Length contraction
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Length contraction, according to Albert Einstein's special theory of relativity, is the decrease in length observed in objects traveling, relative to an observer, at a substantial fraction of the speed of light. The effect is observed parrallel to the direction in which the observed body is travelling.
It is important to note that this effect is negligible at everyday speeds, and can be ignored for all regular purposes. It is only when an object approaches speeds on the order of 30,000,000 m/s, i.e. 1/10 of the speed of light, that it becomes important. As the magnitude of the velocity approaches the speed of light, the effect becomes dominant, as we can see from the formula:
<math>L_1 = \frac{L_0}{\gamma} </math> where
- L0 is the proper length (the length of the object in its rest frame),
- L1 is the length observed by an observer,
- <math>\gamma \equiv \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}}</math> is the Lorentz factor,
- u is the relative velocity between the observer and the object, and
- c is the speed of light.
Note that this equation assumes that both the two ends of an object (the length) is measured at the same time, and that the +x direction of their coordinate systems are the same. For more general conversions, see the Lorentz transformations.
An observer at rest viewing an object travelling at the speed of light would observe the length of the object in the direction of motion as zero. Among other reasons, this suggests that objects with mass cannot travel at the speed of light.
Physical origin of length contraction?
Length contraction as a physical effect on bodies composed of atoms held together by electromagnetic forces was proposed by George Fitzgerald based on a paper by Oliver Heaviside in the 1880s and worked out in more detail by Hendrik Lorentz (1895, 1899) and Joseph Larmor (1897, 1900). The following quote from Larmor is indicative of the pre-Relativity view of the effect as a consequence of James Clerk Maxwell's electromagnetic theory:
- "... if the internal forces of a material system arise wholly from electromagnetic actions between the system of electrons which constitute the atoms, then the effect of imparting to a steady material system a uniform velocity of translation is to produce a uniform contraction of the system in the direction of motion, of amount (1-v2/c2)1/2" Joseph Larmor (1900) Aether and Matter (Cambridge University Press)
The extension of this specific result to a general result was (and is) considered "ad hoc" by many who prefer Einstein's deduction of it from the Principle of Relativity without reference to any physical mechanism. Apparently Lorentz did not agree as this draft of a letter to Einstein in 1915 shows (Janssen 1995, see Lorentz-FitzGerald contraction hypothesis)
- "... the interpretation given by me and FitzGerald was not artificial. It was more so that it was the only possible one, and I added the comment that one arrives at the hypothesis if one extends to other forces what one could already say about the influence of a translation on electrostatic forces. Had I emphasized this more, the hypothesis would have created less of an impression of being invented ad hoc." (empahsis added)
The Trouton-Rankine experiment in 1908 showed that length contraction of an object according to one frame, did not cause changes in the resistance of the object in its rest frame. This is in agreement with some current theories at the time (Special Relativity and Lorentz ether theory) but in disagreement with Trouton and Rankine's ideas on length contraction.
See also
es:Contracción de Lorentz nl:Lengtecontractie sv:Längdkontraktion