The Quantization of Time

Abstract

In quantum theory there is an uncertainty relation between time and energy which forms an incomplete analogy to that between position and momentum. A time operator conjugate to the Hamiltonian cannot be defined in a natural way, and a classical time parameter t is used in quantum mechanics. In Chap. 1 the concept of mechanistic (‘Aristotelian’) time was defined by motion. There remained then only the possibility of comparing (within the relativistic modifications of the concept of simultaneity) the positions of moving objects, among them those of the ‘hands’ of appropriate clocks. The time read from such classical clocks is also used to define the ‘parameter of time’ in quantum mechanical wave functions.