Question about Gravity according to GR: Earth Rises, Time Axis Curves

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Discussion Overview

The discussion revolves around the interpretation of gravity in the context of General Relativity, specifically focusing on the visual representation of an apple falling towards the Earth and the implications of curved time axes. Participants explore the meaning of the Earth "rising" to meet the apple and the concept of Closed Timelike Curves (CTCs) in relation to falling objects.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the meaning of the Earth "rising" to catch the apple and suggests that the time axis curving could imply the formation of a Closed Timelike Curve with enough time falling.
  • Another participant counters that the video illustrates intersecting worldlines rather than implying absolute motion, emphasizing that the paths shown are open, not closed.
  • A different participant discusses the nature of spacetime, noting that while curves of constant curvature in flat spacetime form circles, in actual spacetime they form hyperbolas due to the metric's properties.
  • Another reply asserts that the representation of the Earth rising has no physical meaning and is merely a layout issue in the diagram, suggesting that more time would require a new layer in the illustration.

Areas of Agreement / Disagreement

Participants express differing interpretations of the video and its implications, particularly regarding the representation of motion and the nature of time in General Relativity. No consensus is reached on the implications of the curved time axis or the meaning of the Earth's motion.

Contextual Notes

Participants highlight that the visual representation in the video may not accurately reflect the underlying physics, indicating potential limitations in understanding based on the diagram's layout.

TheQuestionGuy14
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Recently I watched a video on Gravity according to General Relativity. The video shows that the Earth rises up to catch the apple, what does this mean? It also shows the time axis being curved as the apple falls. Doesn't this mean that with enough time falling, the time axis will curve into a circle, making a Closed Timelike Curve?

Here is the video:
 
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TheQuestionGuy14 said:
Recently I watched a video on Gravity according to General Relativity. The video shows that the Earth rises up to catch the apple, what does this mean? It also shows the time axis being curved as the apple falls. Doesn't this mean that with enough time falling, the time axis will curve into a circle, making a Closed Timelike Curve?

The last part of the video clearly shows the paths being open, not closed.

Also, it doesn't imply that the Earth "rises up" to meet the apple. It shows that the surface of the Earth and the apple have different worldlines that intersect. You shouldn't think of either of these as "absolutely" moving. It's just an illustration.
 
TheQuestionGuy14 said:
It also shows the time axis being curved as the apple falls. Doesn't this mean that with enough time falling, the time axis will curve into a circle, making a Closed Timelike Curve?
This is a good question. It shows that you are really thinking this through.

Indeed, if you have a flat piece of paper then curves of constant curvature form circles. However, spacetime is different. In flat spacetime curves of constant curvature in time form hyperbolas with asymptotes at c. This is due to the minus sign in the metric.
 
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TheQuestionGuy14 said:
Recently I watched a video on Gravity according to General Relativity. The video shows that the Earth rises up to catch the apple, what does this mean?
It has no physical meaning, it's just how the diagram is spread out in the plane. Look at the rolled up version at 1:10min in the video, where the lowest space coordinate (Earth's surface) is at the same height everywhere.

TheQuestionGuy14 said:
Doesn't this mean that with enough time falling, the time axis will curve into a circle, making a Closed Timelike Curve?
No, to represent more time in the initial flat diagram, you would have to start a new layer every time you come around. This is a purely an illustration layout issue, and has nothing to do with the actual physics.

To understand it better check out the links in the video description (click "MORE INFO" below the video).

See also these:



 
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