Clock synchronization for ring-riding observers on rotating disk

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Discussion Overview

The discussion revolves around the synchronization of clocks for observers riding on a rotating disk, specifically focusing on the challenges faced by Langevin observers. Participants explore the implications of local versus global synchronization, the mathematical framework involved, and the physical interpretations of these concepts.

Discussion Character

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

Main Points Raised

  • Some participants note that while co-rotating clocks can be synchronized locally, global synchronization is not possible due to the nature of the rotating frame.
  • There is a discussion about the mathematical representation of events on the worldlines of observers and the implications of spacelike and timelike vectors in this context.
  • One participant suggests using standard Einstein synchronization to locally synchronize neighboring clocks, which involves reflecting a light signal between two points.
  • Another participant raises the issue of the non-static nature of the ring-riding Langevin congruence, questioning the existence of a family of spacelike hypersurfaces orthogonal to the congruence.
  • There is a reference to a condition from Landau's book regarding the selection of coordinate charts for synchronization, with some participants agreeing that Minkowski charts may be applicable in this scenario.
  • Participants discuss the limitations of coordinate charts in mapping local inertial frames for arbitrary collections of observers, particularly for Langevin observers.
  • The relationship between the existence of hypersurfaces and the geometry of spacetime is examined, with emphasis on how non-static congruences affect the uniformity of geometry across hypersurfaces.

Areas of Agreement / Disagreement

Participants generally agree that local synchronization is feasible, but there is no consensus on the implications for global synchronization or the existence of hypersurfaces that can maintain consistent geometry across the rotating frame.

Contextual Notes

Limitations include the dependence on the definitions of synchronization and the specific conditions under which the discussions are framed, particularly regarding the nature of the rotating disk and the observers involved.

  • #61
At the beginning of this thread we talked about 'stationary' congruence like the Langevin congruence in Minkowski spacetime. Langevin congruence is defined as stationary just because its worldlines are integral orbits of a timelike Killing vector field (KVF).

If the above is correct then, by definition, given a spacetime the existence of at least one stationary congruence suffices to define it as a stationary spacetime, right ?
 
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  • #62
cianfa72 said:
by definition, given a spacetime the existence of at least one stationary congruence suffices to define it as a stationary spacetime, right ?
Yes.
 
  • #63
So in Minkowski spacetime there are some types of timelike KVFs (actually an infinite families of them): inertial KVFs, Rindler KVFs and Langevin KVFs (the corresponding integral orbits define indeed stationary congruences). Both the first two are also static since they are hypersurface orthogonal whilst the third is not.
 
  • #64
cianfa72 said:
So in Minkowski spacetime there are some types of timelike KVFs (actually an infinite families of them): inertial KVFs, Rindler KVFs and Langevin KVFs (the corresponding integral orbits define indeed stationary congruences). Both the first two are also static since they are hypersurface orthogonal whilst the third is not.
Yes. Note, however, that while the inertial KVFs are timelike everywhere, the others are not; they are only timelike in restricted open regions of the spacetime (in the Rindler case, the appropriate "wedges" where the hyperbolas that are the integral curves of the KVF are timelike; in the Langevin case, an open "tube" where the radius is small enough to make the helical integral curves of the KVF timelike).
 
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