Inertia in 4D-mechanics

TL;DR

This paper explores inertia within 4D Minkowski space-time, deriving balance equations for inertia forces in moving media, and clarifies the distinction between real and imaginary forces using energy-momentum conservation.

Contribution

It introduces a unified approach to inertia in relativistic mechanics by deriving balance equations from the energy-momentum tensor in four-dimensional space-time.

Findings

Derived non-relativistic inertia force equations from energy-momentum tensor

Separated real inertia forces from fictitious ones in different frames

Unified classical and relativistic inertia concepts in a single framework

Abstract

An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows us to combine the laws of conservation of momentum and angular momentum into a single law and separate the forces of inertia that actually exist in nature from the imaginary forces introduced to simplify calculations or arising from the transition from one frame of reference to another. From the energy-momentum tensor, in a non-relativistic approximation, the equation of balance of inertia forces existing in nature for a moving continuous medium and a material point in an inertial frame of reference is obtained. It follows from this equation that the pseudo-Euclidean geometry of our world plays an important role in the manifestation of inertia forces. The tensor and the balance equations of all inertia forces in a continuous medium a moving with angular acceleration are obtained. This allows uniform formulation and presentation of the original categories and concepts of classical and relativistic mechanics in educational and scientific literature within the framework of the current paradigm.