How does Curvature Relate to 'Gravitation'?

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    Curvature Gravitation
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Discussion Overview

The discussion centers on the relationship between curvature in general relativity and the Newtonian concept of gravitation. Participants explore how the geometric interpretation of gravity relates to Newton's law of gravitation and seek clarification on the concept of geodesic deviation.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how curvature translates into Newton's idea of gravitation and seeks a clearer explanation of this relationship, particularly in the context of geodesic deviation.
  • Another participant proposes a new concept of "G-for-geometry-acceleration," suggesting that in a gravitational field, an accelerometer reads zero during free fall, indicating that objects move along geodesics in curved space.
  • A participant expresses frustration that existing general relativity texts do not adequately emphasize the connection between curvature and gravitation.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing differing views on the clarity and emphasis of curvature's relationship to gravitation in existing literature.

Contextual Notes

Participants note limitations in the existing texts regarding the explanation of curvature and gravitation, indicating a potential gap in understanding or emphasis on certain aspects of general relativity.

Karl G.
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I have searche many general relativity texts and have not found an answer to the following question: How does curvature translate into the Newtonian idea of gravitation? For example, how is Newton's law of gravitation, where all matter attracts all matter, an approximation to the idea of curvature? I vaguely know that the idea is related to the equation of geodesic deviation, but could somebody explain this more clearly?

Thanks!
 
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The handwavy idea is to define a new sort of acceleration. In Newtonian physics, a force produces an acceleration. This can be measured by an accelerometer. The funny thing is that when an object is acted on by gravity alone, ie. when it is falling freely, an accelerometer attached to it reads zero, even though the acceleration is not zero. If we define a new sort of "G-for-geometry-acceleration" that is what the accelerometer reads, then we end up with a geometric theory of gravity. In this view, gravity curves space, and freely falling particles move with zero G-acceleration which means they move on "straight lines" in curved spaces called geodesics.
 
Thanks! Unfortunately, all GR yests I have pored over do not emphasize this aspect of GR enough, in my opinion.
 
Sorry! Substitute 'texts' for 'yests'. To say my keyboard is antiquated would be quite an understatement.
 
Karl G. said:
Sorry! Substitute 'texts' for 'yests'. To say my keyboard is antiquated would be quite an understatement.
You can edit your own posts.
 

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