Abstract
In this paper a direct derivation of the dynamics of objects moving with relativistic speeds is presented, based on two assumptions: (i) energy and mass of an object in motion are equivalent (mass-energy equivalence, known in special relativity and confirmed in experiments), (ii) an object can be considered as a variable-mass object with mass increasing with velocity (in some interpretations referred to as relativistic mass). In the presented approach the postulate on the constancy of the speed of light is not necessary. Also, the four-dimensional Minkowski spacetime is not used and no assumptions on symmetries are made. Therefore, it applies for sub- and superluminal speeds with the speed of light in a vacuum c being the critical speed, which separates the two interesting regions of speeds. The solution for v c opens an unknown and unintuitive behavior, which should be subjected to experimental investigation. In the range of superluminal speeds, a solution in which the energy of the material particle decreases as its speed increases is obtained. The critical speed in media other than a vacuum should be replaced to a speed environment-dependent, other than c.
Highlights
The motion of objects moving in a vacuum at subluminal speeds is conventionally described within the 115-year-old special theory of relativity in Minkowski's four-dimensional space
The new approach to relativistic dynamics presented in [2] is based on two assumptions: (i) mass and energy equivalence and (ii) the well-known in classical and relativistic physics equation of dynamics for variable mass systems
The critical dependence of mass on velocity and the relativistic energy-momentum invariant are the direct results of the dynamical equation for systems with variable mass with the additional assumption of the mass-energy equivalence
Summary
The motion of objects moving in a vacuum at subluminal (slower-than-light) speeds is conventionally described within the 115-year-old special theory of relativity in Minkowski's four-dimensional space (spacetime). Modern special relativity is the theory based on the tensor formalism applied to the four-dimensional Minkowski spacetime [1]. This description uses the unique geometry of the spacetime with a characteristic metric. The answer within the special relativity is: certainly not This possibility is created by a new approach to relativistic dynamics [2], in which the assumption of the maximum speed of light in a vacuum is abandoned and replaced by another assumption about the equivalence of mass and energy. The new theory requires compliance with commonly known results of the special relativity in the range of subluminal speeds, with the possibility of extending this range
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