- Title Pages
- Preface
- 1 Introduction
- 2 Observers and time
- 3 Subjective images of time
- 4 Cultural images of time
- 5 Literary images of time
- 6 Objective images of time
- 7 Mathematical images of time
- 8 Illusionary images of time
- 9 Causal images of time
- 10 Physics and time
- 11 Biological time
- 12 The dimensions of time
- 13 The architecture of time
- 14 Absolute time
- 15 The reparametrization of time
- 16 Origins of relativity
- 17 Special relativity
- 18 Generalized transformations
- 19 General relativistic time
- 20 Time travel
- 21 Imaginary time
- 22 Irreversible time
- 23 Discrete time
- 24 Time and quanta
- 25 Temporal correlations
- 26 Time reversal
- 27 Quantized spacetime
- 28 Epilogue
- Appendix
- Bibliography
- Index
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
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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- Title Pages
- Preface
- 1 Introduction
- 2 Observers and time
- 3 Subjective images of time
- 4 Cultural images of time
- 5 Literary images of time
- 6 Objective images of time
- 7 Mathematical images of time
- 8 Illusionary images of time
- 9 Causal images of time
- 10 Physics and time
- 11 Biological time
- 12 The dimensions of time
- 13 The architecture of time
- 14 Absolute time
- 15 The reparametrization of time
- 16 Origins of relativity
- 17 Special relativity
- 18 Generalized transformations
- 19 General relativistic time
- 20 Time travel
- 21 Imaginary time
- 22 Irreversible time
- 23 Discrete time
- 24 Time and quanta
- 25 Temporal correlations
- 26 Time reversal
- 27 Quantized spacetime
- 28 Epilogue
- Appendix
- Bibliography
- Index
