Derivation of the relativistic momentum and relativistic equation of motion from Newton's second law and Minkowskian space-time geometry

TL;DR

This paper derives the relativistic momentum and equations of motion directly from Newton's second law within Minkowskian spacetime, demonstrating Lorentz invariance without tensor calculus and introducing a new force transformation method.

Contribution

It presents a novel derivation of relativistic momentum and motion equations from classical mechanics principles in Minkowskian spacetime, avoiding tensor formalism.

Findings

Relativistic momentum derived without collision assumptions

Lorentz invariance proved without tensor formalism

Introduces a new force transformation method

Abstract

Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion $\vec{F}=d\vec{p}/dt$, where $\vec{p}$ is the relativistic momentum. The relativistic momentum is then derived without referring to any additional assumptions concerning elastic collisions of bodies. Lorentz-invariance of the relativistic law is proved without tensor formalism. Some new method of force transformation is also presented.