Thomas Precession and the Bargmann-Michel-Telegdi Equation (original) (raw)
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Thomas Precession in Spacetime Geometries
The authors of a recently published paper (Sonego S and Pin M 2005 Eur. J. Phys. 26 851-6) have erroneously asserted that Einstein's velocity addition law is associative. Moreover, they have attributed the alleged associativity of Einstein's velocity addition law to 'The relativity principle[, which] requires that [Einstein's velocity addition] gives the composition law of a group'. Accordingly, we note that Einstein's velocity addition is non-associative and demonstrate that the breakdown of associativity and commutativity in Einstein's velocity addition law results from the presence of Thomas precession.
Thomas precession in post-Newtonian gravitoelectromagnetism
Physical review, 1994
The well-known Thomas precession effect is discussed in the context of the post-Newtonian approximation to general relativity using the language of gravitoelectromagnetism (3-plus-1 splitting of gravitational theory). Preliminary discussion anchors the post-Newtonian coordinate system and choice of gravitational variables in the mathematical structure of fully nonlinear general relativity, linking the post-Newtonian gravitoelectric and gravitomagnetic fields to kinematical properties of the associated observer congruence. The transformation laws for these fields under a change of post-Newtonian coordinate system are derived first within the post-Newtonian theory and then by taking the limit of their fully nonlinear form to reveal the interpretation of the various terms in the post-Newtonian case. These transformation laws are then used to make a case for the existence of a gravitational analogue of the ordinary Thomas precession of the spin of a gyroscope.
The geodetic precession as a 3-D Schouten precession and a gravitational Thomas precession
Canadian Journal of Physics, 2014
The Gravity Probe B (GP-B) experiment measured the geodetic precession due to parallel transport in a curved space–time metric, as predicted by de Sitter, Fokker, and Schiff. The Schiff treatment included Thomas precession and argued that it should be zero in a free fall orbit. We review the existing interpretations regarding the relation between the Thomas precession and the geodetic precession for a gyroscope in a free fall orbit. Schiff and Parker had contradictory views on the status of the Thomas precession in a free fall orbit, a contradiction that continues to exist in the literature. In the second part of this paper we derive the geodetic precession as a global Thomas precession by use of the equivalent principle and some elements of hyperbolic geometry, a derivation that allows the treatment of GP-B physics in between special and general relativity courses.
The geodesic precession as a 3-D Schouten precession plus a
The Gravity Probe B (GP-B) experiment measured the geodetic precession due to parallel transport in a curved space-time metric, as predicted by de Sitter, Fokker and Schiff. Schiff included the Thomas precession in his treatment and argued that it should be zero in a free fall orbit. We review the existing interpretations regarding the relation between the Thomas precession and the geodetic precession for a gyroscope in a free fall orbit. Schiff and Parker had contradictory views on the status of the Thomas precession in a free fall orbit, a contradiction that continues to exist in the literature. In the second part of this paper we derive the geodetic precession as a global Thomas Precession by use of the Equivalent Principle and some elements of hyperbolic geometry, a derivation that allows the treatment of GP-B physics in between SR and GR courses.
Foundations of Physics, 1997
Gyrogroup theol 3' and its applications is introduced and explored, exposing the jascinating inteugay between Thomas precession o/' special relatirity theory and hyperbolic geometJ 7. The abstract Thomas precession, called Thomas gyration, gives rise to grouplike ot?jeets called gyrogroups [ A. A. U~gar, Am. J. Phys. 59, 824 (1991) ] the under(ring axioms of which are presented. The prefix gyro extensively used in terms like gyrogroups, gyroassociative and gyrocommutative laws, gyroautomolThisms, and gyrosemidirect produets, stems fi'om their underlying abstract Thomas gyration. Thomas gw'ation is tailor made for hyperbolic geometry. In a similar way that commutative groups underlie vector spaces, gyrocommutative gyrogroups underlie gyrot'ector spaces. Gyrovector s7~aces, in turn, provide a most natural setting)'or hyperbolic geometry in full analogy with vector spaces that provide the setting/br Euclidean geometry. As such, their applicability to relativistic" physics and its s7)acetime geomet~2p is' obvious. 1. INTRODUCTION. HYPERBOLIC GEOMETRY BECOMES COORDINATE BY MEANS OF THOMAS PRECESSION Thomas precession of special theory of relativity (STR) has reached a milestone in 1988 following the discovery of the mathematical regularity that it storesjl 2) Resulting links with hyperbolic geometry now follow, giving rise to coordinate hyperbolic geometry analogous to coordinate Euclidean geometry in the sense indicated by Eqs. (1.3) and (1.4) below. Links between hyperbolic geometry and Thomas precession are not unexpected/3) Unexpectedly, however, the recent exposition of the symmetries concealed in Thomas precession places it centrally in the foundations of hyperbolic geometry.
Physics Essays, 2020
This article introduces a new field theory formulation. The new field theory formulation recognizes vector continuity as a general principle and begins with a field that satisfies vector continuity equations. Next, independent of the new formulation, this article introduces a new space-time adjustment. Then, we solve the one-body gravitational problem by applying the space-time adjustment to the new field theory formulation. With the space-time adjustment, the new formulation predicts precisely the same precession of Mercury and the same bending of light as general relativity. The reader will find the validating calculations to be simple. The equations of motion that govern the orbital equations are in terms of Cartesian coordinates and time. An undergraduate college student, with direction, can perform the validations.
Classical interpretations of relativistic precessions
Relativists have exposed various precessions and developed ingenious experiments to verify those phenomena with extreme precisions. The Gravity Probe B mission was designed to study the precessions of the gyroscopes rotating round the Earth in a nearly circular near-Earth polar orbit to demonstrate the geodetic effect and the Lense–Thirring effect as predicted by the general relativity theory. In this paper, we show in a very simple and novel analysis that the precession of the perihelion of Mercury, the Thomas precession, and the precession data (on the de Sitter and Lense–Thirring precessions) collected from the Gravity Probe B mission could easily be explained from classical physics, too.
Thomas-Wigner rotation and Thomas precession: Actualized approach
Thomas-Wigner rotation and Thomas precession: Actualized approach, 2014
We show that the explanation of Thomas-Wigner rotation (TWR) and Thomas precession (TP) in the framework of special theory of relativity (STR) contains a number of points of inconsistency, in particular, with respect to physical interpretation of the Einstein velocity composition law in successive space-time transformations. In addition, we show that the common interpretation of TP falls into conflict with the causality principle. In order to eliminate such a conflict, we suggest considering the velocity parameter, entering into expression for the frequency of TP, as being always related to a rotation-free Lorentz transformation. Such an assumption (which actually resolves any causal paradoxes with respect to TP), comes however to be in contradiction with the spirit of STR. The results obtained are discussed.