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 [131]; a survey of precision electroweak
measurements can be found in an article by Langacker [105]). 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 [155]. (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 [119] – 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, [120].) 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.
