How can a square-based lattice turn into a circular-based one?

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Discussion Overview

The discussion revolves around the transition of geodesics in general relativity (GR) from a mass-free space represented by square or cubic cells to a geodesic system around a mass, typically depicted as circular curves. Participants explore the implications of introducing mass into a previously empty space and the associated challenges in modeling this transition within the framework of GR.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions how a mass can smoothly grow from zero in a mass-free geodesic system, suggesting a function for mass growth over time.
  • Another participant asserts that this scenario violates the principles of GR, stating that mass cannot be created from nothing.
  • Some participants discuss the implications of energy densities producing effects similar to mass distributions, referencing electromagnetic waves and their potential influence on geodesics.
  • There are claims that GR does not allow for a transition from flat to curved spacetime without violating local conservation of energy.
  • One participant expresses confusion about the transition between straight lines and circles in geodesics, suggesting a potential topological issue.
  • Several participants emphasize the importance of local conservation laws in GR and challenge the validity of certain graphical representations of geodesic transitions.
  • Another participant suggests that the discussion may stem from misunderstandings based on poor sources of information regarding GR.

Areas of Agreement / Disagreement

Participants generally disagree on the feasibility of transitioning from a mass-free to a mass-influenced geodesic system. Multiple competing views remain regarding the implications of energy and mass in GR, and the discussion remains unresolved.

Contextual Notes

Participants highlight limitations in understanding the transition between different geodesic systems, particularly regarding the assumptions about mass creation and the conservation of energy in GR. There are also references to the challenges of interpreting graphical representations of these concepts.

  • #31
DaTario said:
Yes, Dale, I am aware of this fact. It is like the extended parabola I presented in #25 (not the 2D one).
Ok, I just thought that would have been one possible reason for believing that a linear geodesic could turn into a circular one.
 
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  • #32
Dale said:
Ok, I just thought that would have been one possible reason for believing that a linear geodesic could turn into a circular one.
Thank you, Dale. This comment of yours was enlightening. So, it seems that we can say that there are no circular geodesics, at least as long as no time travel is considered.
If this is the case, then it could have been a nice answer to my question.
 

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