  By studying the set of correlations that are theoretically possible between
physical systems without allowing for signalling of information backwards in
time, we here identify correlations that can only be achieved if the time
ordering between the systems is fundamentally indefinite. These correlations,
if they exist in nature, must result from non-classical, non-deterministic
time, and so may have relevance for quantum (or post-quantum) gravity, where a
definite global time might not exist.
