Abstract
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.