Local Lorentz transformations and Thomas effect in general relativity

Silenko, Alexander J.

doi:10.1103/physrevd.93.124050

Cited by 23 publications

(43 citation statements)

References 75 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The spatial inhomogeneity significantly influences the form of the equations of motion. The terms different for the Schwarzschild field and the uniformly accelerated frame (g = −a) are of the same order of magnitude as the corresponding terms different for the Schwarzschild field in the Cartesian and isotropic coordinates [2]. Therefore, the difference between the equations of motion in the Schwarzschild field and the uniformly accelerated frame does not violate the EEP.…”

Section: Review Of Previous Resultsmentioning

confidence: 84%

“…Nevertheless, it has been certified in Ref. [2] that their differences do not violate the EEP. In Einstein's papers [1], the equivalence principle has been formulated only relative to constant uniform gravitational fields.…”

Section: Review Of Previous Resultsmentioning

confidence: 99%

“…To calculate the metric tensor, we need to use the known equation for the metric of a weak Schwarzschild source in the Cartesian coordinates (x, y, z) numerated as (1,2,3):…”

Section: B Field Of a Gravitating Diskmentioning

confidence: 99%

See 2 more Smart Citations

Quasi-uniform gravitational field of a disk revisited

Silenko

Tsalkou

2019

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

We calculate the quasi-uniform gravitational field of a disk in the weak-field approximation and demonstrate an inappropriateness of preceding results. The Riemann tensor of this field is determined. A nonexistence of the uniform gravitational field is proven. It is shown that a difference between equations of a particle motion and a spin rotation in the accelerated frame and in the quasi-uniform gravitational field of a disk does not violate the Einstein equivalence principle.

show abstract

Section: Review Of Previous Resultsmentioning

confidence: 84%

Section: Review Of Previous Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Quasi-uniform gravitational field of a disk revisited

Silenko

Tsalkou

2019

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

show abstract

“…He also described which is the most efficient method for each possible applications. The explicit calculations are performed in the series of three works where the generality for the exact procedure becomes evident [27,28,29].On [30,31,32], the authors worked on a series of papers in which the EFWT conditions were not satisfied. In these articles, the study of the CPT-Lorentz violating terms was used as a background to this transformation.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Exact Foldy-Wouthuysen transformation for a Dirac theory revisited

2019

View full text Add to dashboard Cite

The Exact Foldy-Wouthuysen transformation (EFWT) method is generalized here. In principle, it is not possible to construct the EFWT to any Hamiltonian. The transformation conditions are the same but the involution operator has a new form. We took a particular example and constructed explicitly the new involution operator that allows one to perform the transformation. We treat the case of the Hamiltonian with 160 possible CPT-Lorentz breaking terms, using this new technique. The transformation was performed and physics analysis of the equations of motion is shown.Another possible phenomenological approach to this problem can be constructed step by step by searching for new terms in the Hamiltonian that describes this situation. Thinking this way, it makes sense the appearance of some terms in the equations of motion that could give a mix between an external known field with sufficient enough big amplitude to compensate the fact that the CPT-Lorentz terms have small amplitudes.The idea is the same shown in [15], where the strong magnetic field could, in principle, change the trajectory of the Dirac particle that interacts with gravitational waves. It is important to take into account the corrections, made with canonical FW, to these results that were shown in [16]. In [17], the massive linearized gravity was studied and some possible experiments that could measure indirect effects of gravitational waves on Dirac fermions were indicated. However, solving the Dirac equation for the general case is not a simple procedure [18]. It is well known in literature that working with the EFWT is a more prominent approach to interpret a Dirac Hamiltonian than the canonical transformation [19]. But this is true not only for the fact that it can give us new terms, but it is a faster and more economic (in terms of algebraic calculation) procedure [15,20,21,22]. One can see this transformation as a generalization of the usual FWT.Let us perform a comparison on the two procedures. It is possible to see that in the usual FWT the multiplication on each step (on each order on 1/m) by the term that makes the Hamiltonian even, generates a maximum of 1 + 2n even terms, where n represents the number of terms of the previous Hamiltonian (see, for example, pages 48-51 in [23]). The maximum number of terms in the nth-Hamiltonian is straightforward obtained by the fact that this is an expansion in power series of an operator. The factor 2 on 1 + 2n expression is obtained in case when it does not commute with all original terms.On the other hand, the EFWT impose the multiplication of all terms of the Hamiltonian by themselves. Analogous arguments give us the maximum of 1+2n 2 on the expanded Hamiltonian. If the parameter of expansion here is also taken to be 1/m, one can see that the possibility of having new terms in comparison with the usual method is greater. In many particular known cases [21,24,25], the anti-commutators on both cases are such that the results are the same! But it is not the general case. This was explicitly shown on [19]. ...

show abstract

The relativistic mechanism of the Thomas–Wigner rotation and Thomas precession

Kholmetskii¹,

Yarman²

2020

Eur. J. Phys.

View full text Add to dashboard Cite

We consider the Thomas-Wigner rotation of coordinate systems under successive Lorentz transformations of inertial reference frames and disclose its physical mechanism on the basis of relativistic contraction of moving scale and relativity of simultaneity of events for different inertial observers. This result allows us to understand better the physical meaning of the Thomas precession and to indicate some of the missed points in the physical interpretation of this effect with two particular examples: the circular motion of a classical electron around a heavy nucleus and the motion of a classical electron along an open path, where its initial velocity and acceleration are mutually orthogonal to each other.

show abstract

Local Lorentz transformations and Thomas effect in general relativity

Abstract: The tetrad method is used for an introduction of local Lorentz frames and a detailed analysis

Cited by 23 publications

References 75 publications

Quasi-uniform gravitational field of a disk revisited

Quasi-uniform gravitational field of a disk revisited

Exact Foldy-Wouthuysen transformation for a Dirac theory revisited

The relativistic mechanism of the Thomas–Wigner rotation and Thomas precession

Contact Info

Product

Resources

About