Space-Time Fabric: Understanding 3D & Time Together

[gsingh2011]

I don't understand how the space-time fabric works. I've seen videos where the sun is in the space-time fabric and it makes a ripple in it and the Earth revolves around this. This works fine if our universe was 2D, but what if there was something above the sun in that diagram? Basically, I'm confused on how you put 3D space along with a fourth dimension time in a 2D plane...

 

[Dale]

You are right, it is a really poor analogy and quite useless.

 

[A.T.]

I don't understand how the space-time fabric works. I've seen videos where the sun is in the space-time fabric and it makes a ripple in it and the Earth revolves around this.

This is a common misconception. In this analogy the fabric doesn't represent space-time, just reduced space (2D dimensions of it). It shows just the spatial curvature which has some effects on its own, but the main effect of gravitation (mass attraction), cannot be explained without the time dimension. Here are links to better visualizations:
http://www.relativitet.se/spacetime1.html
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.adamtoons.de/physics/gravitation.swf

This works fine if our universe was 2D,

Yes you have to imagine we live in an universe with less dimensions to understand this curvature visualizations by embedding. The illustrations are 3D, so a curved diagram in it can be 2D at max. The space-time diagrams linked above are not different that that aspect. They just use 1 space & 1 time dimension instead of 2 space dimensions.

but what if there was something above the sun in that diagram?

If there was something above the sun in that diagram, it would not be in our universe. The 3D dimensions of these illustrations are a virtual embedding space without physical meaning. It is needed to visualize curvature of the diagram.

This sun and Earth are actually not spheres above the fabric, but circles within the fabric in a space-space diagram, even if they are often shown as spheres.

Basically, I'm confused on how you put 3D space along with a fourth dimension time in a 2D plane...

Well you don't. You can only visualize 2 of the 4 space-time dimensions in a 2D diagram.

 

[haushofer]

I don't understand how the space-time fabric works. I've seen videos where the sun is in the space-time fabric and it makes a ripple in it and the Earth revolves around this. This works fine if our universe was 2D, but what if there was something above the sun in that diagram? Basically, I'm confused on how you put 3D space along with a fourth dimension time in a 2D plane...

The best way, I suppose, is to suppress two spatial dimensions and view space-time as 2-dimensional.