Special-relativistic Mechanics for Pedestrians, Including a Generalization of Newton’s Axiomatic and A Dynnnic Derivation of the Poincare Transformation Zritbout Evoking the Principle of Relativity and Any Non-Mechanical Quantities

Abstract

Peter M. Enders*

The special-relativistic equation of motion is derived from first principles by generalizing Newton’s steps from the change of stationary states to the equation of motion. Most important, the change of the mass of a particle is allowed to intrinsically depend on its velocity, while a dependence on time, position, acceleration etc. is nonphysical. (An extrinsic dependence would occur when the external force acting upon it would depend on the velocity.) Generalizations of Newton’s definition of momentum and axioms are proposed which enable that. If the mass depends on the velocity and the space is still flat, the Minkowski spacetime inevitably emerges.

When compared with kinematic derivations, this treatment exhibits the advantage to show the applicability of the Poincare transformation to the case of a particle subject to an external force. Even more important, not special relativity needs an additional assumption for introducing the — when compared with classical mechanics — new parameter c. On the contrary, classical mechanics (often implicitly and unconsciously) makes one or more additional assumptions which suppress the appearance of c.

Last but not least, we are not aware of another related text which needs NEITHER the principle of relativity NOR the properties of light, NOR using any non-mechanical quantity.

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