A Transformation Factor for Superluminal Motion That Preserves Symmetrically the Spacetime Intervals

Abstract

While superluminal phenomena are not empirically substantiated, they present an intriguing hypothetical case. For this speculative framework, the Lorentz transformations would necessitate a revision: instead of the standard γ(x−vt), the absolute value of x′ ought to be expressed as γ(vt−x), because if v were to exceed c, then the interval vt traversed by the superluminal frame S′ would surpass the distance covered by light. Under the postulates of relativity, the subluminal scenario leads to the conventional Lorentz factor. Meanwhile, the superluminal scenario introduces an alternative transformation factor that accounts for the presence of the speed of light (c) barrier. This factor is also invariant within Minkowski spacetime, meaning it symmetrically preserves spacetime intervals. The details of this derivation become more evident when using a reverse coordinate system. This result is not, per se, evidence for the existence of superluminal phenomena, but it does allow us to speculate with a new argument about the possibility of their existence.