  Quantum theory is a probabilistic theory with fixed causal structure. General
relativity is a deterministic theory but where the causal structure is dynamic.
It is reasonable to expect that quantum gravity will be a probabilistic theory
with dynamic causal structure. The purpose of this paper is to present a
framework for such a probability calculus. We define an operational notion of
space-time, this being composed of elementary regions. Central to this
formalism is an object we call the causaloid. This object captures information
about causal structure implicit in the data by quantifying the way in which the
number of measurements required to establish a state for a composite region is
reduced when there is a causal connection between the component regions. This
formalism puts all elementary regions on an equal footing. It does not require
that we impose fixed causal structure. In particular, it is not necessary to
assume the existence of a background time. Remarkably, given the causaloid, we
can calculate all relevant probabilities and so the causaloid is sufficient to
specify the predictive aspect of a physical theory. We show how certain
causaloids can be represented by suggestive diagrams and we show how to
represent both classical probability theory and quantum theory by a causaloid.
We do not give a causaloid formulation for general relativity though we
speculate that this is possible. The work presented here suggests a research
program aimed at finding a theory of quantum gravity. The idea is to use the
causaloid formalism along with principles taken from the two theories to marry
the dynamic causal structure of general relativity with the probabilistic
structure of quantum theory.

General Relativity and Quantum Cosmology;Quantum Physics