Why Do the Relativistic Masses and Momenta of Faster-than-Light Particles Decrease as their Speeds Increase?

[摘要] It has recently been shown within a formal axiomatic framework using a definition of four-momentum based on the Stückelberg-Feynman-Sudarshan-Recami ''switching principle'' that Einstein's relativistic dynamics is logically consistent with the existence of interacting faster-than-light inertial particles. Our results here show, using only basic natural assumptions on dynamics, that this definition is the only possible way to get a consistent theory of such particles moving within the geometry of Minkowskian spacetime. We present a strictly formal proof from a streamlined axiom system that given any slow or fast inertial particle, all inertial observers agree on the value of $\mathsf{m}\cdot \sqrt{|1-v^2|}$, where $\mathsf{m}$ is the particle's relativistic mass and $v$ its speed. This confirms formally the widely held belief that the relativistic mass and momentum of a positive-mass faster-than-light particle must decrease as its speed increases.

[关键词] special relativity;dynamics;faster-than-light particles;superluminal motion;tachyons;axiomatic method;first-order logic