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Impossibility of having less than 3 dimensions?

  1. Apr 5, 2014 #1
    I have heard of Flatland and seen many analogies regarding a 2 dimensional world but, can such exist? Considering that even subatomic particles move in 3 dimensions then am I to assume that a 2 dimensional world is an impossibility? Even a line is 3 dimensional for if a line were only 1 subatomic particle thick it still would be 3 dimensional.

    Furthermore; can 3 dimensions exist without Time?
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  3. Apr 5, 2014 #2


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    The physical laws of our universe require at least three spatial and one temporal dimension.

    Mathematical systems can use any number of dimensions, but that does not mean that they correspond to the physical world.

    Speculating about other "possible worlds" is not science.
  4. Apr 6, 2014 #3


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    Oh come on, why are there so many scientists talking about many worlds theory then? Also, there is something two dimensional about the information content of the universe. The holographic principle says that the information in a volume of space is somehow encoded on the 2D surface surrounding it. It isn't really all figured out yet, and it's kind of a wacky idea, but I think there must be at least some truth to it.
  5. Apr 6, 2014 #4


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    It's not a theory, it's an interpretation of Quantum Mechanics, which is an actual theory.
  6. Apr 6, 2014 #5


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    Are you asking why we live in a universe whose laws require at least three spatial and one temporal dimension? No one knows why, but it clearly is that way because we can observe and count that many dimensions.

    Or are you asking why the physical laws require at least three spatial and one temporal dimension to work properly? Well, if they didn't include at least that many, they wouldn't accurately describe the universe we live in, so they would more or less by definition not be working properly.

    We maybe could have more dimensions than that - there's an interesting sidebar in Hartle's GR text about how we could incorporate a few more dimensions into our physical laws and what that would mean for the metric structure of spacetime.
  7. Apr 6, 2014 #6


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    Please note that the density of states of free electrons look VERY different when they are confined to 1D and 2D and when they are in 3D space. In fact, in 2D and 1D situations, you can have exotic properties of conduction electrons, such as spin-charge separation (Luttinger liquid), fractional quantum effects, etc.

    So yes, we do know what some things will behave when they are confined to lower dimensions, and the fact that we do see properties that are very different than 1D and 2D properties, AND the fact that we can theoretically describe those in 3D, are very strong evidence that we live in an extended 3D spatial universe.

    This, however, does not negate the possibility of higher, compacted dimensions that have yet to be discovered and verified.

  8. Apr 6, 2014 #7


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    The encoding is only approximate so a 3D-2D mapping is incomplete afaik.
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