lorentz term is a quantity
Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assi ...

correction. Such a correction was observed, from which was concluded that the frequency of a moving atomic clock is altered according to special relativity.
Those classic experiments have been repeated many times with increased precision. Other experiments include, for instance, relativistic energy and momentum increase at high velocities, experimental testing of time dilation
Time dilation as predicted by special relativity is often verified by means of particle lifetime experiments. According to special relativity, the rate of a clock C traveling between two synchronized laboratory clocks A and B, as seen by a laborato ...

, and modern searches for Lorentz violations.
Tests of general relativity

General relativity has also been confirmed many times, the classic experiments being the perihelion precession ofMercury
Mercury usually refers to:
* Mercury (planet)
Mercury is the smallest planet in the Solar System and the closest to the Sun. Its orbit around the Sun takes 87.97 Earth days, the shortest of all the Sun's planets. It is named after the Roman g ...

's orbit, the by the Sun
The Sun is the star
A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

, and the gravitational redshift
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

of light. Other tests confirmed the equivalence principle
In the theory
A theory is a rational
Rationality is the quality or state of being rational – that is, being based on or agreeable to reason
Reason is the capacity of consciously making sense of things, applying logic
Logic (fr ...

and frame dragging
Frame-dragging is an effect on spacetime
In physics, spacetime is any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional manifold. Minkowski diag ...

.
Modern applications

Far from being simply of theoretical interest, relativistic effects are important practical engineering concerns. Satellite-based measurement needs to take into account relativistic effects, as each satellite is in motion relative to an Earth-bound user and is thus in a different frame of reference under the theory of relativity. Global positioning systems such asGPS
The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government
The federal government of the United States (U.S. federal government) is the national ...

, GLONASS
GLONASS (russian: ГЛОНАСС, ; , Global Navigation Satellite System) is a Russian space-based satellite navigation
A satellite navigation or satnav system is a system that uses satellite
File:ERS 2.jpg, alt=, A full-size model of ...

, and Galileo
Galileo di Vincenzo Bonaiuti de' Galilei ( , ; 15 February 1564 – 8 January 1642), commonly referred to as Galileo, was an astronomer
An astronomer is a in the field of who focuses their studies on a specific question or field o ...

, must account for all of the relativistic effects, such as the consequences of Earth's gravitational field, in order to work with precision. This is also the case in the high-precision measurement of time. Instruments ranging from electron microscopes to particle accelerators would not work if relativistic considerations were omitted.
Asymptotic symmetries

The spacetime symmetry group for Special Relativity is thePoincaré group
The Poincaré group, named after Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French
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, which is a ten-dimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is logical to ask what symmetries if any might apply in General Relativity. A tractable case may be to consider the symmetries of spacetime as seen by observers located far away from all sources of the gravitational field. The naive expectation for asymptotically flat spacetime symmetries might be simply to extend and reproduce the symmetries of flat spacetime of special relativity, ''viz.'', the Poincaré group.
In 1962 Hermann Bondi
Sir Hermann Bondi (1 November 1919 – 10 September 2005) was an Austria
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, M. G. van der Burg, A. W. Metzner and Rainer K. Sachs addressed this asymptotic symmetry problem in order to investigate the flow of energy at infinity due to propagating gravitational waves. Their first step was to decide on some physically sensible boundary conditions to place on the gravitational field at light-like infinity to characterize what it means to say a metric is asymptotically flat, making no ''a priori'' assumptions about the nature of the asymptotic symmetry group — not even the assumption that such a group exists. Then after designing what they considered to be the most sensible boundary conditions, they investigated the nature of the resulting asymptotic symmetry transformations that leave invariant the form of the boundary conditions appropriate for asymptotically flat gravitational fields. What they found was that the asymptotic symmetry transformations actually do form a group and the structure of this group does not depend on the particular gravitational field that happens to be present. This means that, as expected, one can separate the kinematics of spacetime from the dynamics of the gravitational field at least at spatial infinity. The puzzling surprise in 1962 was their discovery of a rich infinite-dimensional group (the so-called BMS group) as the asymptotic symmetry group, instead of the finite-dimensional Poincaré group, which is a subgroup of the BMS group. Not only are the Lorentz transformations asymptotic symmetry transformations, there are also additional transformations that are not Lorentz transformations but are asymptotic symmetry transformations. In fact, they found an additional infinity of transformation generators known as ''supertranslations''. This implies the conclusion that General Relativity does ''not'' reduce to special relativity in the case of weak fields at long distances.
See also

* Doubly special relativity * Galilean invariance * General relativity#References, General relativity references * Special relativity#References, Special relativity referencesReferences

Further reading

* * * * *The Meaning of Relativity

Albert Einstein: Four lectures delivered at Princeton University, May 1921

How I created the theory of relativity

Albert Einstein, December 14, 1922; Physics Today August 1982

Relativity

Sidney Perkowitz Encyclopædia Britannica

External links

* * * {{Authority control Theories by Albert Einstein Theoretical physics Theory of relativity