INTERNAL CLOCKS IN QUANTUM MECHANICS

Canonical formalism for general relativity involves a Hamiltonian which is a constraint. In this talk I will show you a principal difficulty in quantizations of Hamiltonian constraint systems. The Hamiltonian constraint reflects the lack of external time in the theory. The concept of quantum dynamics is introduced with help of internal clocks, i.e. monotonically evolving internal degrees of freedom inside a given system. As there is no preferred choice of internal clock, one faces the problem of possible incompatibility of quantum dynamics derived with distinct clocks. I will develop a methodology for making a comparison between distinct clock-based quantum dynamics and next apply it to a simple model. Then I will discuss the obtained result.

All interested persons are invited
M. Kowal, W. Piechocki, L. Roszkowski, J. Skalski