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What made the universe have 3 dimensions, instead of some other number?

  1. Sep 19, 2010 #1
    I think because the number 3 is still pretty low it isn't so suspicious to people, but imagine we lived in some universe with, say, 186 dimensions (that miraculously supported intelligent life, so there's someone to ask the question - I know about the anthropic principle). Wouldn't we have asked ourselves something like "Hey wait a minute, 186 seems pretty arbitrary, what's so special about this number that it should be the number of dimensions in our universe?".

    I know that string theory says there's 10 or 11 dimensions (or was it 26?), and space-time is really 4d not 3d, so let me generalize the question. What made the universe have the number of dimensions it happens to have, whatever this number happens to be?

    I'm wondering if maybe there was a dimension-making mechanism, like the Higgs mechanism is supposed to create mass.
     
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  3. Sep 19, 2010 #2
    Higher-dimensional spaces become unstable essentially, we aren't sure why but this is in the context of String Cosmology (http://en.wikipedia.org/wiki/String_cosmology) and String Gas Cosmology (http://arxiv.org/abs/0808.0746). String Gas Cosmology attempts to explain the compactification processes with regards to inflation/inflaton, dilaton field/dilatons, string gases, the string landscape and String Winding Modes. 26 dimensional String Theory is Bosonic String Theory (http://en.wikipedia.org/wiki/Bosonic_string_theory) and is used in String Cosmology models.
     
    Last edited by a moderator: Apr 25, 2017
  4. Sep 20, 2010 #3
    3 is a nice number because quaternions are still associative. So, perhaps, the answer is in the http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_%28normed_division_algebras%29" [Broken]. All the rest, like stability of matter, may well be its (hidden) consequence.
     
    Last edited by a moderator: May 4, 2017
  5. Sep 20, 2010 #4
    Thanks for the replies. Another question: Any idea why is the universe not zero-dimensional? Zero is just a more fundamental number than 3. I'm wondering if there could be a cause that's different than the anthropic principle.
     
  6. Sep 20, 2010 #5
    Perhaps because you should not divide by zero? By the way, perhaps it is zero-dimensional. But it feels like three-dimensional, and we like to have science that corresponds to our feelings. We are then motivated to develop it.
     
  7. Sep 20, 2010 #6
    I think it's fair to say that the beliefs about how many spatial dimensions the universe is composed of vary in the semi-mainstream from 2, to 10+. After all, while String Theory is still young, it posits a glut of extra spatial dimensions that we don't experience... which goes to arkajad's last post. The Holographic Principle goes for 2 embedded... so really , we don't know. It APPEARS that there are 3 spatial dimensions, and if there are more or less, it is yet to be demonstrated.

    I would just add, beyond the fact that dividing by 0 is a no-no... wouldn't a 0 dimensional universe... not exist, or at least, not in a manner that could allow ANY degrees of freedom that we observe?
     
  8. Sep 20, 2010 #7
    Dimensions per se do not exist, any more than miles, yards, inches etc.. They are communicable tools of concept that have been devised to allow us to better understand, and explain, our surroundings. Three appear to be adequate for this, whilst the passage of events, time, is regarded as the fourth.
     
  9. Sep 20, 2010 #8
    That's true for colloquial descriptions of dimensions, but in terms of Relativity, and String Theory they are in fact REAL things. If they were not, then gravity would also be merely a concept... that is not what we observe to be the case.
     
  10. Sep 21, 2010 #9
    So, do we assume that an the 3 dimensional space (+ 1 dimension for time) needs to be in-place before the Big Bang for the laws of physics to work - placed there by an Act of God? Or did the Big Bang itself create 3 dimensions + 1 time from (zero dimensional) nothing? I do the physical laws predict that the known Universe can be created starting from a zero-dimensional universe?

    Could you please elaborate. I couldn't find much about zero-dimensional spaces, but there is one article in http://en.wikipedia.org/wiki/Zero-dimensional_space" [Broken] about zero-dimensional spaces but it doesn't mention about that problem. I was wondering if the equations for General Relativity can be adapted to work for any number of dimensions, and what would happen if you tried with 0, but I really don't have the knowledge to try it or even know if I'm talking sense.

    Stephen Hawking in his book 'The Grand Design' says that the universe came from Nothing - did he mean a 3-dimensional Nothing or a 0-dimensional Nothing? I hope that his book wouldn't be just metaphysics but maybe has some mathematics in it.
     
