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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. [1] It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald ) and is usually only noticeable ...
Time dilation and length contraction. Length of the atmosphere: The contraction formula is given by = /, where L 0 is the proper length of the atmosphere and L its contracted length. As the atmosphere is at rest in S, we have γ=1 and its proper Length L 0 is measured.
The famous Michelson–Morley experiment of 1887 showed that the then-accepted aether theory needed to be modified. FitzGerald and Lorentz, independently of each other, proposed a length contraction of the experimental apparatus in the direction of motion (with respect to the luminiferous aether) that would explain the almost null result of the Michelson–Morley experiment.
(The Trouton–Rankine experiment conducted in 1908 also gave a negative result when measuring the influence of length contraction on an electromagnetic coil.) [1] To explain all experiments conducted before 1904, Lorentz was forced to again expand his theory by introducing the complete Lorentz transformation.
The ladder paradox (or barn-pole paradox) is a thought experiment in special relativity.It involves a ladder, parallel to the ground, travelling horizontally at relativistic speed (near the speed of light) and therefore undergoing a Lorentz length contraction.
For instance, Bell argued that the length contraction of objects as well as the lack of length contraction between objects in frame S can be explained using relativistic electromagnetism. The distorted electromagnetic intermolecular fields cause moving objects to contract, or to become stressed if hindered from doing so.
In addition, the negative result of the Michelson–Morley experiment led to the introduction of the hypothesis of length contraction in 1892. However, other experiments also produced negative results and (guided by Henri Poincaré 's principle of relativity ) Lorentz tried in 1899 and 1904 to expand his theory to all orders in v / c by ...
This also affects the role of time dilation in the Kennedy–Thorndike experiment, because its value depends on the value of length contraction used in the analysis of the experiment. Therefore, it's necessary to consider a third experiment, the Ives–Stilwell experiment, in order to derive the Lorentz transformation from experimental data alone.