Milne vs. Minkowski metric

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SUMMARY

The discussion centers on the differences between Milne and Minkowski spacetimes, both of which are flat manifolds but differ in their global properties. Milne spacetime is geodesically incomplete, while Minkowski spacetime is geodesically complete, indicating that there is no global isometry between them despite a homeomorphism existing. The conversation also emphasizes the importance of how metrics are defined and applied to the underlying topology of R^4, leading to distinct interpretations of these spacetimes.

PREREQUISITES
  • Understanding of differential geometry and manifolds
  • Familiarity with the concepts of geodesics and isometries
  • Knowledge of the FLRW metric and its implications in cosmology
  • Basic grasp of spacetime diagrams and their representations
NEXT STEPS
  • Research the properties of geodesically incomplete manifolds in general relativity
  • Explore the implications of homeomorphisms in differential topology
  • Study the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and its applications
  • Investigate the concept of time dilation in various spacetime geometries
USEFUL FOR

The discussion is beneficial for theoretical physicists, mathematicians specializing in topology, and cosmologists interested in the nuances of spacetime metrics and their implications in general relativity.

  • #31
(We have found that @rocco is a sockpuppet of a recently banned member, so they are gone now.)
 
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  • #32
rocco said:
Does it produce time dilation between the observers living in different cosmological epochs?
There is no such thing; it's not a well-defined concept. It's only well-defined between observers that can exchange round-trip light signals and use them to compare the elapsed times on their clocks. You can't exchange round-trip light signals with someone in the past.
 

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