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I Why does physical space have to be three-dimensional?

  1. Jun 6, 2017 #1
    There's a question that's been in my mind for quite a while but I cannot figure out what the answer is. I't probably an ill posed question but I will ask it anyway:

    1.- Do we know what the dark-matter statistical distribution in our Universe is (at large scales)?

    2.- In case we do, could this distribution function be self-similar?

    3.- If it is, would not space be better described by a fractal?
     
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  3. Jun 6, 2017 #2

    Drakkith

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    The concept of dimension is actually quite complicated, but a simplified explanation is that a three-dimensional space means that there are three coordinates necessary to specify a point within that space. These coordinates are commonly labeled X, Y, and Z when talking about Cartesian Coordinates.

    Geometrically, a three-dimensional space has the property that you can have at most 3 lines of which each one is perpendicular to the other two.

    Approximately homogeneous at the largest scales, but at smaller scales there is significant inhomogeneity.

    No, because you're describing the distribution of dark matter within space, not of space itself.
     
  4. Jun 6, 2017 #3
    What's space itself? It is OK to state that energy-momentum defines the geometry of space-time but it's not OK to question yourself if it could define its topology?
     
    Last edited: Jun 6, 2017
  5. Jun 6, 2017 #4

    Drakkith

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    Perhaps I've misunderstood you. What do you mean when you ask if space could be described by a fractal?
     
  6. Jun 6, 2017 #5
    If I knew exactly what I mean I'd probable not need to ask anything at all but I'll try,

    (Almost) everyone thinks that the SM of particle physics is just a phenomenological low energy theory that breaks at a sufficiently high energies. I've been wondering for a time if something similar could happen with GR. It works fine in our solar system (where gravitational interactions are strong) and, probably, in our galaxy, where you clearly need 4 parameters to describe an event. However, galaxies and galaxy clusters and superclusters are not randomly distributed in space-time. Their distribution seems to fractal. Can we really make such a wild extrapolation from what we know to be locally true? After all the Lambda-CDM will not be satistactory until we find out what dark matter and energy are. Could it be that our Universe is, in terms of gravitation, locally 3-d and less that 3-d at a much larger scales?

    I am perfectly aware of how this sounds, but I cannot keep the idea out of my mind.
     
  7. Jun 6, 2017 #6
    How so?.
    Can you provide examples?
     
  8. Jun 6, 2017 #7
    So, is this the time when I start posting refererences and you kep telling that they are fringe theories and, therefore, not accepted in this forum? Because if it is, I think I'll pass.
     
  9. Jun 6, 2017 #8
    If they will tell you that your sources are not accepted on this forum, then you should give up with that sources, not with discussions... Rules concerning sources are the way they are for a reason. You can't you have a productive scientific discussion when you assume things about "reality" that are not necessarily true.
     
  10. Jun 6, 2017 #9

    PeterDonis

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    So are lots of other people--all of the physicists who are working on quantum gravity theories. There's plenty of literature available, not to mention plenty of threads here on PF.

    This has nothing to do with whether spacetime itself is really a classical 4-dimensional manifold, or whether that is only an approximation that breaks down at high energies. "High energies" here means very small distance scales--on the order of the Planck length, according to our best current guess. You are looking at the opposite extreme, very large distance scales. There is no reason whatever to suppose that our classical model of spacetime itself breaks down on those scales, and plenty of evidence that it doesn't (for one thing, our cosmological models of the universe would not make such good predictions about things like the relative abundance of light elements if their assumptions about classical 4-d spacetime were wrong). The fact that we don't have a very good understanding of why particular pieces of matter are distributed the way they are in space is a separate question.

    No. See above.

    Also, if you look at the literature on quantum gravity, you will find that the only proposals along the lines of the actual number of dimensions being different from 4 involve the number being larger, not smaller (as in the string theory models with 10 or 11 or 26 dimensions).

    That would depend on what references you post. But my sense from your posts so far is that you are not familiar with the current literature, so your best bet is probably to get familiar with it.
     
  11. Jun 6, 2017 #10
    This is really the kind of discussion I don't want to get involved in. I'm outta here.
     
  12. Jun 6, 2017 #11
    I don't know if your idea relates to a fringe theory or not, however "seems to fractal" isn't any kind of theory.
    I was asking for clarification of what it is that seems to be fractal in character.
     
  13. Jun 6, 2017 #12
    So you're not interested in science then. Sorry, but that's how it works.
     
  14. Jun 6, 2017 #13

    PeterDonis

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    Fine. Thread closed.
     
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