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

Krzysztof Rębilas

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arXiv · 1408.3381

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

Krzysztof Rębilas

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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.

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Krzysztof Rębilas. 2013-09-17. Derivation of the relativistic momentum and relativistic equation of motion from Newton's second law and Minkowskian space-time geometry. https://arxiv.org/abs/1408.3381

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