92

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?

Nat
  • 4,640
DonielF
  • 952
  • 3
    Perhaps this previous question I asked and the answer therein would provide a little illumination (the question is regarding the same paper): https://physics.stackexchange.com/q/428790/ – enumaris Sep 26 '18 at 22:56
  • 4
    For those too lazy to click, extra dimensions of size > 1 mile are ruled out, so ~40 orders of magnitude from string theory. – user126527 Sep 27 '18 at 08:25
  • 3
    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. :) – aroth Sep 27 '18 at 15:27
  • 2
    @aroth You misunderstand. I wasn’t asking how we know they don’t - I’m asking how this experiment explicitly disproves their existence. – DonielF Sep 27 '18 at 15:33
  • Another answer referring to the same paper: Why does only gravity leak into extra non-compact dimensions? – Rob Sep 27 '18 at 21:39
  • 1
    PBS Space Time made a video about the paper. – Lucas Trzesniewski Oct 03 '18 at 21:35
  • @LucasTrzesniewski Does the video say that the Randall-Sundrum model is ruled out? – SRS Oct 22 '18 at 12:53
  • The paper says ", we find that Randall-Sundrum II and DGP are poorly constrained by GW170817. In RandallSundrum II, the massless mode for the graviton is constrained to the 3D-brane; thus, energy cannot efficiently leak into extra non-compact dimension". – jinawee Oct 26 '18 at 19:01

3 Answers3

170

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)

kris
  • 1,116
  • 16
    welcome, kris!! – niels nielsen Sep 27 '18 at 03:30
  • 10
    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? – DonielF Sep 27 '18 at 03:39
  • 18
    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 ;) – kris Sep 27 '18 at 10:17
  • 17
    @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. – Acccumulation Sep 27 '18 at 16:39
  • @Acccumulation It's also self-evident that no experiment can say "We've proven that any two electrons are completely indistinguishable", and yet, apparently there were such experiments, so appeal to "obviousness" is a dubious argument. – Joker_vD Sep 27 '18 at 21:26
  • @Acccumulation My experience is that with science, the more formal and powerful of wording one seeks, the more exacting it has to be. It's very effective to communicate to laypeople that "There aren't higher dimensions," and, frankly, that's good enough for most. Push on that wording a little, as the OP did, and we have to back off to a more conservative "There aren't higher dimensions that gravity can leak into." Push harder, and we have to fall back on the very conservative "Here's the the precise conclusion we were able to draw from the data." – Cort Ammon Sep 28 '18 at 02:32
  • 1
    In my opinion, the strength of science is its willingness to limit itself to only what the data says, while being able to paraphrase it for those who need the 30 second version! – Cort Ammon Sep 28 '18 at 02:34
  • 18
    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. – Peter - Reinstate Monica Sep 28 '18 at 12:11
  • 1
    @Joker_vD First, I didn't appeal to obviousness. Simply noting that one finds something obvious is not appealing to that fact. Second, experiments have shown that a particular model of fermions is inconsistent with electron are being distinguishable. They haven't proven that electrons are indistinguishable. – Acccumulation Sep 28 '18 at 14:34
  • 1
    @CortAmmon It's not clear what you mean by "effective". Simplification of results often leads to completely false beliefs, such as "Quantum mechanics experiments have shown that the universe is non-deterministic". Making assumptions about the universe, and then making statements based specifically on those assumptions, is a dangerous thing to do. – Acccumulation Sep 28 '18 at 14:38
  • @Acccumulation Yes it is dangerous. And that is unavoidable. After all, we are communicating via language, and language has known limits. But we find it effective to communicate none the less. For example, most people know enough of quantum entanglement to understand that their simple model of the world breaks down when you push on it, even if they've never seen an integral sign before. We can contrast that with, say, abstract math. I find abstract math has a frustratingly difficult time forming accessible versions of their precise discoveries – Cort Ammon Sep 28 '18 at 15:54
36

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".

