A Finite State Model for Time Travel

TL;DR

This paper introduces a finite state model to analyze the logical consistency of time travel via closed time-like curves, showing that paradoxes are prevented by probability axioms but self-consistent backward travel remains possible.

Contribution

It presents a simple finite state model demonstrating how basic probability axioms prevent common time travel paradoxes while allowing consistent backward influence.

Findings

Paradoxes like grandfather paradox are precluded by probability axioms.

The model allows for self-consistent time travel to influence past events.

Time travel can be logically consistent without paradoxes.

Abstract

A time machine that sends information back to the past may, in principle, be built using closed time-like curves. However, the realization of a time machine must be congruent with apparent paradoxes that arise from traveling back in time. Using a simple model to analyze the consequences of time travel, we show that several paradoxes, including the grandfather paradox and Deutsch's unproven theorem paradox, are precluded by basic axioms of probability. However, our model does not prohibit traveling back in time to affect past events in a self-consistent manner.