The time-reverse of any causal theory is eternal noise

TL;DR

This paper shows that reversing the direction of causality in physical theories results in a trivial state space of eternal noise, highlighting a fundamental asymmetry in the structure of causal theories.

Contribution

It proves that the time-reversal of causal theories leads to a single, noise-like state, contrasting with the rich state space of the original theories, including quantum mechanics.

Findings

Time-reversal of causal theories yields only a noise state.

Causal theories are fundamentally asymmetric under time-reversal.

The result applies to quantum theory and strengthens previous signaling constraints.

Abstract

We consider a very general class of theories, process theories, which capture the underlying structure common to most theories of physics as we understand them today (be they established, toy or speculative theories). Amongst these theories, we will be focusing on those which are `causal', in the sense that they are intrinsically compatible with the causal structure of space-time -- as required by relativity. We demonstrate that there is a sharp contrast between these theories and the corresponding time-reversed theories, where time is taken to flow backwards from the future to the past. While the former typically feature a rich gamut of allowed states, the latter only allow for a single state: eternal noise. We illustrate this result by considering of the time-reverse of quantum theory. We also derive a strengthening of the result in PRL 108, 200403 on signalling in time-reversed theories.