Approaches to Quantum Gravity

23Quantum Gravity and precision testsC. BURGESS23.1 IntroductionAny of us who has used the Global Positioning System (GPS) in one of the gadgetsof everyday life has also relied on the accuracy of the predictions of Einstein’stheory of gravity, General Relativity (GR). GPS systems accurately provide yourposition relative to satellites positioned thousands of kilometres from the Earth, andtheir ability to do so requires being able to understand time and position measurementstobetterthan1partin1010 . Such an accuracy is comparable to the predictedrelativistic effects for such measurements in the Earth’s gravitational field, whichare of order GM ⊕ /R ⊕ c 2 ∼ 10 −10 , where G is Newton’s constant, M ⊕ and R ⊕ arethe Earth’s mass and mean radius, and c is the speed of light. GR also does wellwhen compared with other precise measurements within the solar system, as wellas in some extra-solar settings [1].So we live in an age when engineers must know about General Relativity in orderto understand why some their instruments work so accurately. And yet we also areoften told there is a crisis in reconciling GR with quantum mechanics, with thesize of quantum effects being said to be infinite (or – what is the same – to beunpredictable) for gravitating systems. But since precision agreement with experimentimplies agreement within both theoretical and observational errors, and sinceuncomputable quantum corrections fall into the broad category of (large) theoreticalerror, how can uncontrolled quantum errors be consistent with the fantasticsuccess of classical GR as a precision description of gravity?This chapter aims to explain how this puzzle is resolved, by showing whyquantum effects in fact are calculable within GR, at least for systems which aresufficiently weakly curved (in a sense explained quantitatively below). Since all ofthe extant measurements are performed within such weakly curved environments,quantum corrections to them can be computed and are predicted to be fantasticallysmall. In this sense we quantitatively understand why the classical approximationto GR works so well within the solar system, and so why in practical situationsApproaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter, ed. Daniele Oriti.Published by Cambridge University Press. c○ Cambridge University Press 2009.