Theoretical Investigation of Lorentz Transformation of Relativistic Quantities in Two-Dimensional Spacetime Continuum

Abstract

In the current study, we conducted a theoretical study to derive the Lorentz transformation between inertial frames of reference moving in two-dimensional spacetime continuum. The invariance of the space–time interval equation, with use of the derived two-dimensional transformations, yields the notion of 2+2-dimensional spacetime continuum which consists of two space and two time coordinates. The velocity addition formulas, Lorentz transformations of energy and momentum are then investigated in 2+2-dimensional spacetime frame. Additionally, we investigated the concept of four-vector in 2+2 dimensions and further discussed their transformation based on the matrix equation, which is fully consistent with the Lorentz invariant energy–momentum relation.