Velocity Requirements for Causality Violation

Abstract

It is known that the hypothetical existence of superluminal signals would imply the logical possibility of active causal violation: an observer in relative motion with respect to a primary source could in principle emit secondary superluminal signals (triggered by the primary ones) which go back in time and deactivate the primary source before the initial emission. This is a direct consequence of the structure of the Lorentz transformations, sometimes called "Regge-Tolman paradox". It is straightforward to find a formula for the velocity of the moving observer required to produce the causality violation. When applied to some recent claims of slight superluminal propagation, this formula yields a required velocity very close to the speed of light; this raises some doubts about the real physical observability of such violations. We re-compute this velocity requirement introducing a realistic delay between the reception of the primary signal and the emission of the secondary. It turns out that for -any- delay it is possible to find moving observers able to produce active causal violation. This conclusion looks physically absurd and is mathematically due to the singularity of the Lorentz transformations for beta to 1-. It appears to undermine the connection between superluminal signals and active causality violation. We also briefly consider further paradoxes raised by superluminal propagation: the contemporary emission of several superluminal signals from a source and the interaction of two particles through the exchange of superluminal virtual particles.