Gravitational Length Contraction

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Discussion Overview

The discussion centers on the concept of gravitational length contraction, particularly in the context of the Schwarzschild metric. Participants explore whether such a phenomenon exists, how it might be derived, and its implications in relation to time dilation and the behavior of light in gravitational fields.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the existence of gravitational length contraction and its derivation from the Schwarzschild metric.
  • Another participant suggests that in Schwarzschild coordinates, the speed of light is anisotropic, leading to the idea of "gravitational length contraction" in the radial direction.
  • A different viewpoint expresses skepticism about the common belief in gravitational length contraction, noting a lack of discussion in textbooks or papers, and proposes that it could be defined analogously to time dilation, dependent on the coordinates used.
  • A participant references a related thread discussing the warping of space in the presence of mass, which may provide additional context to the discussion.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the existence or significance of gravitational length contraction, with multiple competing views and uncertainties expressed throughout the discussion.

Contextual Notes

Participants note that the concept of gravitational length contraction may depend on the choice of coordinates, and there is an acknowledgment of the potential for missing assumptions or definitions in the discussion.

nigelscott
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I understand the concepts of time dilation and length contraction in SR. I also understand the concept of time dilation in a gravitational field. But what about length contraction in a gravitational field? Is there such a thing and can it be derived from the Schwarzschild metric?
 
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I believe that in the Schwarzschild solution expressed in Schwarzschild coordinates the speed of light is anisotropic and that in order to explain this a "gravitational length contraction" in the radial direction is sometimes thought of.
 
A lot of lay people seem to think that gravitational length contraction should exist for reasons that are unclear, but I don't think I've ever seen a textbook or paper discussing the concept specifically. (It's possible I could have missed a paper on the topic, of course.)

Going from analogy with time dilation, though, I'd guess one could define it as the ratio between proper distance and changes in coordinates.

The value of this ratio will be dependent on the coordinates used of course, just as in the case of time dilation. So I don't see any coordinate-independent significance to the term.
 

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