Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B What would a universe with two time dimensions be like?

  1. Jun 15, 2016 #1
    Just what would a universe be like if it had two time dimensions?
     
  2. jcsd
  3. Jun 15, 2016 #2

    Paul Colby

    User Avatar
    Gold Member

    How would you generalize equations of motion? What would the action principle look like?
     
  4. Jun 15, 2016 #3

    OmCheeto

    User Avatar
    Gold Member
    2016 Award

    hmmm....
    I've heard about something called "spooky at a distance".
    I do not understand it at all, but from what I've heard, it seems to violate "my" notion of our one dimension of time.
    Perhaps we already have two time dimensions.

    hmmmm.... Perhaps this thread belongs in the sci-fi section.
     
  5. Jun 16, 2016 #4
    The idea of two time directions is sometimes used in string theory/supergravity.
    A paper by Itzhak Bars http://de.arxiv.org/abs/hep-th/9809034
    And more recent results can be found at INSPIRE

    I'm not sure how interesting it is but it does exist (in 12 dimensions or more)
     
  6. Jun 17, 2016 #5

    arivero

    User Avatar
    Gold Member

    For the sake of discussion, I would like to see how it works with two macroscopic time dimensions and flat space, with minkowsky product coming from the matrix diag(1,1,1,-1,-1).
     
  7. Jun 17, 2016 #6
    I have absolutely no idea, I encountered a mention of it in a master thesis (and some articles I believe).
    Maybe some day I'll find the time to check it out.
     
  8. Jun 17, 2016 #7

    fresh_42

    Staff: Mentor

    Where's the problem is a macroscopic diag(1,1,1,-1,-1) world?
     
  9. Jun 17, 2016 #8
    Nothing from a mathematical point of view, I figure the physics would look quite different.

    A guess would be that consistency of dimensional reductions can do some weird things.
    I'm only a little aware of the consistency of those procedures so I have to look into it on Monday since the document that might give me a hint whether more time directions mess things up is in my dorm room.
     
  10. Jun 17, 2016 #9

    arivero

    User Avatar
    Gold Member

    For a classical non-relativistic particle, it seems that instead of conditions in two extremes [a,b] in the time-line we should impose them in a circle of the time-"plane".
     
  11. Jun 17, 2016 #10

    fresh_42

    Staff: Mentor

    Even if we get the geometry somehow explained, what about entropy?
     
  12. Jun 18, 2016 #11
    From a purely mathematical point of view, having an additional time dimension would fundamentally change the form of the general wave equation, turning it into what I believe is called an "ultra-hyperbolic equation" ( correct me on this if I'm wrong ). The question then becomes how the solutions to this equation behave under a given set of initial values - for example, in a theory of electromagnetism in (3+2) dimensions, do we still get a nice, well behaved wave solution, or do we get something that evolves chaotically ? Or worse still, would we be faced with a situation where no general solution even exists ?

    I am not qualified to answer any of this ( not having studied this type of PDE ), but I would also be interested to hear what the mathematicians here have to say on this. My intuition tells me that things won't work out nicely if you add an extra ( macroscopic ) time dimension, but I may well be wrong. And then of course there is the option of having the extra dimension compactified.
     
  13. Jun 18, 2016 #12

    Fervent Freyja

    User Avatar
    Gold Member

    Two different universes.
     
  14. Jun 18, 2016 #13
    Well, for one you'd have trivially easily occurring closed timelike curves.
     
  15. Jun 20, 2016 #14

    Demystifier

    User Avatar
    Science Advisor

    The Cauchy problem is not well posed for such spacetime signatures. See e.g.
    http://arxiv.org/abs/gr-qc/9702052
    http://arxiv.org/abs/gr-qc/9901045
     
  16. Jun 20, 2016 #15
  17. Jun 20, 2016 #16

    arivero

    User Avatar
    Gold Member

    We could try some list of priviledged D = d + t combinations. To start with, let me note the classical signatures to have susy and other stuff related to division algebras:
    R: d - t = 1
    C: d - t = 2 This is our spacetime, 3-1=2
    H: d - t = 4
    O: d - t = 8. I think this is the 9-1 = 8 of string theory and perhaps the 10 - 2 mentioned by JorisL above
    I am not sure if there is some mod8 periodicity here or the list just stops at 8.
     
  18. Jun 22, 2016 #17
  19. Jun 23, 2016 #18
    For the more interested in 2 k, 4 n as 6 dimensional model you should look at Itzhak Bars work. He has interesting stringy ideas. Gravitational constant looks normal for observer but is a "shadow" of a dilaton field. He worked on many examples with many interpretations and seems to get a consistent framework for a working theory.
    Here one impressing work as you see the mathematical beauty in it.
    http://arxiv.org/abs/0804.1585
     
  20. Jun 23, 2016 #19

    haushofer

    User Avatar
    Science Advisor

    Isn't that related to the fact that AdS-space can be described as being embedded in Minkowski spacetime with two timelike directions? (the AdS group is SO(D-2,2) )
     
  21. Jun 24, 2016 #20
    Seems like a good starting point to look at.
    Maybe if I can find some time in the next couple of weeks I'll look into it.

    This seems like the idea that underlies the arxiv-notes I linked.
    I'm not well-versed in the terminology of a "target space" so I'm not sure this would lead to the AdS group?
    Neither what ##d## means in this context, from the abstract it follows that ##D## is the number of spacetime dimensions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: What would a universe with two time dimensions be like?
  1. Time dimension (Replies: 4)

  2. Dimensions and time (Replies: 30)

Loading...