Lorentz Transformation

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.

It is named after the Dutch physicist Hendrik Lorentz. It reflects the fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events.

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. Albert Einstein later re-derived the transformation from his postulates of special relativity. The Lorentz transformation supersedes the Galilean transformation of Newtonian physics, which assumes an absolute space and time (see Galilean relativity). According to special relativity, the Galilean transformation is a good approximation only at relative speeds much smaller than the speed of light.

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. The Lorentz transformation describes only the transformations in which the spacetime event at the origin is left fixed, so they can be considered as a hyperbolic rotation of Minkowski space. The more general set of transformations that also includes translations is known as the Poincaré group.

Read more about Lorentz TransformationHistory, Lorentz Transformation For Frames in Standard Configuration, Visualizing The Transformations in Minkowski Space, Transformation of Other Physical Quantities, Special Relativity, Spacetime Interval, Derivation

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... A particular Minkowski diagram illustrates the result of a Lorentz transformation ... The Lorentz transformation that moves the vertical to α also moves the horizontal by α ... After the Lorentz transformation the new simultaneous events lie on the α-inclined line ...
History Of Lorentz Transformations - Poincaré (1900, 1905) - Lorentz Transformation
... algebraically equivalent to those of Larmor and Lorentz) and gave them the modern form (Poincaré set the speed of light to unity) Apparently Poincaré was unaware of Larmor's ... He modified/corrected Lorentz's derivation of the equations of electrodynamics in some details in order to fully satisfy the principle of relativity ... So by pointing out the group characteristics of the transformation Poincaré demonstrated the Lorentz covariance of the Maxwell-Lorentz equations ...
Lorentz Transformation - Derivation - From Group Postulates
... Coordinate transformations as a group The coordinate transformations between inertial frames form a group (called the proper Lorentz group) with the group ... are satisfied Closure the composition of two transformations is a transformation consider a composition of transformations from the inertial frame K to inertial frame K′, (denoted as K → K′), and then from K ... Identity element there is an identity element, a transformation K → K ...
History Of Special Relativity - Special Relativity - Spacetime Physics - Lorentz Transformation Without Second Postulate
... There were some attempts to derive the Lorentz transformation without the postulate of the constancy of the speed of light ... Their own calculation was based on the assumptions that a) the Lorentz transformation forms a homogeneous linear group, b) when changing frames, only the sign of the relative speed ... Pauli and Miller such models were insufficient to identify the invariant speed in their transformation with the speed of light — for example, Ignatowski was forced to recourse to electrodynamics to include the ...
Lorentz Ether Theory - Historical Development - Lorentz Transformation
... Further information History of Lorentz transformations While local time could explain the negative aether drift experiments to first order to v/c, it was necessary – due to ... The mathematical tool for that is the so-called Lorentz transformation ... Afterwards, Larmor in 1897 and Lorentz in 1899 derived equations in an algebraically equivalent form to those, which are used up to this day (however, Lorentz ...