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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.


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