# Is Time Travel Too Strange to Be Possible? Determinism and Indeterminism on Closed Timelike Curves

## TL;DR

This paper explores the implications of closed timelike curves in general relativity, analyzing how they can lead to both indeterminism and determinism, and argues these features are not sufficient to dismiss CTCs as physically impossible.

## Contribution

It investigates the nature of indeterminism and determinism associated with CTCs, showing their analogues in familiar physics and challenging the view that CTCs are conceptually inadmissible.

## Key findings

- CTCs can produce both indeterminism and determinism.
- Indeterminism on CTCs resembles statistical physics.
- Determinism on CTCs aligns with common physical principles.

## Abstract

Notoriously, the Einstein equations of general relativity have solutions in which closed timelike curves (CTCs) occur. On these curves time loops back onto itself, which has exotic consequences. However, in order to make time travel stories consistent constraints have to be satisfied, which prevents seemingly ordinary and plausible processes from occurring. This, and several other "unphysical" features, have motivated many authors to exclude solutions with CTCs from consideration, e.g. by conjecturing a chronology protection law. In this contribution we shall investigate the nature of one particular class of exotic consequences of CTCs, namely those involving unexpected cases of indeterminism or determinism. Indeterminism arises even against the backdrop of the usual deterministic physical theories when CTCs do not cross spacelike hypersurfaces outside of a limited CTC-region (such hypersurfaces fail to be Cauchy surfaces). By contrast, a certain kind of determinism appears to arise when an indeterministic theory is applied on a CTC: things cannot be different from what they already were. We shall argue that on further consideration both this indeterminism and determinism on CTCs turn out to possess analogues in other, familiar areas of physics. CTC-indeterminism is close to the epistemological indeterminism we know from statistical physics, while the "fixedness" typical of CTC-determinism is pervasive in physics. CTC-determinism and CTC-indeterminism therefore do not provide incontrovertible grounds for rejecting CTCs as conceptually inadmissible.