- 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 dimensions of time
The dimensions of time
- Chapter:
- (p.113) 12 The dimensions of time
- Source:
- Images of Time
- Author(s):
George Jaroszkiewicz
- Publisher:
- Oxford University Press
This chapter discusses the mathematical reasons why time has one dimension rather than two or more dimensions. It examines the flow of information, through a spacetime with a given signature, in terms of partial differential equations. These are classified as elliptic, parabolic or hyperbolic. The role of boundary conditions in ruling out different temporal dimensions is explained. The chapter discusses the stability of solutions in spacetimes with various signatures and give a mathematical explanation for the observation that the world we live in has four spacetime dimensions best described by hyperbolic partial differential equations. The chapter ends with commentary on empirical studies in cosmology and biology that have used multi-component time concepts to fit their data.
Keywords: temporal dimensions, partial differential equations, elliptic equations, parabolic equations, hyperbolic equations, spacetime signature, boundary conditions, stability of solutions, empirical studies
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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