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

Symmetry Integrability and Geometry-Methods and Applications

article

Judit X. Madarász¹  Mike Stannett²  Gergely Székely¹ 

[1] Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences;University of Sheffield, Department of Computer Science, United Kingdom

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

DOI  :  10.3842/SIGMA.2014.005

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown