Velocity, acceleration and gravity in Einstein's relativity

TL;DR

This paper emphasizes the importance of covariant, coordinate-independent definitions of velocity, acceleration, and gravity in Einstein's relativity, criticizing common misconceptions rooted in Newtonian intuition.

Contribution

It clarifies the correct covariant definitions of fundamental concepts in relativity and addresses prevalent misconceptions and non-covariant approaches.

Findings

Relativistic definitions should be covariant and coordinate-independent.

Common non-covariant definitions are based on Newtonian intuition and can be misleading.

The paper discusses recent misconceptions and emphasizes proper relativistic formulations.

Abstract

Einstein's relativity theory demands that all meaningful physical objects should be defined covariantly, i.e. in a coordinate independent way. Concepts of relative velocity, acceleration, gravity acceleration and gravity potential are fundamental in Newton's theory and they are imprinted in everyone's physical intuition. Unfortunately, relativistic definitions of them are not commonly known or appreciated. Every now and then some confused authors use wrong, non-covariant, definitions of velocity, acceleration and gravity, based on their vague Newtonian intuitions and hidden in a superficial, often purely semantic, relativistic disguise. A recent example of such a confusion (Gorkavyi & Vasilkov, 2016) is discussed at the end of this Note.