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Images of TimeMind, Science, Reality$
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George Jaroszkiewicz

Print publication date: 2016

Print ISBN-13: 9780198718062

Published to Oxford Scholarship Online: January 2016

DOI: 10.1093/acprof:oso/9780198718062.001.0001

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The reparametrization of time

The reparametrization of time

Chapter:
(p.148) 15 The reparametrization of time
Source:
Images of Time
Author(s):

George Jaroszkiewicz

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198718062.003.0015

This chapter reviews the parametrization of absolute time and develop the concept of temporal reparametrizations, or changes in our clocks. Using the action integral and Dirac’s constraint mechanics, the chapter discusses the mathematics of temporal reparametrization and reparametrization form invariance. This latter is related to general covariance in general relativity. Working in an extended phase space that now includes time and its associated ‘momentum’, the chapter derives the result that the extended Hamiltonian is zero on the surface of constraints, that is, over the true or classical trajectory. The implications of this for quantum cosmology and the ‘problem of time’ discussed in Chapter 8 are examined and analysed in terms of contextual completeness.

Keywords:   temporal reparametrization, constraint mechanics, form invariance, extended phase space, surface of constraints, quantum cosmology, problem of time

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