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Is there any physics theory that depicts our universe as $2+1$ dimensional?

I heard that black holes seem to suggest that the world might be $2+1$ dimensional, so I am curious whether such theory exists?

Just for curiosity.

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Any chance you're thinking of the holographic principle? –  David Z Mar 19 '12 at 5:47
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Note to OP: $2+1\neq 3$. Qmechanic has edited that in to signify that you mean 2 space dimensions and 1 time dimension. –  Manishearth Mar 19 '12 at 9:03

2 Answers 2

You've probably come across the holographic principle: see http://en.wikipedia.org/wiki/Holographic_principle for details.

The idea is that because the entropy of a black hole is proportional to the area of the event horizon, this means all the information about the black hole is present on the event horizon, and this has dimension 2+1D. However I don't think this should be taken to mean that our universe is 2+1 dimensional.

Having said that, there are ideas from the more fringe areas of physics that at a very small scale/high energy the universe may be 1+1 dimensional. For example causal dynamical triangulation (http://en.wikipedia.org/wiki/Causal_dynamical_triangulation) seems to show 2D behaviour at very small scales.

There is an idea from string theory called the AdS/CFT correspondence (http://en.wikipedia.org/wiki/AdS/CFT_correspondence) that physics in an n dimensional gravity theory can be encoded by a n-1 dimensional bounding surface. However this doesn't mean our world is 2+1D, but rather that our physics can be represented by a theory in 4+1D.

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I personally haven't heard of one, but then again I haven't heard much.

First thing, are you sure that it's two you want? Or four? Because by relativity et al, our universe is 4D. Go into string theory, it becomes 10/11/26 D.

I think you may have misinterpreted the rubber-sheet explanation of gravity in general relativity as a theory. The 2D rubber sheet is only a way for us to imagine gravity acting, since it bends space. We can easily imagine a 2D sheet bending into the third dimension, as we live in a 3D world (3 macroscopic spatial dimensions, ti be exact). What's actually happening; a 3D bit of space bending into the fourth dimension, is not that easy to imagine. Possibly impossible to imagine. So the 2D-rubber-sheet-and-rock is just a visual aid.

On a side note, the reason I doubt that there is any such theory is this:

  • We percieve 3 spatial dimensions, so there are atleast 3.
  • Electric/magnetic fields vary inversly to square of distance, which indicates ap3 macroscopic spatial dimensions. This is because they are mediated by EM waves, and intensity is proportional to $r^{1-N}$ for $N$ dimensions. Then again, if our universe was 2D I guess the nature if EM waves could be different.
  • We have 3 translational degrees of freedom in thermodynamics.
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