    Last edited by a moderator: May 4, 2017
  11. Sep 21, 2010 #10

    apeiron

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    I agree with those like Baez who feel that the normed division algebras tell us something important about self-consistent dimensionality, but quaternions don't seem a good explanation of 3D, or even 4D. Why stop at 4 when 2 and even 1 dimensional algebra is even more regular in its behaviour? It would seem more likely that by this argument we should make more of the absence of trionions.

    But perhaps you have some specific argument or reference in mind here? As I say, it does seem the right way to start thinking about the reasons why dimensionality is so low. This was Baez's essential point. Algebra could have an infinity of dimensions, but it only starts to produce self-reinforcing patterns as dimensionality becomes strongly constrained.
     
    Last edited by a moderator: May 4, 2017
  12. Sep 21, 2010 #11

    Drakkith

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    I believe that someone rolled the dice and ended up with a 2 and a 1.

    But really, your question is pretty difficult to answer. We live in a 3d universe because it happens to be 3d for whatever reasons. Where did it come from? NO ONE KNOWS!!!
     
  13. Sep 21, 2010 #12
    Grrr... Einstein no like, EINSTEIN SMASH! :wink:


    Your last point seems to be the most convincing however unsatisfying it may be, especially if some form of MWI holds; it's 3D because we wouldn't be here if it were not... elsewhere it's more or less, but we're not there to observe it.
     
  14. Sep 21, 2010 #13
    Maybe because there is a cross product in 3D. In higher dimensions you can't form a cross product that takes vectors to vectors - you have to take vectors to bivectors (or whatever they are called).

    without a cross product (e.g. in 4D or 5D) how will you build a bicycle!
     
  15. Sep 21, 2010 #14
    You can do it in 7D - using octonions.
     
  16. Sep 21, 2010 #15
    You can rule out some configurations just by the anthropic principle. <2 dimensional beings would have a hard time pondering the nature of the universe. Even 2 dimensional animals couldn't have traditional digestive systems (as any path through them would split them in half). In other configurations, the relationship between forces is probably such that life as we know it couldn't form (for example if there were many more dimensions and gravity were significantly weaker, we might not get star birth).
     
  17. Sep 21, 2010 #16

    apeiron

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    This is the key I believe as well. 3D is the simplest possible arrangement of degrees of freedom, if degrees of freedom need to be shaped by a measuring context.

    It is like the way in network theory, all more complex networks (with many edges meeting) reduce to just networks of three edges.

    You can take two positions: either the number of dimensions is arbitrary, any number being possible, or the number of dimensions is constrained for some reason.

    If the number is random and all arrangements probably exist "somewhere", then we indeed have only an anthropic explanation for why we find ourselves in a 3-space.

    But if instead dimensionality is subject to the principle of constraint, then it seems only logical that one solution, one arrangement, can count as the "most constrained" - the lowest possible dimensional minima.

    Given we exist in an incredibly low-D realm (just 3 when there could have been any number up to infinity?) should suggest that the second view is the more likely.

    And least action has touched on exactly the reason why the minima would be 3-space and no lower. The least amount of context needed to measure/constrain the least amount of event is 2D to measure/constrain 1D.

    If you just take dimensionality to exist, then there is no reason to take this view. But if you see crisp degrees of freedom arising by way of contexts that constrain, then 3D has obvious unique properties.

    Time then arises as "fourth dimension" in this approach as unfinished business. Constraint being an active process implies a gradient. To create a flat 3-space "everywhere", it has to expand. Which takes time.
     
  18. Sep 21, 2010 #17
    This is a good argument for experiencing only 3 spatial and one temporal dimension, and for having no less than 3+1... but does nothing for the existence of extra dimensions we don't experience as with String Theory or the like. Would you agree, or am I missing your point?
     
  19. Sep 21, 2010 #18

    Chronos

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    I'm sympathetic with Peter Watkins. No observations to date suggest the need for more than 3+1 dimensions to adequately describe its position in space-time - at least so far as the macroscopic [GR] universe is concerned. String theory is the main driver in the search for extra dimensions, and the LHC is currently testing this proposition. It is worth noting the 'universe' may have been dimensionless prior to the big bang.
     
  20. Sep 21, 2010 #19
    I'm personally not a fan of String Theory, but I felt the need to mention it in this context, I am by no means trying to promote it.
     
  21. Sep 21, 2010 #20

    apeiron

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    No, that is a sharp question. And indeed, six compactified dimensions would be a prediction of a constraints-based logic.

    If you are interested in a fuller explanation, perhaps PM me.
     
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