Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald) and is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only measured in the direction in which the body is travelling. For normal objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer.
History
Length contraction was postulated by George FitzGerald (1889) and Hendrik Antoon Lorentz (1892) to explain the negative outcome of the Michelson–Morley experiment and to rescue the hypothesis of the stationary aether (Lorentz–FitzGerald contraction hypothesis). Although both FitzGerald and Lorentz alluded to the fact that electrostatic fields in motion were deformed ("Heaviside-Ellipsoid" after Oliver Heaviside, who derived this deformation from electromagnetic theory in 1888), it was considered an ad hoc hypothesis, because at this time there was no sufficient reason to assume that intermolecular forces behave the same way as electromagnetic ones. In 1897 Joseph Larmor developed a model in which all forces are considered to be of electromagnetic origin, and length contraction appeared to be a direct consequence of this model. Yet it was shown by Henri Poincaré (1905) that electromagnetic forces alone cannot explain the electron's stability. So he had to introduce another ad hoc hypothesis: non-electric binding forces (Poincaré stresses) that ensure the electron's stability, give a dynamical explanation for length contraction, and thus hide the motion of the stationary aether. Lorentz believed that length contraction represented a physical contraction of the atoms making up an object. He envisioned no fundamental change in the nature of space and time. Lorentz expected that length contraction would result in compressive strains in an object that should result in measurable effects. Such effects would include optical effects in transparent media, such as optical rotation and induction of double refraction, and the induction of torques on charged condensers moving at an angle with respect to the aether. Lorentz was perplexed by experiments such as the Trouton–Noble experiment and the experiments of Rayleigh and Brace, which failed to validate his theoretical expectations. For mathematical consistency, Lorentz proposed a new time variable, the "local time", called that because it depended on the position of a moving body, following the relation t′ = t − vx/c2. Lorentz considered local time not to be "real"; rather, it represented an ad hoc change of variable. Impressed by Lorentz's "most ingenious idea", Poincaré saw more in local time than a mere mathematical trick. It represented the actual time that would be shown on a moving observer's clocks. On the other hand, Poincaré did not consider this measured time to be the "true time" that would be exhibited by clocks at rest in the aether. Poincaré made no attempt to redefine the concepts of space and time. To Poincaré, Lorentz transformation described the apparent states of the field for a moving observer. True states remained those defined with respect to the ether. Albert Einstein removed the ad hoc character from the contraction hypothesis, declared the aether to be "superfluous" along with the concept of any absolutely stationary space and discussed length contraction effects in his 1905 paper on his theory of special relativity. Einstein proposed that Lorentz's transformation apply to both electromagnetism and mechanics. Hermann Minkowski gave the geometrical interpretation of all relativistic effects by introducing his concept of four-dimensional spacetime. The numerous and confusing visual effects of combination of length contraction and the finite speed of light were poorly understood at first. Lorentz erroneously claimed in 1922 that they could be photographed. George Gamow showed bicycles as only foreshortened in his illustrations for Mr Tompkins in Wonderland. Even though a paper with the correct appearance of a moving rod was published in 1924, it was not widely read. Only in 1959 when James Terrell and Roger Penrose wrote about the visual effect now called Terrell rotation were the difficulties clear. Terrell's paper named "Invisibility of the Lorentz Contraction" said a meter stick would appear to be rotated and the contraction itself could measure from photographs without corrections for the finite velocity of light.
Basis in relativity
First it is necessary to carefully consider the methods for measuring the lengths of resting and moving objects. Here, "object" simply means a distance with endpoints that are always mutually at rest, i.e., that are at rest in the same inertial frame of reference. If the relative velocity between an observer and the observed object is zero, then the proper length L 0 {\displaystyle L_{0}} of the object can simply be determined by directly superposing a measuring rod. However, if the relative velocity is greater than zero, then one can proceed as follows:
… excerpt ends here. Continue reading the full article.
