Calling time on digital clocks. (English) Zbl 1329.81078
Summary: I explore two logical possibilities for the discretization of time, termed “instantaneous” and “smeared”. These are found by discretizing a continuous theory, and the resulting structure of configuration space and velocities are described. It is shown that results known in numerical methods for integration of dynamical systems preclude the existence of a system with fixed discrete time step which conserves fundamental charges universally, and a method of avoidance of this “no-go” theorem is constructed. Finally the implications of discrete time upon quantum cosmology are discussed.
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 83F05 | Relativistic cosmology |
| 39A12 | Discrete version of topics in analysis |
| 00A79 | Physics |
Keywords:
digital time; clocks; quantum mechanics; cosmology; foundations of physics; perfect actionsReferences:
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