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In 2012, Barry Cox and James Hill published a new and elegant way to deduce the formulae of extended relativity, developed by Erasmo Recami and others during the 1960s and 1970s. Extended relativity applies to superluminal or FTL (faster than light in the vacuum) particles, called tachyons by the late American physicist Gerald Feinberg. However, tachyons generate causality paradoxes in special relativity when used for signalling. These paradoxes are safely removed only in a space–time containing a preferred inertial reference frame. Moreover, quantum properties should be taken into account. They cause further trouble for tachyons because, for instance, spin-zero FTL particles satisfying the Klein–Gordon equation cannot be localized as pointlike particles, contrary to all other known fundamental constituents of matter. Perhaps the most interesting suggestion in Cox and Hill's paper is that a certain freedom is allowed in the theory of superluminal particles as no such particle has been reliably detected until now, so that it is worthwhile exploring theoretical alternatives. We shall prove that an idea from Cox and Hill's paper, when applied not in the context of extended relativity but in the framework of F. R. Tangherlini's absolute synchronization, allows the problem of tachyon localization for spinless particles to be solved.

Revisiting Barry Cox and James Hill's theory of superluminal motion: a possible solution to the problem of spinless tachyon localization