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  In theoretical physics, the composition of two noncollinear Lorentz boosts results in a Lorentz transformation that is not a pure boost but is the composition of a boost and a rotation. This rotation is called Thomas rotation, Thomas–Wigner rotation or Wigner rotation. The rotation was discovered by Thomas in 1926, and derived by Wigner in 1939. If a sequence of noncollinear boosts returns an object to its initial velocity, then the sequence of Wigner rotations can combine to produce a net rotation called the Thomas precession. Einstein's principle of velocity reciprocity (EPVR) reads

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  In theoretical physics, the composition of two noncollinear Lorentz boosts results in a Lorentz transformation that is not a pure boost but is the composition of a boost and a rotation. This rotation is called Thomas rotation, Thomas–Wigner rotation or Wigner rotation. The rotation was discovered by Thomas in 1926, and derived by Wigner in 1939. If a sequence of noncollinear boosts returns an object to its initial velocity, then the sequence of Wigner rotations can combine to produce a net rotation called the Thomas precession. There are still ongoing discussions about the correct form of equations for the Thomas rotation in different reference systems with contradicting results. Goldstein: The spatial rotation resulting from the successive application of two noncollinear Lorentz transformations have been declared every bit as paradoxical as the more frequently discussed apparent violations of common sense, such as the twin paradox. Einstein's principle of velocity reciprocity (EPVR) reads We postulate that the relation between the coordinates of the two systems is linear. Then the inverse transformation is also linear and the complete nonpreference of the one or the other system demands that the transformation shall be identical with the original one, except for a change of v to −v With less careful interpretation, the EPVR is seemingly violated in some models. There is, of course, no true paradox present.

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  The decomposition process described can be through on the product of two pure Lorentz transformations to obtain explicitly the rotation of the coordinate axes resulting from the two successive "boosts". In general, the algebra involved is quite forbidding, more than enough, usually, to discourage any actual demonstration of the rotation matrix

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