physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

, 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 physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system, whose origin, orientation, and scale have been specified in physical space. It is based on a set of reference points, defined as geometric ...

. For example, in the framework of

special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...

, the Maxwell equations have the same form in all inertial frames of reference. In the framework of general relativity, the Maxwell equations or the

Einstein field equations In the General relativity, general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of Matter#In general relativity and cosmology, matter within it. ...

have the same form in arbitrary frames of reference. Several principles of relativity have been successfully applied throughout

science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...

, whether implicitly (as in

Newtonian mechanics Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body r ...

) or explicitly (as in

Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

's special relativity and

general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...

Basic concepts

Certain principles of relativity have been widely assumed in most scientific disciplines. One of the most widespread is the belief that any law of nature should be the same at all times; and scientific investigations generally assume that laws of nature are the same regardless of the person measuring them. These sorts of principles have been incorporated into scientific inquiry at the most fundamental of levels. Any principle of relativity prescribes a

symmetry Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is Invariant (mathematics), invariant und ...

in natural law: that is, the laws must look the same to one observer as they do to another. According to a theoretical result called

Noether's theorem Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems (see Noether's second theorem) published by the mat ...

, any such symmetry will also imply a

conservation law In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momen ...

alongside. For example, if two observers at different times see the same laws, then a quantity called

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

will be conserved. In this light, relativity principles make testable predictions about how nature behaves.

Special principle of relativity

According to the first postulate of the special theory of relativity: This postulate defines an inertial frame of reference. The special principle of relativity states that physical laws should be the same in every

inertial frame of reference In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative ...

, but that they may vary across non-inertial ones. This principle is used in both

and the theory of

. Its influence in the latter is so strong that

Max Planck Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...

named the theory after the principle.Extract of page 272
/ref> The principle requires physical laws to be the same for any body moving at constant velocity as they are for a body at rest. A consequence is that an observer in an inertial reference frame cannot determine an absolute speed or direction of travel in space, and may only speak of speed or direction relative to some other object. The principle does not extend to

non-inertial reference frame A non-inertial reference frame (also known as an accelerated reference frame) is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-z ...

s because those frames do not, in general experience, seem to abide by the same laws of physics. In

classical physics Classical physics refers to physics theories that are non-quantum or both non-quantum and non-relativistic, depending on the context. In historical discussions, ''classical physics'' refers to pre-1900 physics, while '' modern physics'' refers to ...

, fictitious forces are used to describe acceleration in non-inertial reference frames.

In Newtonian mechanics

The special principle of relativity was first explicitly enunciated by

Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...

in 1632 in his ''

Dialogue Concerning the Two Chief World Systems ''Dialogue Concerning the Two Chief World Systems'' (''Dialogo sopra i due massimi sistemi del mondo'') is a 1632 book by Galileo Galilei comparing Nicolaus Copernicus's Copernican heliocentrism, heliocentric system model with Ptolemy's geocen ...

'', using the metaphor of Galileo's ship. Newtonian mechanics added to the special principle several other concepts, including laws of motion, gravitation, and an assertion of an

absolute time Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame. Early concept A version of the concept of absolute space (in the sense of a prefe ...

. When formulated in the context of these laws, the special principle of relativity states that the laws of mechanics are ''invariant'' under a

Galilean transformation In physics, a 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. These transformations together with spatial rotati ...

In special relativity

Joseph Larmor and

Hendrik Lorentz Hendrik Antoon Lorentz ( ; ; 18 July 1853 – 4 February 1928) was a Dutch theoretical physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for their discovery and theoretical explanation of the Zeeman effect. He derive ...

discovered that

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...

, used in the theory of

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

, were invariant only by a certain change of time and length units. This left some confusion among physicists, many of whom thought that a

luminiferous aether Luminiferous aether or ether (''luminiferous'' meaning 'light-bearing') was the postulated Transmission medium, medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empt ...

was incompatible with the relativity principle, in the way it was defined by

Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...

