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I recently read this article which claims that last year’s LIGO observation of gravitational waves is proof that, at least on massive scales, there cannot be more than three spatial dimensions.

I don’t understand the physics fully, so could someone please explain this to me? I know it’s been theorized that gravity is relatively weak when compared to other forces because it leeches into other dimensions, and I think I understand how these observations disprove that, but how does this prove that there must be three and only three spatial dimensions?

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    $\begingroup$ Perhaps this previous question I asked and the answer therein would provide a little illumination (the question is regarding the same paper): physics.stackexchange.com/q/428790 $\endgroup$ – enumaris Sep 26 '18 at 22:56
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    $\begingroup$ For those too lazy to click, extra dimensions of size > 1 mile are ruled out, so ~40 orders of magnitude from string theory. $\endgroup$ – JollyJoker Sep 27 '18 at 8:25
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    $\begingroup$ Wouldn't the default hypothesis be that higher dimensions are presumed to not exist unless/until there's evidence suggesting otherwise? Having to explicitly prove the non-existence of every thing that's imaginable but not actually real seems...quite tedious. :) $\endgroup$ – aroth Sep 27 '18 at 15:27
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    $\begingroup$ @aroth You misunderstand. I wasn’t asking how we know they don’t - I’m asking how this experiment explicitly disproves their existence. $\endgroup$ – DonielF Sep 27 '18 at 15:33
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    $\begingroup$ PBS Space Time made a video about the paper. $\endgroup$ – Lucas Trzesniewski Oct 3 '18 at 21:35
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I’m the lead author of the paper. Thanks for being interested in the work! Your question is a good one. Really, our work can’t say anything about extra spatial dimensions if they’re not doing anything to gravity or light. As you correctly mention, we can only constrain higher dimensions where gravity is actually leaking into them.

If there are higher dimensions, but our physics experiments can’t see or hear them, are they really there? :p (this isn’t to say there might not be other ways of detecting extra spatial dimensions — but really, if they aren’t affecting physics in any measurable way, there’s not much we can say)

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    $\begingroup$ welcome, kris!! $\endgroup$ – niels nielsen Sep 27 '18 at 3:30
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    $\begingroup$ So, if I’m reading this correctly, you’re saying that what I said in the OP is correct, that you can’t disprove higher dimensions, just that you ruled out gravity as being a way to determine their existence? $\endgroup$ – DonielF Sep 27 '18 at 3:39
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    $\begingroup$ Yeah, I wouldn’t quite word it that way though: it could be that we could use gravity in some other way to rule out extra dimensions (for example, some theories affect gravity in some frequency dependent way — so they would affect higher frequency gravitational waves differently than lower ones). We can’t rule those out. We can really only rule out extra dimensions where they would damp gravitational waves at this frequency. I think @The_Sympathizer had the right idea with their comment ;) $\endgroup$ – kris Sep 27 '18 at 10:17
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    $\begingroup$ @DanielF It seems self-evident to me that no experiment can say "We've proven that extra dimensions are impossible"; at most, it can say "We've shown that models with such-and-such characteristics are inconsistent with the data". That is, the experiment could contradict certain classes of models of extra dimensions, but they can't rule out extra dimensions in total. $\endgroup$ – Acccumulation Sep 27 '18 at 16:39
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    $\begingroup$ I love it that you ask a question on StackExchange and the author of the paper answers you. Thank you for taking time for this. $\endgroup$ – Peter A. Schneider Sep 28 '18 at 12:11
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It doesn't disprove all possibilities for higher dimensions - technically, you can't really disprove something so broad because there's always another way to phrase it that will put it out of reach of existing experimental data. This is a common theme with science, and thus why that scientific claims and hypotheses have to be specific and stated precisely.

What it does do is, as you've surmised, disprove the idea, or at least the idea specifically tested, that gravity "leaks" into higher dimensions as a specific explanation for why it is so weak. This is in turn posited by some conceptions of string theory, but not all.

