Time Travel Without Motion: A Block Universe Formalization of Temporal Re-indexing

The idea of time travel has persisted as both a scientific speculation and a philosophical problem. In most treatments, time travel is implicitly assumed to be motion through time, analogous to spatial displacement. However, this assumption introduces severe conceptual difficulties, including violations of causality and paradoxes such as the grandfather paradox. This paper argues that these difficulties arise not from time travel itself, but from an incorrect model of time. Modern physics, particularly general relativity, does not require time to flow. Instead, space-time is modeled as a four-dimensional geometric structure in which all events coexist. Under this interpretation—commonly known as the Block Universe—time travel must be reconceptualized.