2013/09/30 by Judit X. Madarász, Mike Stannett, Gergely Székely · 12 citations
Mathematics · Physics and Astronomy · #Axiom #Center of mass (relativistic) #Classical mechanics #Cosmology and Gravitation Theories #Dynamics (music) #Einstein #Energy–momentum relation #Feynman diagram #Geometry #Inertial frame of reference #Mathematical physics #Mathematics #Momentum (technical analysis) #Physics #Quantum Mechanics and Applications #Quantum mechanics #Relativistic dynamics #Relativistic mechanics #Relativistic particle #Relativistic quantum chemistry #Relativistic speed #Relativity and Gravitational Theory #Spacetime #Speed of light (cellular automaton) #Theory of relativity #gr-qc #math-ph #math.LO #math.MP #msc:03B30 #msc:70A05 #msc:83A05
paper · pdf · doi:10.3842/sigma.2014.005
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
arxiv created 2014/01/11 · openalex publication_date 2014/01/11 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It has recently been shown within a formal axiomatic framework using a definition of four-momentum based on the Stckelberg-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 m |1 -v 2 |, where 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.