Other New Kinematics Laws, Causality and Accelerated Trajectories
Paul Bruma · 2022
The new velocity composition laws will be demonstrated, showing in particular that c is the only invariant speed, and that it cannot be exceeded without contradicting the fundamental principle of causality. This principle will then be examined, and as it refers to notions of past, present and future, its necessary adaptations to Relativity will be presented, leading to the distinction between time-like, space-like and light-like intervals. Then, the invariance of the space-time interval will be demonstrated, a key result showing the existence of a new metric in our 4D universe. The concept of time-distance equivalence will be carefully presented, particularly the fact that time and distance can be naturally expressed with a single unit, leading to simpler expressions of physical laws. Then, the general case of accelerated objects will be presented, with emphasis on Langevin’s twin paradox. Its resolution will lead us to examine additional fundamental postulates and laws: the clock postulate, the inertial tangent frame law, the surprising triangle inequality of the new metric and its consequence regarding the law of inertia: an inertial object now chooses the path that maximizes the distance covered.