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Invariant (physics)

 

 
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Invariant (physics)
 
 
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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 and theoretical physics
Theoretical physics

Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world....
, an invariant is a property of a system which remains unchanged under some transformation
Transformation (mathematics)

In mathematics, a transformation could be any function from a set X to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself which preserves this structure....
.

The gravitational field of the Sun is invariant under a change of time (from, say, now to tomorrow). It is also invariant under change of angular position.

Examples of invariants include the speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
 under a Lorentz transformation
Lorentz transformation

In physics, the Lorentz transformation converts between two different observers' measurements of space and time, where one observer is in constant motion with respect to the other....
 and time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 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....
. Many such transformations represent shifts between the reference frames of different observers, and so by Noether's theorem
Noether's theorem

Noether's theorem states that any derivative Symmetry in physics of the action of a physical system has a corresponding conservation law. The action of a physical system is an integral of a so-called Lagrangian function, from which the system's behavior can be determined by the principle of least action....
 invariance under a transformation represents a fundamental 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....
.






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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 and theoretical physics
Theoretical physics

Theoretical physics employs mathematical models and abstractions of physics in an attempt to explain experimental data taken of the natural world....
, an invariant is a property of a system which remains unchanged under some transformation
Transformation (mathematics)

In mathematics, a transformation could be any function from a set X to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself which preserves this structure....
.

The gravitational field of the Sun is invariant under a change of time (from, say, now to tomorrow). It is also invariant under change of angular position.

Examples of invariants include the speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
 under a Lorentz transformation
Lorentz transformation

In physics, the Lorentz transformation converts between two different observers' measurements of space and time, where one observer is in constant motion with respect to the other....
 and time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 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....
. Many such transformations represent shifts between the reference frames of different observers, and so by Noether's theorem
Noether's theorem

Noether's theorem states that any derivative Symmetry in physics of the action of a physical system has a corresponding conservation law. The action of a physical system is an integral of a so-called Lagrangian function, from which the system's behavior can be determined by the principle of least action....
 invariance under a transformation represents a fundamental 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....
. For example, invariance under translation leads to conservation of momentum, and invariance in time leads to conservation of energy.

Invariants are very important in modern theoretical physics, and many theories are in fact expressed in terms of their symmetries
Symmetry in physics

Symmetry in physics includes all features of a physical system that exhibit the property of symmetry?that is, under certain transformation , aspects of these systems are "unchanged", according to a particular observation....
 and invariants.

Covariance and contravariance
Covariance and contravariance

DefinitionIn mathematics and theoretical physics, covariance and contravariance refer to how coordinates change under a change of basis ....
 generalize the mathematical properties of invariance
Invariant

Invariant and invariance may have several meanings, among which are:* Invariant , an expression whose value doesn't change during execution ...
 in tensor mathematics
Tensor

A tensor is an object which extends the notion of Scalar , Vector , and Matrix . The term has slightly different meanings in mathematics and physics....
, and are frequently used in electromagnetism
Electromagnetism

Electromagnetism is the physics of the electromagnetic field, a field which exerts a force on Elementary particles with the property of electric charge and which is reciprocally affected by the presence and motion of such particles....
, special relativity
Special

selfref|In Wikipedia,...
, and general relativity
General relativity

General relativity or the general theory of relativity is the Geometry Theoretical physics of gravitation published by Albert Einstein in 1916....
.

See also

invariant (mathematics)
Invariant (mathematics)

In mathematics, an invariant is something that does not change under a set of Transformation s. The property of being an invariant is invariance....