George Jaroszkiewicz
- Published in print:
- 2016
- Published Online:
- January 2016
- ISBN:
- 9780198718062
- eISBN:
- 9780191787553
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198718062.003.0015
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
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, ...
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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.Less
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.
