From an earlier version of the Wikipedia article on Thomas precession concerning

Question

From an earlier version of the Wikipedia article on Thomas precession concerning TP and LP=Larmor precession, regarding the paper: G B Malykin, "Thomas precession: correct and incorrect solutions", Physics-Uspekhi 49 (8) 837-853 (2006)

In a 2006 survey of the literature Malykin notes that there are numerous conflicting expressions for Thomas precession. This is partly explained by the fact that different authors use "Thomas precession" to refer to different things, often without saying what they are referring to and subsequent authors then misinterpret the results and apply them to other things, but, even taking this into account, some of the expressions in the literature are just plain wrong.

Malykin explains the source of some of these errors: "We emphasize that Thomas considered the rotation of the axes of the coordinate system accompanying the electron in its motion rather than the electron spin rotation. Subsequently, this led to a misunderstanding and the emergence of incorrect work on the TP problem. It is possible to introduce three different reference frames accompanying the electron motion around a circular orbit and, in the most general case, along a curvilinear trajectory: (i) a reference frame whose coordinate axes remain parallel or retain their angular position relative to the axes of a laboratory IRF, (ii) a reference frame one of whose coordinate axes is always coincident with the electron velocity vector, and (iii) a reference frame in which the electron spin vector retains its orientation relative to the coordinate axes. It is evident that the electron spin vector precesses relative to the coordinate axes of the two first systems, but the angular velocity of its precession is different in these systems. ... In several papers concerned with the TP, calculations are performed in the first approximation in v^2/c^2, where v is the speed of an elementary particle in the laboratory IRF and c is the speed of light. In this case, all authors arrive at the same expression first derived by Thomas, this being so irrespective of whether they consider the relativistic rotation of the particle spin or the relativistic rotation of the axes of the coordinate system comoving with the particle. In the most general case, however, the expressions for the TP obtained by different authors are radically different. As noted above, the problem is complicated by the fact that different authors assign different meaning to this expression: some imply the relativistic rotation of the particle spin in the laboratory IRF, some in the comoving reference frame (in this case, as noted above, the rotation law for the axes of this system may be defined in three ways), while others refer to the relativistic rotation of the axes of the coordinate system accompanying the particle in motion. ... As noted above, the expression for the TP in Thomas's first paper was obtained in the first approximation in v^2/c^2 and is always correct when this condition is fulfilled. In his subsequent work, on performing calculations for an arbitrary electron velocity v, Thomas derived an expression that correctly describes the relativistic rotation of the axes of the comoving coordinate system relative to the rest-frame (laboratory) system. However, because the majority of authors use the term TP in reference to the precession of the spin of an elementary particle, this subsequently led to several errors and misunderstandings. ... In 1952, in his famous monograph [78], the Danish scientist C M

Explanation / Answer

Here's a new arxiv posting which addresses Malykin's paper: http://arxiv.org/abs/1302.5678

"An important question about the Thomas precession angle ? and its generating angle ? is whether or not ? and ? have equal signs. According to Malykin, some explorers claim that ? and ? have equal signs while some other explorers claim that ? and ? have opposite signs. Malykin claims that these angles have equal signs while, in contrast, we demonstrate here convincingly that these angles have opposite signs. Our demonstration is convincing since it accompanies a focal identity, that interested explorers can test numerically in order to corroborate our claim that ? and ? have opposite signs."

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