The Special Theory of Relativity in Six Dimensions of Spacetime Continuum

In this work we extend the four-dimensional space time theory of special relativity to six dimensions by adding two extra time coordinates, thereby we propose here six Lorentz transformation equations between inertial frames of reference moving in the three dimensions of space. The Lorentz matrix of order 6 × 6 using new six transformation equations is presented for the case when the coordinate systems have a relative velocity in three dimensions. Also, an elementary derivation of the new transformations in terms of hyperbolic functions including its matrix formulation has been thoroughly discussed. In addition to these, the invariance of differential space-time interval, invariance of d’Alembert operator, transformation of energy and momentum have been theoretically interpreted on the basis of the extended Lorentz transformation equations.