Introduction

Any of us who has used the Global Positioning System (GPS) in one of the gadgets of everyday life has also relied on the accuracy of the predictions of Einstein's theory of gravity, General Relativity (GR). GPS systems accurately provide your position relative to satellites positioned thousands of kilometres from the Earth, and their ability to do so requires being able to understand time and position measurements to better than 1 part in 1010. Such an accuracy is comparable to the predicted relativistic effects for such measurements in the Earth's gravitational field, which are of order GM⊕/R⊕c2 ~ 10−10, where G is Newton's constant, M⊕ and R⊕ are the Earth's mass and mean radius, and c is the speed of light. GR also does well when compared with other precise measurements within the solar system, as well as in some extra-solar settings.

So we live in an age when engineers must know about General Relativity in order to understand why some their instruments work so accurately. And yet we also are often told there is a crisis in reconciling GR with quantum mechanics, with the size of quantum effects being said to be infinite (or – what is the same – to be unpredictable) for gravitating systems.