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Thread: Limits on the number of spacetime dimensions

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    Limits on the number of spacetime dimensions

    This paper constrains the number of spacetime dimensions to, essentially, 3+1, with a pretty small margin of error, using the detection of the gravitational wave GW170817 along with its electromagnetic counterpart. Clever!


    The observation of GW170817 in both gravitational and electromagnetic waves provides a number of unique tests of general relativity. Certain modifications of gravity involve the presence of additional spacetime dimensions. In these models, as the gravitational waves propagate they "leak" into the extra dimensions, leading to a reduction in the amplitude of the observed gravitational waves, and a commensurate systematic error in the inferred distance to the gravitational wave source. Electromagnetic waves would remain unaffected. We compare the inferred distance to GW170817 from the observation of gravitational waves.... with the inferred distance to the electromagnetic counterpart....
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    3 and 1

    Excellent. Thank you, Cougar ..

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    I like this result, because 3+1 is a lot easier to visualize than higher dimensions, but I'd like to point out that this is based on one (very meaningful) observation, and that in the near future there will be longer observing runs with more GW detectors. VIRGO & ALIGO (Hanford) will both be upgraded to match the one in Louisiana, and the one in India will come online... so in a few years several of these events per year will be observed and we'll have a better statistical sample. Another point is that the paper made some assumptions about leakage of gravitational wave energy into other dimensions, and I'm not sure that would apply to the tightly wound dimensions that models like String Theory need to explain fields and particles. ... so yes, 3+1 macroscopic dimensions. Yay for simplicity!
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    Quote Originally Posted by antoniseb View Post
    ....Another point is that the paper made some assumptions about leakage of gravitational wave energy into other dimensions, and I'm not sure that would apply to the tightly wound dimensions that models like String Theory need to explain fields and particles....
    Right. The "leakage" assumption seems to speak to a particular conjecture. Leakage was also speculated to explain the appearance of the acceleration of the expansion, claiming then that no "dark energy" was needed. Well... dark energy is still in the game!
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    What would a universe with 3+2 dimensions (three space, two time) be like? Many-Worlds, perhaps?

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    Does this invalidate the many (10+) dimensionality needed by some variants of string theory?

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    Quote Originally Posted by swampyankee View Post
    Does this invalidate the many (10+) dimensionality needed by some variants of string theory?
    I'm surely no expert, but I think it's more a problem for the braneworld model of Dvali, Gabadadze, and Porrati (DGP), which proposes that gravity is modified at large distances by the arrested leakage of gravitons off our four-dimensional universe.
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    Quote Originally Posted by swampyankee View Post
    Does this invalidate the many (10+) dimensionality needed by some variants of string theory?
    No - first off the critical dimensionality of the theory doesn't distinguish extended and compact dimensions. Secondly the initial versions of String Theory had all the dimensions other than the 3+1 we see compactified. (there are energetic reasons why that was the case). What it may rule out is some of the brane cosmologies that have worldsheets floating the bulk and interacting gravitationally.

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    Quote Originally Posted by Tom Mazanec View Post
    What would a universe with 3+2 dimensions (three space, two time) be like? Many-Worlds, perhaps?
    Weirder. For many of the equations we use to describe the universe, there's no way to generalize them to having two time dimensions and still have consistent solutions.
    Conserve energy. Commute with the Hamiltonian.

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    Quote Originally Posted by Grey View Post
    Weirder. For many of the equations we use to describe the universe, there's no way to generalize them to having two time dimensions and still have consistent solutions.
    Greg Egan tried doing the math for a 2+2 universe, and that was quite weird. Iím thinking 3+2 would be very weird, indeed.

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    Quote Originally Posted by swampyankee View Post
    Greg Egan tried doing the math for a 2+2 universe, and that was quite weird. I’m thinking 3+2 would be very weird, indeed.
    Itzhak Bars has a number of two-time-dimension papers on arxiv if people are interested. He mostly works with more than 3D space though.

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    Quote Originally Posted by swampyankee View Post
    Greg Egan tried doing the math for a 2+2 universe, and that was quite weird. I’m thinking 3+2 would be very weird, indeed.
    If you're thinking about Orthogonal, that's not quite it. He's really imagining a "4 + 0" universe, where instead of our Lorentzian geometry, where a time dimension is clearly distinct from a space dimension (you and I might disagree about which way is left and which way is forward, depending on how we're facing, but we'll both agree that neither of those directions could be the past) he has a universe of Riemannian geometry, where all of them are on equal footing. So it's possible that, depending on the motion of different observers, one observer might call a direction "east" while a different observer might call that direction "the future". And he tries to explore the possible ramifications of such a universe. It's an interesting idea.
    Conserve energy. Commute with the Hamiltonian.

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    Quote Originally Posted by Grey View Post
    If you're thinking about Orthogonal, that's not quite it. He's really imagining a "4 + 0" universe, where instead of our Lorentzian geometry, where a time dimension is clearly distinct from a space dimension (you and I might disagree about which way is left and which way is forward, depending on how we're facing, but we'll both agree that neither of those directions could be the past) he has a universe of Riemannian geometry, where all of them are on equal footing. So it's possible that, depending on the motion of different observers, one observer might call a direction "east" while a different observer might call that direction "the future". And he tries to explore the possible ramifications of such a universe. It's an interesting idea.
    No, Dichronauts. See http://www.gregegan.net/DICHRONAUTS/00/DPDM.html In it, is invariant, vs
    Last edited by swampyankee; 2018-Jan-31 at 11:04 PM.

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    Quote Originally Posted by swampyankee View Post
    Cool; I hadn't seen that one. Hmm, now he needs to write a story in 1 + 3; I'm pretty sure that 0 + 4 would be functionally equivalent to 4 + 0.
    Conserve energy. Commute with the Hamiltonian.

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