Revisiting the old problem of the relativistic train that enters (or not) in a garage

This text discusses some concepts of the special theory of relativity, in a well-known situation, such as a moving train entering in a garage smaller than its length at rest. In the context of relativity, it is known that there is a length contraction, however, when changing the reference frame and considering the observer on the train, the garage moves and also suffers a contraction, resulting in an apparent paradox. The question is presented from the perspective of events and treated with Lorentz transformations in two different frames of reference, which allows a more detailed solution of the problem and shows that the paradox does not exist, highlighting the consistency of the theory of relativity. This way, one explores a series of nuances about relativity, normally absent in a traditional approach, such as measuring the length of moving bodies, simultaneity, inversion of events and elements of the light cone.

Keywords:
Special relativity; Lorentz transformations; Length contraction; causality; events