On the theoretical reliability of a three-temporal Lorentz transformation

Abstract

Let us consider the following fmldamen ta l postulates of special re la t iv i ty : a) o rd inary space is three-dimensional and Eucl idean, b) light speed is invariant . As ~ direct consequence of a), two general geometr ical requi rements should still be fulfilled even in the relat ivis t ical f ramework: i) Any (pointlike) object which is free (i.e., subjected to no force) has three degrees of freedom when moving in (empty) space. Namely , in order tha t it.s ( ins tantaneous) spat ial posi t ion m a y be univocal ly determined, i t always needs to be assigned a number of three i ndependen t funct ions of t ime. ii) The mot ion of a n y free (pointlike) object can always be characterized by three independent {Cartesian) veloci ty components whose m u t u a l orthogonality requires any variation of each one of t hem to cause by itself no change in the remain ing two components. On the other h,md, by a caroful inspect ion, i t is easy to realise tha t neither (i)) nor (ii)) would seem to be ful ly satisfied by the s t andard k inemat ics of any free photon. In fact, let us suppose, e.g., t ha t ~ given free photon, emi t t ed a.t t ime t = 0 from the origin of (our) frame ]s y, z), is t rave l l ing on the xy-plane. I f the a-co-ordinate is neglected, its motion will be rclar ivis t ieal ly described by the two equat ions