Zero-Less Mechanics: A Speculative Minimum-Length Regularization for Singularities and Time Dilation

Abstract

Disclaimer: This is a speculative, non-peer-reviewed preprint. It is not established physics. It does not claim backward time travel or a working time machine. AbstractWe explore a speculative framework, Zero-Less Mechanics, in which zero is replaced by a minimum length L. The force law F = k/(r² + L²) is used as a toy regularization that removes the r = 0 singularity and yields a finite maximum force F_max = k/L². We define a minimum time t_min = L/c and retain the entropy condition ΔS ≥ 0. We compare this proposal with selected approaches to time travel in general relativity and quantum theory: Gödel-type closed timelike curves, traversable wormholes, the Alcubierre warp drive, and many-worlds interpretations. We argue that the proposal does not permit backward time travel and does not solve causality paradoxes. Its only physically established overlap is ordinary relativistic time dilation, as confirmed by GPS. The model is not derived from general relativity or quantum mechanics, makes no experimental predictions beyond known time dilation, and should be treated as a conceptual/philosophical toy model rather than a validated physical theory. We invite criticism, refinement, or refutation.