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

[TheQuestionGuy14]

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:

 

[PeroK]

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.

 

[Dale]

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.

 

[A.T.]

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.

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).

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