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Thomas precession

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In physics the Thomas precession, named after Llewellyn Thomas, is a relativistic correction that applies to the spin of an elementary particle or the rotation of a macroscopic gyroscope and relates the angular velocity of the spin of a particle following a curvilinear orbit to the angular velocity of the orbital motion. It can be understood geometrically as a consequence of the fact that the space of velocities in relativity is hyperbolic, and so parallel transport of a vector (the gyroscope's angular velocity) around a circle (its linear velocity) leaves it pointing in a different direction, or understood algebraically as being a result of the non-associativity of the relativistic velocity-addition formula.It gives a correction to the spin–orbit interaction in quantum mechanics, which takes into account the relativistic time dilation between the electron and the nucleus of an atom.The composition of two Lorentz boosts which are non-collinear, results in a Lorentz transformation that is not a pure boost but is the product 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 non-collinear boosts returns the spatial origins of a sequence of inertial frame to the starting point, then the sequence of Wigner rotations combine to produce a net rotation called the Thomas precession.Thomas precession is a kinematic effect in the flat spacetime of special relativity. In the curved spacetime of general relativity, Thomas precession combines with a geometric effect to produce de Sitter precession. Although Thomas precession (net rotation after a trajectory that returns to its starting point) is a purely kinematic effect, it only occurs in curvilinear motion and therefore cannot be observed independently of some centripetal force causing the curvilinear motion such as that caused by an electromagnetic field, gravitational field or mechanical force so Thomas precession is always accompanied by dynamical effects. In the Lorentz scalar field, spin of the particle does not feel the torque, resulting in the spin dynamics is determined only by the Thomas precession. A single discrete Thomas rotation (as opposed to the series of infinitesimal rotations that add up to Thomas precession) is present in non-dynamical situations whenever you have 3 or more inertial frames in non-collinear motion - see the velocity composition section below.To calculate the spin of a particle in a magnetic field, one must also take into account Larmor precession.

English Wikipedia http://en.wikipedia.org/wiki/Thomas_precession

Spanish wikipedia http://es.wikipedia.org/wiki/Thomas_precession

Wiki page external link http://bohr.physics.berkeley.edu/classes/221/0708/notes/thomprec.pdf http://www.mathpages.com/rr/s2-11/2-11.htm