Precession of Thomas

The precession of Thomas is the name given to the phenomenon of Précession which the kinetic Moment undergoes of an object, or the Spin of a Elementary particle when it has an accelerated trajectory not subjected to the force S nelles Gravitation. The precession of Thomas owes to his name with the Thomas who highlighted it in 1926. The precession of Thomas is one of the two components of what is called the geodetic Précession, which includes also the effects of the gravitational Champ (Effet of Sitter). Historically, the precession of Thomas was highlighted to explain certain properties of the energy levels observed in the Atome of Hydrogène. Those highlighted the fact that the electron had one intrinsic kinetic moment (the Spin), able to be coupled with a external Magnetic field like being affected by the orbital kinetic Moment of the electron subjected to the forces electrostatic S of the Atomic nucleus central (compound of one only Proton).

Formulate precession

The clean kinetic moment $\ mathbf {S}$ of an object undergoing a Accélération $\ mathbf {has}$ and animated from a speed $\ mathbf {v}$ in a Référentiel given goes précesser according to the usual formula

\ frac = {\ mathbf {\ Omega}} \ wedge {\ mathbf {S}}

with

{\ mathbf {\ Omega}} = \ frac {1} {2} \ frac {c^2}

where C is the Speed of light.

In the case of a particle having a circular trajectory Not relativist located by the angular Vector Velocity ${\ mathbf {\ Omega}}$ , the precession is done according to the vector

{\ mathbf {\ Omega}} = - \ frac {1} {2} \ frac {v^2} {c^2} {\ mathbf {\ Omega}}

i.e. in the opposite direction of the rotation of the particle and significantly more slowly than this one.

Physical interpretation

The precession of Thomas is a phenomenon resulting from the laws of the restricted Relativité (within the limit where speed of light becomes infinite, there is no precession). Mathematically, it comes from what the combination of several transformations of Lorentz does not correspond by necessarily to a transformation of Lorentz, but with the combination of such a transformation and a Rotation of space. An accelerated object can be followed by considering the reference frame which is attached to him. From one moment T at one moment T +δ T , acceleration ${\ mathbf {has}}$ undergone by the object can be modelled by changing the reference frame which follows the object, obtained preceding by a transformation of Lorentz determined by the Flight Path Vector ${\ mathbf {v}} = {\ mathbf {has}} \ delta t$ . The successive combination of such transformation of Lorentz infinitesimal corresponds not to a transformation of Lorentz, but the combination of a detranformation of Lorentz and a rotation. The clean kinetic moment of the object, constant during time if no couple applies to him thus will undergo this effect of rotation of the system of axes attached to the object and thus will change direction. Such a reasoning applied to the Cinématique galiléenne does not give the same result, because the combination of several transformations equivalent to the transformation of Lorentz, the Transformations of Galileo gives this time another transformation of Galileo, without addition of a rotation.

See too

Reference

, page 1118 and 1119.

Note

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