Theory of relativity

Encyclopedia

The

: special relativity

and general relativity

. However, the word

.

The term "theory of relativity" was based on the expression "relative theory" used by Max Planck

in 1906, who emphasized how the theory uses the principle of relativity

. In the discussion section of the same paper Alfred Bucherer

used for the first time the expression "theory of relativity" .

and astronomy

during the 20th century. When first published, relativity superseded a 200-year-old theory of mechanics

elucidated by Isaac Newton

. It changed perceptions. However, Einstein denied that Newton could ever be superseded by his own work.

The theory of relativity overturned the concept of motion

from Newton's day, by positing that all motion is relative. Time

was no longer uniform and absolute. Physics could no longer be understood as space by itself, and time by itself. Instead, an added dimension had to be taken into account with curved spacetime

. Time now depended on velocity

, and contraction became a fundamental consequence at appropriate speeds.

In the field of physics, relativity catalyzed and added an essential depth of knowledge to the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age

. With relativity, cosmology

and astrophysics

predicted extraordinary astronomical phenomena

such as neutron stars, black holes, and gravitational waves.

was published in 1905, and the final form of general relativity

was published in 1916.

Second, special relativity fits with and solves for elementary particles and their interactions, whereas general relativity solves for the cosmological and astrophysical realm (including astronomy).

Third, special relativity was widely accepted in the physics community by 1920. This theory rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of atomic physics

, nuclear physics

, and quantum mechanics

. Conversely, general relativity did not appear to be as useful. There appeared to be little applicability for experimentalists as most applications were for astronomical scales. It seemed limited to only making minor corrections to predictions of Newtonian gravitation theory. Its impact was not apparent until the 1930s.

Finally, the mathematics of general relativity appeared to be incomprehensibly dense. Consequently, only a small number of people in the world, at that time, could fully understand the theory in detail. This remained the case for the next 40 years. Then, at around 1960 a critical resurgence in interest occurred which has resulted in making general relativity central to physics and astronomy. New mathematical techniques applicable to the study of general relativity substantially streamlined calculations. From this physically discernible concepts were isolated from the mathematical complexity. Also, the discovery of exotic astronomical phenomena in which general relativity was crucially relevant, helped to catalyze this resurgence. The astronomical phenomena included quasars (1963), the 3-kelvin microwave background radiation (1965), pulsars (1967), and the discovery of the first black hole

candidates (1971).

The special theory of relativity and the general theory of relativity are connected. As stated below, special theory of relativity applies to all inertial physical phenomena except gravity. The general theory provides the law of gravitation, and its relation to other forces of nature.

. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (for the contributions of many other physicists see History of special relativity

). Special relativity is based on two postulates which are contradictory in classical mechanics

:

The resultant theory agrees with experiment better than classical mechanics, e.g. in the Michelson-Morley experiment

that supports postulate 2, but also has many surprising consequences. Some of these are:

The defining feature of special relativity is the replacement of the Galilean transformation

s of classical mechanics by the Lorentz transformation

s. (See Maxwell's equations

of electromagnetism

and introduction to special relativity

).

The development of

, under which the states of accelerated motion

and being at rest in a gravitational field (for example when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall

is inertial motion

; an object in free fall is falling because that is how objects move when there is no force

being exerted on them, instead of this being due to the force of gravity as is the case in classical mechanics

. This is incompatible with classical mechanics and special relativity

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 1915, he devised the Einstein field equations

which relate the curvature of spacetime with the mass, energy, and momentum within it.

Some of the consequences of general relativity are:

Technically, general relativity is a metric

theory of gravitation

whose defining feature is its use of the Einstein field equations

. The solutions of the field equations are metric tensors

which define the topology

of the spacetime and how objects move inertially.

**theory of relativity**, or simply**relativity**, encompasses two theories of Albert EinsteinAlbert Einstein

Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

: special relativity

Special relativity

Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

and general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. However, the word

*relativity*is sometimes used in reference to Galilean invarianceGalilean invariance

Galilean invariance or Galilean relativity is a principle of relativity which states that the fundamental laws of physics are the same in all inertial frames...

.

