# Coordinate and proper time animation

1. Feb 24, 2012

### Naty1

Someone posted this animation in a previous discussion and I just 'rediscovered' it in my notes:

Do you experts think it accurate, and if so, wouldn't this be a nice tool to display coordinate
time versus proper time?? [Is it worth explaining it in FAQ and linking to it??]

[I have found I like it better than these:

Here are two others which have been linked in various discussions:
I find this one difficult to divine....
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

This one always semmed more intuitive showing geodesics which would be nice to display on the adamtoons format....

http://www.relativitet.se/spacetime1.html ]

In the left chart I can see why the coordinate time [stationary at the origin to the left, tallied in the blue circle] runs faster the the proper time [purple] since the clock aboard the moving object apparently runs closer the the 'spherical' mass...assuming relative speed of the proper clock is ignored....why is the spherical mass pictured as an ellipsoid??

In the right hand chart, I believe that the greater curvature of the proper time relative
to the curvature of the distance curvatureis a nice illustration of why 'usually time is more warped than space' absent singularities...

How would you describe the 'distance' curvature which is not depicted in the left hand
chart?.....I would have tended to roll up the left chart and forgotten entirely about SPACEtime curvature since it wasn't depicted in the left chart....
Apparently this preserves distances [the metric] as described on the illustration?? Just
what does this mean??
Thanks.

Last edited: Feb 24, 2012
2. Feb 28, 2012

### A.T.

Here is the simpler one showing coordinate time versus proper time:
However the distortion by gravity in that simpler one ignores the spatial distortion.

It isn't ignored. Time dilation from movement also plays a role.

It is a circle. Check the aspect ratio of your monitor.

Not really. The extrinsic curvature of the proper time axis is a free parameter of the embedding and has no physical meaning. Make the mass zero so the diagram becomes a cylinder : the proper time axis is still extrinsically curved and you can choose any radius for it, without changing the relevant intrinsic curvature.

The spatial distortion is represented by the different lengths of
- spatial segment on the curved diagram
- its projection onto the axis of the cylinder.

It means that the distances in the right hand (3D) diagram are actually those described by the Schwarzschild metric. And the world-line of the free faller is actually a geodesic on the curved surface shown to the right.

The right diagram is to the left diagram like a globe is to a Mercator projection map