Comment on ‘Lorentz transformations with arbitrary line of motion’

Abstract

A short comment regarding the derivation of Lorentz transformation proposed by Iyer and Prabhu (2007 Eur. J. Phys. 11 183–90) is given. It is shown that the proposed derivation is similar to that appearing in the standard textbooks of classical mechanics, electrodynamics and the theory of relativity. In fact, those textbooks also provide an elegant form of the Lorentz matrix for the (3+1)-dimensional case, which Iyer and Prabhu claim to be difficult to attain because of its algebraic complexity. We also provide the derivation of the (3+1)-dimensional version of the Lorentz matrix using a method analogous to that proposed by Iyer and Prabhu, and show that the result is completely equivalent to the (3+1)-dimensional version appearing in the textbooks.

Lorentz transformations with arbitrary line of motion

“…In order to transform from F to O we use the transformation [L xv R θ ] as specified in equations (1) and ( We can apply matrix T as derived in equation (6) to transform the event coordinates from F to O. One end of the rod at t = 0 in F has the coordinates (0, 0, 0) and it transforms to (0, 0, 0) in O.…”

“…The results of this article have been derived earlier by using vector algebra [6]. However, such derivations assume that the axes of K and K' are parallel.…”