* four-vectors and Lorentz transformation

Measurements in one inertial frame can be converted to measurements in another by a simple transformation ( the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity ).

These effects are expressed mathematically by the Lorentz transformation

The Lorentz transformation is equivalent to the Galilean transformation in the limit c < sub > 0 </ sub > → ∞ ( a hypothetical case ) or v → 0 ( low speeds ).

In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, different measurements of space and time by two observers can be converted into the measurements observed in either frame of reference.

The Lorentz transformation was originally the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism.

The Lorentz transformation supersedes the Galilean transformation of Newtonian physics, which assumes an absolute space and time ( see Galilean relativity ).

The Lorentz transformation is a linear transformation.

It may include a rotation of space ; a rotation-free Lorentz transformation is called a Lorentz boost.

Since relativity postulates that the speed of light is the same for all observers, the Lorentz transformation must preserve the spacetime interval between any two events in Minkowski space.

Larmor and Lorentz, who believed the luminiferous ether hypothesis, were seeking the transformation under which Maxwell's equations were invariant when transformed from the ether to a moving frame.

Later in the same year Einstein derived the Lorentz transformation under the assumptions of the principle of relativity and the constancy of the speed of light in any inertial reference frame,

The symmetric form highlights that all physical laws should remain unchanged under a Lorentz transformation.

The Lorentz transformation for frames in standard configuration can be shown to be ( see for example and ):

That resulted in the formulation of the so called Lorentz transformation by Joseph Larmor ( 1897, 1900 ) and Lorentz ( 1899, 1904 ), whereby it was noted by Larmor that the complete formulation of local time is accompanied by some sort of time dilation of moving electrons in the aether.

The possibility that Lorentz symmetry may be violated has been seriously considered in the last two decades, particularly after the development of a realistic effective field theory that describes this possible violation, the so-called Standard-Model Extension.

* The Lorentz transformation: The simplest case is a boost in the x-direction ( more general forms including arbitrary directions and rotations not listed here ), which describes how spacetime coordinates change from one inertial frame using coordinates ( x, y, z, t ) to another ( x ', y ', z ', t ' ) with relative velocity v:

The Lorentz Force Law describes the effects of a charged particle moving in a constant magnetic field.

The first equation describes a Lorentz force-free fluid: the forces are everywhere zero.

-argues that only the Lorentz force can explain Faraday's disc and describes some experimental evidence for this

The Lorentz reciprocity theorem describes this case as well, assuming ohmic materials ( i. e. currents that respond linearly to the applied field ) with a 3 × 3 conductivity matrix σ that is required to be symmetric, which is implied by the other conditions below.

In this approach the physical vacuum is viewed as the quantum superfluid which is essentially non-relativistic whereas the Lorentz symmetry is not an exact symmetry of nature but rather the approximate description valid only for the small fluctuations of the superfluid background.

This article will not follow this nomenclature: In what follows, the term " Lorentz force " will refer only to the expression for the total force.

In general, magneto-optic effects break time reversal symmetry locally ( i. e. when only the propagation of light, and not the source of the magnetic field, is considered ) as well as Lorentz reciprocity, which is a necessary condition to construct devices such as optical isolators ( through which light passes in one direction but not the other ).

Governor Lorentz raised enormous taxes upon them and seized warehouses and cargoes of tobacco, sugar, and slaves in 1689 only to have his actions repudiated by the authorities in Copenhagen ; his hasty action to seize Crab Island prohibited the Brandenburgers from establishing their own Caribbean colony, however.

It can be derived directly from Maxwell's equations in terms of total charge and current and the Lorentz force law only.

However, Alfred Potier ( and later Hendrik Lorentz ) pointed out to Michelson that he had made an error of calculation, and that the expected fringe shift should only have been 0. 02 fringes.

Since the space is then a pseudo-Euclidean space, the rotation is a representation of a hyperbolic rotation, although Poincaré did not give this interpretation, his purpose being only to explain the Lorentz transformation in terms of the familiar Euclidean rotation.

The original Michelson – Morley experiment was useful for testing the Lorentz – FitzGerald contraction hypothesis only.

