

1.1 Against the split brain
The long-standing nature of this difficulty has driven some
physicists to a state of intellectual despair, wherein they
conclude that a crisis exists in physics which might be called the
crisis of the split brain. On one
hand, quantum mechanics (and its offspring quantum field theory)
provides an incredibly successful description of all known
non-gravitational phenomena, with agreement between predictions and
experiment sometimes taking place at the part-per-billion level
(for a recent precision test of QED, see for example [132]; a survey of precision
electroweak measurements can be found in an article by
Langacker [106]). On the other hand,
classical general relativity is also extremely successful, with its
predictions being well tested within the solar system and for some
binary pulsar systems; a survey of tests of gravity with references
may be found in [156]. (The cosmological
evidence for dark matter and dark energy is sometimes proposed as
indicating the failure of gravity over long distances - perhaps the
most successful such proposal for galaxies is given by [120] - but at present the
evidence for new gravitational physics at large distances does not
seem compelling; a summary of some of the observational
difficulties of replacing dark matter with new physics at long
distances is given in [4], see, however,
[121].) The perceived
crisis is the absence of an over-arching theoretical framework
within which both successes can be accommodated. Our brains are
effectively split into two incommunicative hemispheres, with
quantum physics living in one and classical general relativity in
the other.
The absence of such a framework would indeed be a
crisis for theoretical physics, since real theoretical predictions
are necessarily approximate. Controllable results always require
some understanding of the size of the contributions being neglected
in any given calculation. If quantum effects in general relativity
cannot be quantified, this must undermine our satisfaction with the
experimental success of its classical predictions.
It is the purpose of this article to present the
modern point of view on these issues, which has emerged since the
early 1980’s. According to this point of view there is no such
crisis, because the problems of quantizing gravity within the
experimentally accessible situations are similar to those which
arise in a host of other non-gravitational applications throughout
physics. As such, the size of quantum corrections can be safely
estimated and are extremely small. The theoretical framework which
allows this quantification is the formalism of effective field theories, whose explanation
makes up the better part of this article. In so doing we shall see
that although there can be little doubt of the final outcome, the
explicit determination of the size of sub-leading quantum effects
in gravity has in many cases come only relatively recently, and a
complete quantitative analysis of the size of quantum corrections
remains a work in progress.

