Principle of relativity

# Principle of relativity

Overview
In physics
Physics
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...

, 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
Frames of Reference
Frames of Reference is a 1960 educational film by Physical Sciences Study Committee.The film was made to be shown in high school physics courses. In the film University of Toronto physics professors Patterson Hume and Donald Ivey explain the distinction between inertial and nonintertial frames of...

.

For example, in the framework of special relativity 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
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...

have the same form in arbitrary frames of reference.

Several principles of relativity have been successfully applied throughout science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

, whether implicitly (as in Newtonian mechanics) or explicitly (as in Albert Einstein
Albert 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...

's 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...

).

Certain principles of relativity have been widely assumed in most scientific disciplines.
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Encyclopedia
In physics
Physics
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...

, 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
Frames of Reference
Frames of Reference is a 1960 educational film by Physical Sciences Study Committee.The film was made to be shown in high school physics courses. In the film University of Toronto physics professors Patterson Hume and Donald Ivey explain the distinction between inertial and nonintertial frames of...

.

For example, in the framework of special relativity 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
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...

have the same form in arbitrary frames of reference.

Several principles of relativity have been successfully applied throughout science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

, whether implicitly (as in Newtonian mechanics) or explicitly (as in Albert Einstein
Albert 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...

's 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...

).

## Basic relativity principles

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
Law of nature
Law of Nature may refer to:* Physical law, a scientific generalization based upon empirical observation* Natural law, any of a number of doctrines in moral, political and legal theory...

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
Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...

in natural law: that is, the laws must look the same to one observer as they do to another. According to a deep theoretical result called Noether's theorem
Noether's theorem
Noether's theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918...

, any such symmetry will also imply a conservation law
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....

alongside. For example, if two observers at different times see the same laws, then a quantity called energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

will be conserved
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

. In this light, relativity principles make testable predictions about how nature behaves, and are not just statements about how scientists should write laws.

## 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
Inertial frame of reference
In 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...

, but that they may vary across non-inertial ones. This principle is used in both Newtonian mechanics and the theory of 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...

. Its influence in the latter is so strong that 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...

named the theory after the principle.

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
Non-inertial reference frame
A non-inertial reference frame is a frame of reference that is under acceleration. The laws of physics in such a frame do not take on their most simple form, as required by the theory of special relativity...

s because those frames do not, in general experience, seem to abide by the same laws of physics. In classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...

, 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 Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

in 1632 in his Dialogue Concerning the Two Chief World Systems
Dialogue Concerning the Two Chief World Systems
The Dialogue Concerning the Two Chief World Systems was a 1632 Italian language book by Galileo Galilei comparing the Copernican system with the traditional Ptolemaic system. It was translated to Latin as Systema cosmicum in 1635 by Matthias Bernegger...

, using the metaphor of Galileo's ship
Galileo's ship
Galileo's ship is a physics experiment proposed by Galileo Galilei, the famous 16th and 17th century physicist, astronomer, and philosopher. The experiment was created to disprove popular arguments against the idea of a rotating Earth.-Background:...

.

Newtonian mechanics added to the special principle several other concepts, including laws of motion, gravitation, and an assumption of an absolute time. 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
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...

.

### In special relativity

Joseph Larmor
Joseph Larmor
Sir Joseph Larmor , a physicist and mathematician who made innovations in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter...

and Hendrik Lorentz
Hendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...

discovered that 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...

, the cornerstone 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...

, were invariant only by a certain change of time and length units. This left quite a bit of confusion among physicists, many of whom thought that a luminiferous aether
Luminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....

is incompatible with the relativity principle, in the way it was defined by Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...

:
In their 1905 papers on electrodynamics, Henri Poincaré and Albert Einstein
Albert 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...

explained that with the Lorentz transformations 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 (in Einstein's treatment, though not in Poincaré's) by a re-examination of the fundamental meanings of space and time intervals.

The strength of special relativity lies in its derivation from simple, basic principles, including the invariance of the laws of physics under a shift of inertial reference frames and the invariance of the speed of light in a vacuum. (See also: Lorentz covariance
Lorentz covariance
In standard physics, Lorentz symmetry is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space"...

.)

It is, in fact, possible to derive the Lorentz transformations from the principle of relativity alone and obtain the constancy of the speed of light as a consequence. 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. In the Lorentzian case, one can then obtain relativistic interval conservation and the constancy of the speed of light.

## General principle of relativity

The general principle of relativity states:
That is, physical laws are the same in all reference frames—inertial or non-inertial. An accelerated charged particle might emit synchrotron radiation
The electromagnetic radiation emitted when charged particles are accelerated radially is called synchrotron radiation. It is produced in synchrotrons using bending magnets, undulators and/or wigglers...

, though a particle at rest doesn't. 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, 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
Rotating reference frame
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. A rotating frame of reference is a special case of a non-inertial reference...

, which can be treated as an inertial reference frame if one adds a fictitious centrifugal force and Coriolis force into consideration.

The problems involved are not always so trivial. Special relativity predicts that an observer in an inertial reference frame doesn't see objects they'd describe as moving faster than the speed of light. However, in the non-inertial reference frame of Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, 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
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...

.

### General relativity

General relativity was developed by Einstein in the years 1907 - 1915. General relativity postulates that the global
Global symmetry
A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.-See also:...

Lorentz covariance
Lorentz covariance
In standard physics, Lorentz symmetry is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space"...

of special relativity becomes a local
Local symmetry
In physics, a local symmetry is symmetry of some physical quantity, which smoothly depends on the point of the base manifold. Such quantities can be for example an observable, a tensor or the Lagrangian of a theory....

Lorentz covariance in the presence of matter. The presence of matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

"curves" 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...

, and this curvature
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...

affects the path of free particles (and even the path of light). General relativity uses the mathematics of differential geometry and tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

s in order to describe 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...

as an effect of the geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

of 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...

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

• Background independence
Background independence
Background independence, also called universality, is the concept or assumption, fundamental to all physical sciences, that the nature of reality is consistent throughout all of space and time...

• Principle of uniformity
Principle of uniformity
The principle of uniformity may refer to* The assumption is that the same natural laws and processes that operate in the universe now, have always operated in the universe in the past and apply everywhere in the universe: Uniformitarianism....

• Principle of covariance
Principle of covariance
In physics, the principle of covariance emphasizes formulation of physical laws using only those physical quantities the measurements of which the observers in different frames of reference could unambiguously correlate....

• Preferred frame
Preferred frame
In theoretical physics, a preferred or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different from those in other frames....

In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

• 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...

including 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
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...

including Introduction to general relativity
Introduction to general relativity
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational attraction between masses results from their warping of space and time....

• Galilean relativity
• List of publications in physics: Theory of relativity
• Invariant
Invariant (physics)
In mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation.-Examples:In the current era, the immobility of polaris under the diurnal motion of the celestial sphere is a classical illustration of physical invariance.Another...

• Conjugate diameters
Conjugate diameters
In geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter...