  The study of causal relations has recently been applied to the quantum realm,
leading to the discovery that not all physical processes have a definite causal
structure. While indefinite causal processes have previously been
experimentally shown, these proofs relied on the quantum description of the
experiments. Yet, the same experimental data could also be compatible with
definite causal structures within different descriptions. Here, we present the
first demonstration of indefinite temporal order outside of quantum formalism.
We show that our experimental outcomes are incompatible with a class of
generalised probabilistic theories satisfying the assumptions of locality and
definite temporal order. To this end, we derive physical constraints (in the
form of a Bell-like inequality) on experimental outcomes within such a class of
theories. We then experimentally invalidate these theories by violating the
inequality using entangled temporal order. This provides experimental evidence
that there exist correlations in nature which are incompatible with the
assumptions of locality and definite temporal order.
