# On a special transformation to a non-inertial, radially rigid reference frame

*V.V. Voytik*^{1}

(1) Bashkir State Pedagogical University, ul. Oktyabr'skoi Revoliutsii 3-a, Ufa, 450077, Russia

### Abstract

We discuss the conditions under which a body, moving non-inertially in Minkowski space, can preserve its size. Under these conditions, using a series expansion of the generalized Lorentz transformation, we find a coordinate transformation connecting the laboratory inertial reference frame *S* and the rigid non-inertial reference frame *s* which moves without its own rotation with respect to *S*. Direct consequences of this transformation are: (a) desynchronization, in system *s*, of the coordinate clocks of *s* which were previously synchronized in *S*, and (b) a kinematic contraction of a ruler of system *s* observed in *S*. We also consider the dependence of the transformation vector parameter on the proper coordinates of *s*.

### References

- R. A. Nelson,
*Generalized Lorentz transformation for an accelerated, rotating frame of reference*, J. Math. Phys. **28**, 2379 (1987).
- V. V. Voytik,
*The general form-invariance principle*, Grav. Cosmol. **17**(3), 218 (2011).
- Ch. Misner, K. S. Thorne, and J. A. Wheeler,
*Gravitation*, vol. 1 (Freeman, San Francisco, 1973).
- V. V. Voytik,
*On the influence of acceleration on rectilinear motion of a rigid body. 1. Length and velocity*. Vestn. Chelyabinsk. Gos. Univ., Fizika **9**(7), 44 (2011).
- V. V. Voytik,
*On the influence of acceleration on rectilinear motion of a rigid body. 2. Clock desynchronization*. Vestn. Chelyabinsk. Gos. Univ., Fizika **9**(7), 50 (2011).
- H. NicoliA?,
*Relativistic contraction of an accelerated rod*, Am. J. Phys. **67**, 1007 (1999).
- S. N. Lyle,
*Rigidity and the ruler hypothesis*. Fundamental Theories of Physics **167**, 61 (2010).
- W. Pauli,
*Theory of Relativity* (Pergamon Press, 1958).
- V. A. Bordovitsyn and V. V. Telushkin,
*Thomas precession and spin*, Russian Physics Journal **11**, 1241 (2006).
- A. A. Logunov,
*On Thomas precession*, preprint 98-85, GNC RF IFVE, 1998 (in Russian).
- S. S. Stepanov,
*Thomas precession for spin and for a rod Physics of Elementary Particles and Atomic Nuclei***43**(1), (2012).

For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page