Discussion Overview
The discussion centers on the concepts of galaxy recession and the expansion of the universe, particularly how these phenomena relate to the notion of velocity in the context of general relativity and the Friedmann-Robertson-Walker (FRW) solutions of Einstein's equations. Participants explore the implications of spacetime curvature on defining velocities and the interpretation of redshift measurements.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants suggest that "ordinary" velocity is defined within flat (Minkowski) spacetime, while the galaxies are situated in a curved spacetime.
- There is a discussion about the ambiguity of defining relative velocities in curved spacetime, as inertial rest frames are local and do not extend globally.
- Participants propose that while a relative velocity can be defined for bodies following timelike paths, it remains unclear if a global expansion velocity can be unambiguously defined for the entire universe.
- Some argue that co-moving coordinates allow for the definition of an expansion rate due to the symmetry of spacetime, while others challenge the existence of a timelike Killing vector field (KVF) in FRW spacetime.
- There is a clarification that the "measured recession" of galaxies is not a direct speed but rather a calculated value based on redshift, brightness, and angular size, with assumptions about comoving worldlines.
- The distinction between comoving coordinate time and FRW coordinate time is discussed, with some participants expressing uncertainty about their equivalence.
Areas of Agreement / Disagreement
Participants express multiple competing views regarding the definition of velocity in the context of cosmic expansion and the implications of spacetime curvature. The discussion remains unresolved on several points, particularly concerning the nature of comoving coordinates and the interpretation of recession speeds.
Contextual Notes
Limitations include the dependence on specific definitions of velocity and coordinate systems, as well as the unresolved nature of assumptions regarding the symmetry of spacetime and the existence of global coordinate systems.