Visualizing 3D Contours of Spacetime

[Easton Morrill]

In every video and educational movie that I've seen, it shows Einstein's vision of Spacetime on an XYZ graph with a fourth dimensional time, but my confusion arises because the videos then put this graph on a two dimensional plane of "Spacetime." My question concerns the visualization of this, I am confused whether one should visualize this in three dimensions, and if so, how do black holes and them tearing a hole in spacetime, rip? I mean to say one always visualizes it on a plane with a singularity stretching downward to infinity, but how would I look at this in three dimensions?
Thank you to everyone/anyone who responds, I'm sure that your comment will be very helpful.

 

[phinds]

All of those "rubber sheet" analogies are poor analogies at best. There is no such thing as the "fabric of space" (or spacetime for that matter). Personally, I've never figured out how to visualize spacetime near a black hole (although I think I've sort of got it) I just concentrate on the properties which is really what matters.

 

[Nugatory]

my confusion arises because the videos then put this graph on a two dimensional plane of "Spacetime."

That could be either of two things. If all the objects involved in the problem lie on a straight line in space (Einstein's classic thought experiments often involved trains and observers along straight railroad tracks for that reason) we only need to draw two dimensions: one for space and one for time, and that's easy to draw on a sheet of graph paper. These diagrams are usually called "Minkowski diagrams" or "space-time diagrams", and they are an essential tools for learning, visualizing, and understanding special relativity. You do not want to take on general relativity and curved spacetime until you are comfortable with reading and interpreting them.

The second common thing you will see is an attempt to explain gravity by showing an illustration of a flat horizontal surface deformed downwards into a funnel shape by the mass at the center. In these pictures, the two dimensions of the sheet are space dimensions and the third dimension through which the sheet is deformed has no physical significance - the artist just needed it to draw the deformation. This is the "rubber sheet" analogy that Phinds disparages above, and he's right - it is very misleading and you might be better off trying to forget that you've ever seen it.

You can find a much more accurate and informative picture by googling for "Flamm's Paraboloid". But as I said, you'll wantbto be comfortable with the two-dimensional Minkowski spacetime diagrams first.