Nonlinear effects in Thomas precession due to the interplay of Lorentz contraction and Thomas–Wigner rotation (original) (raw)
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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.
European Journal of Physics, 2011
The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.
Relativistic velocity space, Wigner rotation, and Thomas precession
American Journal of Physics, 2004
We develop a relativistic velocity space called rapidity space from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-collinear Lorentz boosts. In particular, we show how rapidity space provides a geometric approach to Wigner rotation and Thomas precession in the same way that space-time provides a geometrical approach to kinematic effects in special relativity.
The Thomas Precession and the Transformation to Rotating Frames
2002
The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of v/c, important differences in the predicted angle of precession appear, depending on the transformation used. For smaller values of v/c these differences might be measured by extending the time of observation.
Thomas rotation and Thomas precession
2005
Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinatefree) formulation of special relativity. Besides the simplicity of calculations the absolute treatment of spacetime allows us to gain a deeper insight into the phenomena of Thomas rotation and Thomas precession.
On the relation of Thomas rotation and angular velocity of reference frames
General Relativity and Gravitation, 2007
In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing concepts, introduced in [18], is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper [5], however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of [18] is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of [18]. Along the way we also establish some general properties of rotating reference frames, which may be of independent interest.
Does Thomas-Wigner rotation show the fallacy of " Lorentz rotation "
As a result of the composition of non-collinear relativistic velocities, apart from the resultant velocity, a component of turn is obtained which is called the Thomas-Wigner rotation. The paper discusses the Lorentz transformation using the paravector calculus. It has been shown that any " Lorentz rotation " is a combination of real velocity and a Euclidean rotation, and that as a result of the composition of appropriately selected velocities any object can rotate in place, which may indicate the fallacy of the idea of the " Lorentz rotation " .
Thomas Precession and the Bargmann-Michel-Telegdi Equation
Foundations of Physics, 2011
A direct method showing the Thomas precession for an evolution of any vector quantity (a spatial part of a four-vector) is proposed. A useful application of this method is a possibility to trace correctly the presence of the Thomas precession in the Bargmann-Michel-Telegdi equation. It is pointed out that the Thomas precession is not incorporated in the kinematical term of the Bargmann-Michel-Telegdi equation, as it is commonly believed. When the Bargmann-Michel-Telegdi equation is interpreted in curved spacetimes, this term is shown to be equivalent to the affine connection term in the covariant derivative of the spin four-vector evolving in a gravitational field. It then contributes to the geodetic precession. The described problem is an interesting and unexpected example showing that approximate methods used in special relativity, in this case to identify the Thomas precession, can distort the true meaning of physical laws.
Thomas precession, persistent spin currents and quantum forces
EPL (Europhysics Letters), 2014
We consider T-invariant spin currents induced by spin-orbit interactions which originate from the confined motion of spin carriers in nanostructures. The resulting Thomas spin precession is a fundamental and purely kinematic relativistic effect occurring when the acceleration of carriers is not parallel to their velocity. In the case, where the carriers (e.g. electrons) have magnetic moment the forces due to the electric field of the spin current can, in certain conditions, exceed the van der Waals-Casimir forces by several orders of magnitude. We also discuss a possible experimental setup tailored to use these forces for checking the existence of a nonzero anomalous magnetic moment of the photon.
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.