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RandyD123
2011-May-07, 10:29 PM
Most pictures of the Sun or Black Holes show them as if they were on a sheet of rubber and have a gravity well below them. But there has to be more to it than that as those are only 2 dimensional views. Is there anywhere we can really see how a body in space warps graivity?

Jeff Root
2011-May-08, 05:28 PM
The "warping" is toward the time direction, which of course
isn't visible. diagrams and models use one direction of space
to represent the time direction. That is very typical of graphs:
one or two dimensions of space are used to represent some
dimension that isn't visible, such as temperature or energy.
Of course, it is also very typical for a graph to have time as
one of its dimensions: A graph of distance traveled each day
on a trip, or a graph of the total distance traveled as the trip
progresses, each have time as one dimension.

Obviously a two-dimensional graph is easier to draw on a
two-dimensional sheet of paper than a three-dimensional graph,
which needs to be shown in some kind of perspective view.
A distorted rubber sheet is a three-dimensional graph. When
depicted on paper or a computer monitor, you are looking at a
two-dimensional representation of a three-dimensional object.

What you want is a representation of a four-dimensional object.
That can be done, but just like representing a three-dimensional
object on a flat two-dimensional sheet means making artistic
compromises, representing a four-dimensional object means
further compromises. Typically it means replacing a still image
with a movie. The movie will show the four-dimensional object
from a single viewpoint, or a limited range of viewpoints.

A 3-D holographic view or computer-interactive view generated
in real time allows the viewer to select any viewpoint. I'd like
to see something like that. I'd bet it already exists.

Ironically, similar to how the rubber sheet model uses gravity
to represent gravity, a movie or interactive program uses time
to replace dimensions of space, when one of those dimensions
of space is representing time!

But how to show a three-dimensional object "warped" in a
fourth dimension is something that has puzzled a lot of people
for a long time. If it could be done, it would be.

-- Jeff, in Minneapolis

caveman1917
2011-May-08, 05:55 PM
But how to show a three-dimensional object "warped" in a
fourth dimension is something that has puzzled a lot of people
for a long time. If it could be done, it would be.

It's even worse than that, it's a 4dimensional warped object. If you want to embed it to show it you're going to need five dimensions :s.
That's why we usually reduce it to a 1space+1time object, from which the curvature can be embedded in a 3d space, those are the "gravity well" pictures you see all around. And actually it isn't so bad, usually there are some symmetries involved, for example a non-rotating black hole has spherical symmetry, so a 1radial space + 1time graph is showing most of what really happens.