Geodesic
Why Do the Relativistic Masses and Momenta of Faster-than-Light Particles Decrease as their Speeds Increase?
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: special relativity; dynamics; faster-than-light particles; superluminal motion; tachyons; axiomatic method; first-order logic. 
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Judit X. Madarász; Mike Stannett; Gergely Székely. Why Do the Relativistic Masses and Momenta of Faster-than-Light Particles Decrease as their Speeds Increase?. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a4/

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