A theorem on the photographic process in Special Relativity. The train paradox revisited

TL;DR

This paper resolves the train paradox in special relativity without non-linear Lorentz transformations and formulates a theorem on the photographic process involving two relativistically moving objects.

Contribution

It provides a general resolution to the train paradox and introduces a theorem describing the photographic process of two objects in relativistic motion.

Findings

The train paradox can be resolved with linear Lorentz transformations.

A general theorem on photographing two moving objects under relativistic effects is formulated.

The approach applies to curvilinear motion with variable train speed.

Abstract

The purpose of this letter is to show, on the one hand, how the so-called train paradox could be resolved directly without appealing to non-linear Lorentz transformations. The resolution is established in the most general case of curvilinear motion with a variable speed train. On the other hand, we formulate a theorem on the photographic process of two moving objects with relativistic effects.