  Quantum mechanics and the theory of gravity are presently not compatible. A
particular question is whether gravity causes decoherence - an unavoidable
source of noise. Several models for gravitational decoherence have been
proposed, not all of which can be described quantum mechanically. In parallel,
several experiments have been proposed to test some of these models, where the
data obtained by such experiments is analyzed assuming quantum mechanics. Since
we may need to modify quantum mechanics to account for gravity, however, one
may question the validity of using quantum mechanics as a calculational tool to
draw conclusions from experiments concerning gravity.
  Here we propose an experiment to estimate gravitational decoherence whose
conclusions hold even if quantum mechanics would need to be modified. We first
establish a general information-theoretic notion of decoherence which reduces
to the standard measure within quantum mechanics. Second, drawing on ideas from
quantum information, we propose a very general experiment that allows us to
obtain a quantitative estimate of decoherence of any physical process for any
physical theory satisfying only very mild conditions.Finally, we propose a
concrete experiment using optomechanics to estimate gravitational decoherence
in any such theory, including quantum mechanics as a special case.
  Our work raises the interesting question whether other properties of nature
could similarly be established from experimental observations alone - that is,
without already having a rather well formed theory of nature like quantum
mechanics to make sense of experimental data.