: In their 1905 papers on

electrodynamics In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

, Henri Poincaré and

explained that with the

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

the relativity principle holds perfectly. Einstein elevated the (special) principle of relativity to a postulate of the theory and derived the Lorentz transformations from this principle combined with the principle of the independence of the speed of light (in vacuum) from the motion of the source. These two principles were reconciled with each other by a re-examination of the fundamental meanings of space and time intervals. The strength of special relativity lies in its use of simple, basic principles, including the invariance of the laws of physics under a shift of

inertial reference frame In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative ...

s and the invariance of the speed of light in vacuum. (See also: Lorentz covariance.) It is possible to derive the form of the Lorentz transformations from the principle of relativity alone. Using only the isotropy of space and the symmetry implied by the principle of special relativity, one can show that the space-time transformations between inertial frames are either Galilean or Lorentzian. Whether the transformation is actually Galilean or Lorentzian must be determined with physical experiments. It is not possible to conclude that the speed of light ''c'' is invariant by mathematical logic alone. In the Lorentzian case, one can then obtain relativistic interval conservation and the constancy of the speed of light.Yaakov Friedman, ''Physical Applications of Homogeneous Balls'', Progress in Mathematical Physics 40 Birkhäuser, Boston, 2004, pages 1-21.

General principle of relativity

The general principle of relativity states: That is, physical laws are the same in reference frames—inertial or non-inertial. An accelerated charged particle might emit synchrotron radiation, though a particle at rest does not. If we consider now the same accelerated charged particle in its non-inertial rest frame, it emits radiation at rest. Physics in non-inertial reference frames was historically treated by a

coordinate transformation In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...

, first, to an inertial reference frame, performing the necessary calculations therein, and using another to return to the non-inertial reference frame. In most such situations, the same laws of physics can be used if certain predictable fictitious forces are added into consideration; an example is a uniformly

rotating reference frame A rotating frame of reference is a special case of a non-inertial reference frame that is rotation, rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article co ...

, which can be treated as an inertial reference frame if one adds a fictitious

centrifugal force Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axi ...

and

Coriolis force In physics, the Coriolis force is a pseudo force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motio ...

into consideration. The problems involved are not always so trivial. Special relativity predicts that an observer in an inertial reference frame does not see objects he would describe as moving faster than the speed of light. However, in the non-inertial reference frame of

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

, treating a spot on the Earth as a fixed point, the stars are observed to move in the sky, circling once about the Earth per day. Since the stars are light years away, this observation means that, in the non-inertial reference frame of the Earth, anybody who looks at the stars is seeing objects which appear, to them, to be moving faster than the speed of light. Since non-inertial reference frames do not abide by the special principle of relativity, such situations are not self-contradictory.

General relativity

General relativity was developed by Einstein in the years 1907–1915. General relativity postulates that the

global Global may refer to: General *Globe, a spherical model of celestial bodies *Earth, the third planet from the Sun Entertainment * ''Global'' (Paul van Dyk album), 2003 * ''Global'' (Bunji Garlin album), 2007 * ''Global'' (Humanoid album), 198 ...

Lorentz covariance of special relativity becomes a

local Local may refer to: Geography and transportation * Local (train), a train serving local traffic demand * Local, Missouri, a community in the United States Arts, entertainment, and media * ''Local'' (comics), a limited series comic book by Bria ...

Lorentz covariance in the presence of matter. The presence of

matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic pa ...

"curves"

spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...

, and this

curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...

affects the path of free particles (and even the path of light). General relativity uses the mathematics of

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

and

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

s in order to describe

gravitation In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

as an effect of the

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

. Einstein based this new theory on the general principle of relativity and named the theory after the underlying principle.

Notes and references

External links

Wikibooks: Special Relativity

Living Reviews in Relativity
– An open access, peer-referred, solely online physics journal publishing invited reviews covering all areas of relativity research.

– A complete online course on Relativity.
Special Relativity Simulator

A Relativity Tutorial at Caltech
– A basic introduction to concepts of Special and General Relativity, as well as astrophysics.

– A short course offered at MIT.
Relativity in film clips and animations
from the University of New South Wales.
Animation clip
visualizing the effects of special relativity on fast moving objects.
Relativity Calculator – Learn Special Relativity Mathematics
The mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts. {{Authority control Theory of relativity Theories