The term "theory of relativity" was based on the expression "relative theory" used by Max Planck

Max Planck

Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

in 1906, who emphasized how the theory uses the principle of relativity

Principle of relativity

In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....

. In the discussion section of the same paper Alfred Bucherer

Alfred Bucherer

Alfred Heinrich Bucherer was a German physicist, who is known for his experiments on relativistic mass...

used for the first time the expression "theory of relativity" .

## Scope

The theory of relativity enriched physicsPhysics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

and astronomy

Astronomy

Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

during the 20th century. When first published, relativity superseded a 200-year-old theory of mechanics

Classical mechanics

In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

elucidated by Isaac Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

. It changed perceptions. However, Einstein denied that Newton could ever be superseded by his own work.

The theory of relativity overturned the concept of motion

Motion (physics)

In physics, motion is a change in position of an object with respect to time. Change in action is the result of an unbalanced force. Motion is typically described in terms of velocity, acceleration, displacement and time . An object's velocity cannot change unless it is acted upon by a force, as...

from Newton's day, by positing that all motion is relative. Time

Time

Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

was no longer uniform and absolute. Physics could no longer be understood as space by itself, and time by itself. Instead, an added dimension had to be taken into account with curved spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

. Time now depended on velocity

Velocity

In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

, and contraction became a fundamental consequence at appropriate speeds.

In the field of physics, relativity catalyzed and added an essential depth of knowledge to the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age

Atomic Age

The Atomic Age, also known as the Atomic Era, is a phrase typically used to delineate the period of history following the detonation of the first nuclear bomb Trinity on July 16, 1945...

. With relativity, cosmology

Cosmology

Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

and astrophysics

Astrophysics

Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...

predicted extraordinary astronomical phenomena

Astronomy

Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

such as neutron stars, black holes, and gravitational waves.

### Two theory view

The theory of relativity was representative of more than a single new physical theory. It affected the theories and methodologies across all the physical sciences. However, as stated above, this is more likely perceived as two separate theories. There are some explanations for this. First, special relativitySpecial relativity

Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

was published in 1905, and the final form of general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

was published in 1916.

Second, special relativity fits with and solves for elementary particles and their interactions, whereas general relativity solves for the cosmological and astrophysical realm (including astronomy).

Third, special relativity was widely accepted in the physics community by 1920. This theory rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of atomic physics

Atomic physics

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...

, nuclear physics

Nuclear physics

Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...

, and quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. Conversely, general relativity did not appear to be as useful. There appeared to be little applicability for experimentalists as most applications were for astronomical scales. It seemed limited to only making minor corrections to predictions of Newtonian gravitation theory. Its impact was not apparent until the 1930s.

Finally, the mathematics of general relativity appeared to be incomprehensibly dense. Consequently, only a small number of people in the world, at that time, could fully understand the theory in detail. This remained the case for the next 40 years. Then, at around 1960 a critical resurgence in interest occurred which has resulted in making general relativity central to physics and astronomy. New mathematical techniques applicable to the study of general relativity substantially streamlined calculations. From this physically discernible concepts were isolated from the mathematical complexity. Also, the discovery of exotic astronomical phenomena in which general relativity was crucially relevant, helped to catalyze this resurgence. The astronomical phenomena included quasars (1963), the 3-kelvin microwave background radiation (1965), pulsars (1967), and the discovery of the first black hole

Black hole

A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

candidates (1971).

## On the theory of relativity

Einstein stated that the theory of relativity belongs to the class of "principle-theories". As such it employs an analytic method. This means that the elements which comprise this theory are not based on hypothesis but on empirical discovery. The empirical discovery leads to understanding the general characteristics of natural processes. Mathematical models are then developed which separate the natural processes into theoretical-mathematical descriptions. Therefore, by analytical means the necessary conditions that have to be satisfied are deduced. Separate events must satisfy these conditions. Experience should then match the conclusions.The special theory of relativity and the general theory of relativity are connected. As stated below, special theory of relativity applies to all inertial physical phenomena except gravity. The general theory provides the law of gravitation, and its relation to other forces of nature.

## Special relativity

Special relativity is a theory of the structure of spacetimeSpacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (for the contributions of many other physicists see History of special relativity

History of special relativity

The history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others...

