Three Roads To Quantum Gravity

72 THREE ROADS TO QUANTUM GRAVITY
of all the black holes in the universe, but there may be other
regions hidden as well. For example, if the rate at which the
universe expands increases with time, there will be regions of
the universe from which we shall never receive light signals,
no matter how long we wait. A photon from such a region may
be travelling in our direction at the speed of light, but because
of the increase in the rate of the expansion of the universe it
will always have more distance to travel towards us than it
has travelled so far. As long as the expansion continues to
accelerate, the photon will never reach us. Unlike black holes,
the hidden regions produced by the acceleration of the
expansion of the universe depend on the history of each
observer. For each observer there is a hidden region, but they
are different for different observers.
This raises an interesting philosophical point, because
objectivity is usually assumed to be connected with observer
independence. It is commonly assumed that anything that is
observer dependent is subjective, meaning that it is not
quite real. But the belief that observer dependence rules
out objectivity is a residue of an older philosophy, usually
associated with the name of Plato, according to which truth
resides not in our world but in an imaginary world consisting
of all ideas which are eternally true. According to this
philosophy, anybody could have access to any truth about the
world, because the process of ®nding truth was held to be
akin to a process of remembering, rather than observing. This
philosophy is hard to square with Einstein's general theory of
relativity because, in a universe de®ned by that theory,
something may be both objectively true and at the same
time knowable only by some observers and not others. So
`objectivity' is not the same as `knowable by all'. A weaker,
less stringent interpretation is required: that all those observers
who are in a position to ascertain the truth or falsity of
some observation should agree with one another.
The hidden region of any observer has a boundary that
divides the part of the universe they can see from the part they
cannot. As with a black hole, this boundary is called the
horizon. Like the invisible regions, horizons are observer
dependent concepts. For any observer who remains outside