The Problem of Time In Quantum Geometrodynamics
Karel V. Kuchař
This chapter describes the problem of time in quantum geometrodynamics in more detail. It first describes how the fundamental equation of general relativity can be written as an instantaneous law, indeed as a cousin of a beautiful geometric theorem of Gauss, which Gauss called ‘theoremaegregium’. Then, it describes how the quantization of general relativity leads to the disappearance of time from the formalism, and surveys three ways to respond to the problem. First, one can try to extract a notion of time that will not ‘disappear’ under quantization, from the formalism of classical general relativity. Second, one can try to find a time in the formalism of quantized general relativity. Third, one can conclude that time is only an approximate notion: quantum geometrodynamics, and perhaps quantum theory generally, are to be interpreted in a fundamentally timeless way.
British Academy eBooks•Mar 9, 2006•61 citations