Life on a closed timelike curve

TL;DR

This paper explores the theoretical physics of a spaceship traveling on a closed timelike curve, revealing discretized energy levels, entropy behavior, and implications for time-travel paradoxes within a symmetric universe.

Contribution

It introduces a novel analysis of internal dynamics on a closed timelike curve, demonstrating energy discretization and entropy reversal, with implications for understanding time travel consistency.

Findings

Energy levels are discretized due to the curve's properties.

Entropy decreases after a full loop, reversing initial entropy increase.

No time-travel paradoxes arise from the internal dynamics of the system.

Abstract

We study the internal dynamics of a hypothetical spaceship traveling on a close timelike curve in an axially symmetric universe. We choose the curve so that the generator of evolution in proper time is the angular momentum. Using Wigner's theorem, we prove that the energy levels internal to the spaceship must undergo spontaneous discretization. The level separation turns out to be finely tuned so that, after completing a roundtrip of the curve, all systems are back to their initial state. This implies, for example, that the memories of an observer inside the spaceship are necessarily erased by the end of the journey. More in general, if there is an increase in entropy, a Poincar\'{e} cycle will eventually reverse it by the end of the loop, forcing entropy to decrease back to its initial value. We show that such decrease in entropy is in agreement with the eigenstate thermalization hypothesis. The non-existence of time-travel paradoxes follows as a rigorous corollary of our analysis.