I suspect the reason you are thinking that it somehow disproves higher dimensions generally and thus are confused when you see that it actually doesn't, is because of bad media. The media is not being anywhere close to as precise with these claims as a scientist would or should be, and is touting it as having "disproved higher dimensions", not "disproved a particular gravitational theory that says gravity weakens through leakage into higher-dimensional spaces".

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    $\begingroup$ Mandatory PHD comics - phdcomics.com/comics/archive.php?comicid=1174. $\endgroup$ – Meni Rosenfeld Sep 28 '18 at 8:48
  • $\begingroup$ "you can't really disprove something so broad". Exactly, if you're a 1d being you can only observe in a single direction. If you're a 2d being you can observe in a plane, but not up/down. If you're a 3d being you can observe 3d space, but following this logic you're not able to observe an extra axis. So if higher spatial dimensions exist, we would never be able to directly observe them since we're 3d ourselves. We have to carefully read into measurements that might indicate their existence, drawing conclusions from this is iffy at best. Conclusive evidence to the contrary is even harder to get $\endgroup$ – kevin Sep 28 '18 at 14:28
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    $\begingroup$ @kevin Well, if spacetime was significantly non-homogeneous in some extra dimension, we would notice it. Just like a 1D being in warped space would notice that e.g. they can get back to where they started by walking forward. "We can't see it with our bare eyes" isn't enough to stop us :P What would be a lot worse would be if those extra dimensions weren't available to the interactions we use to observe the universe (electromagnetism etc.) - that's one of the reasons gravity is so attractive - in GR, it should show effects of interactions that we can't interact with in any other way. $\endgroup$ – Luaan Oct 1 '18 at 6:56
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I did not read the article and can not comment about it.

But as a common sense, the inverse square law indicates there are only three spatial dimensions. If there were more, then we would have say inverse cube law of gravity as an example.

Inverse square law applies to most spatial phenomena like EM forces, gravity, light density etc. pretty much nailing down number of spatial dimensions to 3.

It is said that the additional dimensions are small, and curled. Even if that was true, they still curl in 3D space and would not really be additional spatial dimensions.

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    $\begingroup$ Reading the article might actually be helpful in this case... $\endgroup$ – Ilmari Karonen Sep 27 '18 at 19:37
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    $\begingroup$ @kpv we also used to say number line and mean only positive, whole numbers. Then we added 0, the negatives, fractions and complex numbers. Just because existing formula's haven't been proven wrong or incomplete yet doesn't mean they aren't. $\endgroup$ – kevin Sep 28 '18 at 14:18
  • $\begingroup$ @kevin: Concept of fraction has always existed. For example, when we ate anything (bigger than berries), we ate it fraction by fraction. It is just the mathematics that we came to understand and formulate at a later time. Negative is also a representation of positive on other side of the zero. The concept existed as long as we have been exchanging things and we formulated the math later. Similar arguments can be said of complex numbers. Cont.. $\endgroup$ – kpv Sep 28 '18 at 15:23
  • $\begingroup$ @kevin: What is happening here (higher dims) is - we are formulating mathematics first and then wishing that the solution will pertain to reality. It is just opposite of the examples you provided. Concept followed by math VS Math turned out to be real concept. Sometimes math can give you additional real solutions but sometimes they are not real. I would be hopeful, but not adamant about such solutions. In case of higher dims, I am not even hopeful. $\endgroup$ – kpv Sep 28 '18 at 15:26
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    $\begingroup$ There are many "laws" like the inverse square law that we have relied upon in the past, but which turned out to be incorrect, inaccurate or incomplete. Euclidian math is a very good example here, we used to say that the angles of a triangle always add up to 180, but guess what makes this statement false? Another spatial dimension. Anything related to either quantum mechanics or celestial body physics is also throwing a lot of existing "laws" out of the window. Most of our laws of nature really only apply to a certain subset of our observations. $\endgroup$ – kevin Oct 2 '18 at 11:47

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