Cubic and general extensions of the Lorentz transformation

Abstract

The Lorentz transformation involves essentially only two variables, one space and the other time, though space is three dimensional, because the changes in space variables relate only to direction of motion of one observer with respect to the other. The extension to a larger number of variables should not mean the increase in spatial dimensions or the dimensions of time as was attempted earlier for decades, leading to no meaningful results. To understand the meaning of "extension" we first enunciate the "principle of same behaviour" for two variables and we show that the Lorentz transformation obeys that principle. The extension to a larger number of variables using this principle then becomes logical, elegant, and consistent.