Rigidity and Parallelism in the spacetime

TL;DR

This paper investigates how Fock-Lorentz transformations affect parallel lines and rigidity in spacetime, revealing that these transformations do not preserve rigidity and lead to phenomena like growing distances and converging time coordinates.

Contribution

It introduces the concept that Fock-Lorentz transformations do not preserve rigidity, resulting in novel effects on distances and event timings in spacetime.

Findings

Fock-Lorentz transformations map lines to lines and alter velocity combinations.

Rigidity is not preserved under these transformations.

Distances can grow with time, and event times can converge when transformed back.

Abstract

The effect of the linear-fractional transformations on the parallel lines in the spacetime has been studied. Fock-Lorentz transformations maps a line to a line, from which one can obtain the combinations rule for the velocities in the Fock-Lorentz transformations. Rigidity is defined as a consequences of holding parallelism under the transformations. The Fock-Lorentz transformations do not preserve rigidity, which leads to some novel results such as growing distances alongside with advancing time. Also, it is shown that the time coordinates of events will come closer to each other in the transformed coordinates by going back in time