Special Relativity–Temporal Correction Factor

In the depths of special relativity, a fundamental question arises : can the direction of the thought experiment influence the time dilation factor, described by the Lorentz factor ? To answer this question, we will explore a bold thought experiment, where a light beam is emitted in a moving train, precisely in a wagon where the light will be directed towards the ceiling with an inclination relative to the train's motion. Through this study, we will unveil the secrets of spacetime and examine the fascinating implications of special relativity on our understanding of the universe, notably by introducing a new time correction factor that arises from the analysis of this thought experiment and allows to correct the limitations of the Lorentz factor, providing a more precise description of the effects of special relativity on time, which will have significant implications for clock synchronization, such as those in GPS systems.