Relative Velocity II: Defining Relative Velocity in GR

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Discussion Overview

The discussion revolves around the concept of "relative velocity" in the context of General Relativity (GR), exploring how this notion differs from Special Relativity (SR) due to the curvature of spacetime. Participants examine the challenges of defining relative velocity when observers are in curved spacetime and propose various approaches to conceptualize this relationship, particularly through the lens of frequency shifts of light rays connecting observers.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that relative velocity in GR may be derived from the frequency shift of light rays between observers, although this definition may not be universally applicable in all GR scenarios.
  • Another participant questions how to differentiate between Doppler shifts associated with relative velocity and gravitational redshift, indicating a potential complexity in the definitions.
  • A hypothesis is presented that observers exist in a 4-dimensional spacetime manifold, with unique geodesics connecting points, allowing for a geometric approach to defining relative velocity when observers are at the same event.
  • It is proposed that the relative velocity can be expressed through a formula involving the gamma factor and the relative velocity vector, contingent on the observers being at the same event in spacetime.
  • Participants discuss the necessity of a null geodesic connecting two events for defining relative velocity, suggesting that the curvature of spacetime influences how this velocity is perceived.
  • There is a proposal that the relative velocity will depend on the path taken by the velocity vector during parallel transport along the null geodesic, raising questions about the effects of spacetime curvature on this definition.

Areas of Agreement / Disagreement

Participants express differing views on the definition and implications of relative velocity in GR, with no consensus reached on a singular definition or approach. The discussion remains unresolved, with multiple competing ideas and hypotheses presented.

Contextual Notes

Limitations include the dependence on specific conditions such as the existence of null geodesics and the challenges posed by the curvature of spacetime, which complicate the comparison of velocities between distinct events.

  • #31
Thanks Robphy I'll have a look at that one next time I'm at the uni library.
 

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