  The assumption that a complete description of an early state of the universe
does not privilege any position or direction in space leads to a unified
account of probability in cosmology, macroscopic physics, and quantum
mechanics. Such a description has a statistical character. Deterministic laws
link it to statistical descriptions of the cosmic medium at later times, and
because these laws do not privilege any position or direction in space, the
same must be true of these descriptions. If the universe is infinite, we can
identify the probability that the energy density at a particular instant and a
particular point in space (relative to a system of spacetime coordinates in
which the postulated spatial symmetries are manifest) lies in a given range
with the fractional volume occupied by points where the energy density lies in
this range; and similarly with all other probabilities that figure in the
statistical description. The probabilities that figure in a complete
description of the cosmic medium at any given moment thus have an exact and
objective physical interpretation. The statistical entropy and the information
associated with each cosmological probability distribution are likewise
objective properties of the universe, defined in terms of relative frequencies
or spatial averages.