The Aharonov – Bohm effect illustrates the physicality of electromagnetic potentials, Φ and A, whereas previously it was possible to argue that only the electromagnetic fields, E and B, were physical and that the electromagnetic potentials, Φ and A, were purely mathematical constructs ( Φ and A being non-unique, in addition to not appearing in the Lorentz Force formula ).

The observed Lorentz invariance of space-time allows only the formation of condensates which are Lorentz scalars and have vanishing charge.

Lorentz showed that an attractive force between charged particles ( which might be taken to model the elementary subunits of matter ) would indeed arise, but only if the incident energy were entirely absorbed.

This contraction ( more formally called Lorentz contraction or Lorentz – FitzGerald contraction ) is usually only noticeable at a substantial fraction of the speed of light ; the contraction is only in the direction parallel to the direction in which the observed body is travelling.

The current, however, continues to only flow along the material, which indicates that the force on the electrons due to the electric field balances the Lorentz force.

Local Lorentz covariance, which follows from general relativity, refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point.

* Similar to the approximate Lorentz symmetry of phonons in a lattice ( where the speed of sound plays the role of the critical speed ), the Lorentz symmetry of special relativity ( with the speed of light as the critical speed in vacuum ) is only a low-energy limit of the laws of Physics, which involve new phenomena at some fundamental scale.

It is allowed to rescale the number of particles, because the Lorentz force depends only on the charge to mass ratio, so a super-particle will follow the same trajectory as a real particle would.

" Einstein recognized that the general principle of relativity should also apply to accelerated relative motions, and he used the newly developed tool of tensor calculus to extend the special theory's global Lorentz covariance ( applying only to inertial frames ) to the more general local Lorentz covariance ( which applies to all frames ), eventually producing his general theory of relativity.

According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincaré group of symmetry transformations, of which the Lorentz transformations are a subgroup.

Under Lorentz transformations, the time and distance between events may differ among inertial reference frames ; however, the Lorentz scalar distance s between two events is the same in all inertial reference frames

: See also History of Lorentz transformations.

Below the Lorentz transformations are called " boosts " in the stated directions.

whereas in Relativistic mechanics and Lorentz transformations, which were first discovered by Hendrik Lorentz,

is invariant under Lorentz transformations ( in this expression and in what follows the metric signature has been used ).

However, spinors transform well under the infinitesimal orthogonal transformations ( like infinitesimal rotations or infinitesimal Lorentz transformations ).

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations.

Einstein derived the Lorentz transformations from first principles in 1905, but these three experiments allow the transformations to be induced from experimental evidence.

The time differential between two reunited clocks is deduced through purely uniform linear motion considerations, as seen in Einstein's original paper on the subject, as well as in all subsequent derivations of the Lorentz transformations.

For example, Newtonian dynamics ( which is based on Galilean transformations ) is the low speed limit of special relativity ( since the Galilean transformation is the low-speed approximation to the Lorentz transformation ).

The rotational symmetry between time and space coordinate axes ( when one is taken as imaginary, another as real ) results in Lorentz transformations which in turn result in special relativity theory.

Because the probability density now appears as the fourth component of a relativistic vector, and not a simple scalar as in the Schrödinger equation, it will be subject to the usual effects of the Lorentz transformations such as time dilation.

Just as the Lorentz transformation preserves the proper time, the quantity det Ψ = S < sub > 0 </ sub >< sup > 2 </ sup > − S < sub > 1 </ sub >< sup > 2 </ sup > − S < sub > 2 </ sub >< sup > 2 </ sup > − S < sub > 3 </ sub >< sup > 2 </ sup > is invariant within a multiplicative scalar constant under Jones matrix transformations ( dichroic and / or birefringent ).

After graduating from Ridgefield in 1920, Church attended Princeton University where he was an exceptional student, publishing his first paper, on Lorentz transformations, and graduating in 1924 with a degree in mathematics.

However, these properties can turn out to be very meaningful, for instance in describing the Lorentz transformations of special relativity.

The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations.

Other planar algebras are used to represent the shear mapping of classical motion in absolute time and space and to represent the Lorentz transformations of relativistic space and time.