Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Special Relativity: Minkowski Space-Time
- 1 Galilei and Minkowski Space-Times
- 2 Global Non-Inertial Frames in Special Relativity
- 3 Relativistic Dynamics and the Relativistic Center of Mass
- 4 Matter in the Rest-Frame Instant Form of Dynamics
- Part II General Relativity: Globally Hyperbolic Einstein Space-Times
- Part III Dirac–Bergmann Theory of Constraints
- Appendix A Canonical Realizations of Lie Algebras, Poincaré Group, Poincar´e Orbits, and Wigner Boosts
- Appendix B Grassmann Variables and Pseudo–Classical Lagrangians
- Appendix C Relativistic Perfect Fluids and Covariant Thermodynamics
- References
- Index
2 - Global Non-Inertial Frames in Special Relativity
from Part I - Special Relativity: Minkowski Space-Time
Published online by Cambridge University Press: 17 June 2019
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Special Relativity: Minkowski Space-Time
- 1 Galilei and Minkowski Space-Times
- 2 Global Non-Inertial Frames in Special Relativity
- 3 Relativistic Dynamics and the Relativistic Center of Mass
- 4 Matter in the Rest-Frame Instant Form of Dynamics
- Part II General Relativity: Globally Hyperbolic Einstein Space-Times
- Part III Dirac–Bergmann Theory of Constraints
- Appendix A Canonical Realizations of Lie Algebras, Poincaré Group, Poincar´e Orbits, and Wigner Boosts
- Appendix B Grassmann Variables and Pseudo–Classical Lagrangians
- Appendix C Relativistic Perfect Fluids and Covariant Thermodynamics
- References
- Index
Summary
There is a description of the 3+1 approach allowing definition of global non-inertial frames in Minkowski space-time. One gives a time-like observer and a nice foliation with 3-spaces (namely a clock synchronization convention). Then one introduces Lorentz scalar radar 4-coordinates: the time is an increasing function of the proper time of the observer and the 3-coordinates live in the instantaneous 3-spaces. The connection of the radar coordinates with the standard ones defines the four embedding functions describing the foliation with 3-spaces. Then there is the definition of parametrized Minkowski theories for every kind of matter admitting a Lagrangian description. The new Lagrangian is a function of the matter and of the embedding, but is singular so that the embedding variables are gauge variables. As a consequence, the transition from a non-inertial frame to either an inertial or non-inertial frame is a gauge transformation not changing the physics but only the inertial forces.
- Type
- Chapter
- Information
- Non-Inertial Frames and Dirac Observables in Relativity , pp. 12 - 26Publisher: Cambridge University PressPrint publication year: 2019