). Special relativity is based on two postulates which are contradictory in classical mechanics

Classical mechanics

In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

:

- The laws of physicsPhysicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

are the same for all observers in uniform motionInertial frame of referenceIn physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

relative to one another (principle of relativityPrinciple of relativityIn physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....

). - The speed of lightSpeed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

in a vacuumVacuumIn everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

is the same for all observers, regardless of their relative motion or of the motion of the source of the lightLightLight or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

.

The resultant theory agrees with experiment better than classical mechanics, e.g. in the Michelson-Morley experiment

Michelson-Morley experiment

The Michelson–Morley experiment was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University in Cleveland, Ohio. Its results are generally considered to be the first strong evidence against the theory of a luminiferous ether and in favor of special...

that supports postulate 2, but also has many surprising consequences. Some of these are:

- Relativity of simultaneityRelativity of simultaneityIn physics, the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur...

: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion. - Time dilationTime dilationIn the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...

: Moving clockClockA clock is an instrument used to indicate, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell". A silent instrument missing such a mechanism has traditionally been known as a timepiece...

s are measured to tick more slowly than an observer's "stationary" clock. - Length contractionLength contractionIn physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...

: Objects are measured to be shortened in the direction that they are moving with respect to the observer. - Mass–energy equivalence: , energy and mass are equivalent and transmutable.
- Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.

The defining feature of special relativity is the replacement of the Galilean transformation

Galilean transformation

The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. This is the passive transformation point of view...

s of classical mechanics by the Lorentz transformation

Lorentz transformation

In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...

s. (See Maxwell's equations

Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

of electromagnetism

Electromagnetism

Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

and introduction to special relativity

Introduction to special relativity

In physics, special relativity is a fundamental theory concerning space and time, developed by Albert Einstein in 1905 as a modification of Galilean relativity...

).

## General relativity

General relativity is a theory of gravitation developed by Einstein in the years 1907–1915.The development of

**general**relativity began with the equivalence principleEquivalence principle

In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...

, under which the states of accelerated motion

Acceleration

In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

and being at rest in a gravitational field (for example when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall

Free fall

Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...

is inertial motion

Inertia

Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...

; an object in free fall is falling because that is how objects move when there is no force

Force

In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

being exerted on them, instead of this being due to the force of gravity as is the case in classical mechanics

Classical mechanics

In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

. This is incompatible with classical mechanics and special relativity

Special relativity

Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo'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

Curvature

In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

. In 1915, he devised the Einstein field equations

Einstein field equations

The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...

which relate the curvature of spacetime with the mass, energy, and momentum within it.

Some of the consequences of general relativity are:

- Clocks run more slowly in deeper gravitational wells. This is called gravitational time dilationGravitational time dilationGravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes...

. - Orbits precessPrecessionPrecession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...

in a way unexpected in Newton's theory of gravity. (This has been observed in the orbit of MercuryMercury (planet)Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

and in binary pulsarBinary pulsarA binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. Binary pulsars are one of the few objects which allow physicists to test general relativity in the case of a strong gravitational field...

s). - Rays of lightLightLight or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

bend in the presence of a gravitational field. - Rotating masses "drag along" the spacetimeSpacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

around them; a phenomenon termed "frame-draggingFrame-draggingEinstein's general theory of relativity predicts that non-static, stationary mass-energy distributions affect spacetime in a peculiar way giving rise to a phenomenon usually known as frame-dragging...

". - The Universe is expandingMetric expansion of spaceThe metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

, and the far parts of it are moving away from us faster than the speed of light.

Technically, general relativity is a metric

Metric (mathematics)

In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric...

theory of gravitation

Gravitation

Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

whose defining feature is its use of the Einstein field equations

Einstein field equations

The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...

. The solutions of the field equations are metric tensors

Metric tensor (general relativity)

In general relativity, the metric tensor is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation...

which define the topology

Topology

Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

of the spacetime and how objects move inertially.

## See also

- Tests of special relativity
- Tests of general relativityTests of general relativityAt its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...
- Special relativity references
- General relativity references