Animated Gravity : Einstein vs. Newton

[A.T.]

There are many threads about this on this forum: People are confused about the basic idea of Gravitation in General Relativity. They understandably don't understand how the very common balls-on-rubber-sheet-analogy explains anything. I usually post those two links to help them:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html

Now I made an animation based on those illustrations (watch in HD):

https://www.youtube.com/watch?v=izKLw1V7YJ8

 

[elfmotat]

Thanks AT! This will definitely come in handy when trying to correct the misconceptions of people who were mislead by the "rubber sheet" analogy.

 

[nitsuj]

Very Nice Animation!

 

[Zag]

Great animation! Congratulations!

 

[A.T.]

Thanks for the positive feedback. I polished it a bit. The latest version is here (watch in HD):

https://www.youtube.com/watch?v=DdC0QN6f3G4

 

[TurtleMeister]

Thanks A.T. Well done. Your animation has help me better understand GR.

 

[nitsuj]

Thanks for the positive feedback. I polished it a bit. The latest version is here (watch in HD):

A.T. I read on Wiki that gravity is "curved space". Looking at your animation it appears though the time axis is curved.

 

[A.T.]

A.T. I read on Wiki that gravity is "curved space". Looking at your animation it appears though the time axis is curved.

Gravity is distorted space-time. For apples falling on Earth the time part is crucial. Spatial curvature is relevant on a more global level and at higher speeds (orbit precession, light bending).

The term "curvature" is confusing and ambiguous:

What you probably mean is the "extrinsic curvature" of the time axis in the diagram, which is irrelevant physically. What matters are the distances within the diagram (metric). As long you preserve that metric you can roll the the diagram as you wish for better visualization:
- the unrolled state seen initially shows the geodesic property of the falling worldline better
- the cone-like rolled state has better correspondence to the apple as we see it falling radially

What wiki means is the "intrinsic curvature" of the space-time manifold, which is implied globally by the distortion, but not really relevant locally. The diagram in the animation doesn't have intrinsic curvature.

 

[jedishrfu]

Nice video!

How did you do the graphics? and the animation?

 

[nitsuj]

Gravity is distorted space-time. For apples falling on Earth the time part is crucial. Spatial curvature is relevant on a more global level and at higher speeds (orbit precession, light bending).

With curved space,

If i had a "straight" ruler 13,000km long and I made it in absence of gravity. Then brought the ruler next to Earth, would the "straight" ruler appear curved? Having the same curvature as a "light bending" (all else equal).

 

[A.T.]

With curved space, If i had a "straight" ruler 13,000km long and I made it in absence of gravity. Then brought the ruler next to Earth, would the "straight" ruler appear curved?

Locally the ruler would be still straight, but the ends would point into directions that are not 180° apart. So yes, globally it would appear bent.

Having the same curvature as a "light bending" (all else equal).

I think the light ray bends more than the ruler, because it also affected by the time-distortion (like the apple). Gravitational time dilation means that the lower part of a wave front advances slower than the upper one. This adds to the effect from spatial distortion.

 

[A.T.]

Nice video!

How did you do the graphics? and the animation?

Thanks. It's done with a free software called "blender", mostly via the integrated scripting API (python).

 

[nitsuj]

Locally the ruler would be still straight, but the ends would point into directions that are not 180° apart. So yes, globally it would appear bent.

I think the light ray bends more than the ruler, because it also affected by the time-distortion (like the apple). Gravitational time dilation means that the lower part of a wave front advances slower than the upper one. This adds to the effect from spatial distortion.

Thanks so much A.T.!

 

[jedishrfu]

Thanks. It's done with a free software called "blender", mostly via the integrated scripting API (python).

Great I'll check that out.

You should check out processing.org too. Its sw designed for graphic artists that want to paint in code (java). There's also a webish version called processing.js There are some vimeo videos where the art is done with processing search "processing video" on vimeo