The_Sympathizer
  • 20,136
  • 5
    Mandatory PHD comics - http://phdcomics.com/comics/archive.php?comicid=1174. – Meni Rosenfeld Sep 28 '18 at 08:48
  • "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 – kevin Sep 28 '18 at 14:28
  • 1
    @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. – Luaan Oct 01 '18 at 06:56
-7

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.

kpv
  • 4,509
  • 29
    Reading the article might actually be helpful in this case... – Ilmari Karonen Sep 27 '18 at 19:37
  • 3
    @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. – kevin Sep 28 '18 at 14:18
  • @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.. – kpv Sep 28 '18 at 15:23
  • @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. – kpv Sep 28 '18 at 15:26
  • @kpv Not really, I think. The thing is, the idea that there is something such as "one berry" is an abstraction - in reality, you're just eating something berry-like, and you don't bother with thinking about "is this one berry the same size as that one berry, and did I eat one third of a berry or two thirds?". Even jumping to things like "I have 10 apples" is a huge jump in abstraction, it just seems trivial to us since we usually learn that kind of thing long before school (and sadly, forget that it's an abstraction, which leads to many seeming paradoxes schoolkids are plagued with). – Luaan Oct 01 '18 at 06:59
  • @Luaan: I do not agree. What you are talking about is our current formulation of numbers. People who never went to school, also knew the number game. Even animals - one lion runs away from three lions. understanding the concept and formulating it are two very different things. They at least know difference between one and many. Actually in group confrontation, animals can judge more complex numbers than one to many. – kpv Oct 01 '18 at 16:15
  • @kpv That's exactly my point - they don't. They don't consider that two plus one wolves is more than one wolf. They consider that there's this wolf stronger than they are, and it has support from two other wolves. "One wolf" is not a unit; "half a wolf" doesn't really mean anything. – Luaan Oct 01 '18 at 17:10
  • @Luaan: Wow! "2 other wolves" and they do not think about it? How do we know what they think? Fact is that they know the difference between higher number and lower number to some extent. This is that is a concept which even animals understand. How they think about - I can not say. 3>2 is formulation by humans which does not affect the physical concept. Obviously we can not use fractions about being live or dead, that is why I had taken example of eating. Cont.. – kpv Oct 01 '18 at 19:28
  • @Luaan: Physical concepts/phenomena are independent of mathematical formulation, which is used for quantification and sometimes provides additional solutions to a concept - NOT ADDITIONAL CONCEPTS. – kpv Oct 01 '18 at 19:29
  • @kpv If you want to use uppercase... YOU WERE TALKING ABOUT FRACTIONS. And yet all your examples of how I'm wrong are about natural numbers. Also, if you're talking about wolves, two can easily be more than three, and wolves are smart enough to know that. I don't see how that's so hard to understand. – Luaan Oct 02 '18 at 07:12
  • @Luaan: I was talking fractions but your initial comment was on whole numbers,so I was responding about whole numbers. Uppercase was just to emphasize the role of mathematical formulation, not to indicate anything about your comments, but I wish I could change the case, I can not in the comments. Coming back to topic, People have been dividing/exchanging/trading goods long before any schools existed. I do not think we are going to find additional spatial dimensions just because they are mathematically formulated to fit a specific theory. Inverse square law is good enough to prove that. – kpv Oct 02 '18 at 08:51
  • @kpv I'm sorry for triggering this whole discussion, my point was that what you said: "the inverse square law indicates there are only three spatial dimensions", is a fallacious argument. The law could be wrong, or incomplete. Using the current understanding of this law as an argument as to why there are no other spatial dimensions is circular reasoning. We only have this law because we don't know about any other dimensions. It's like saying a father has no more than two kids because he says he loves both his kids. Maybe he's just not aware or doesn't acknowledge the third. – kevin Oct 02 '18 at 09:27
  • 3
    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. – kevin Oct 02 '18 at 11:47
  • @kevin: Because the 180 degree triangle only considered 2 dims which was one less than the actual number of dims. So, same math in 3D turned incorrect. Third dim was always there, it was not discovered with the curved math. Only the curved space was discovered, which by the way, did not change number of dims. Equally wrong or imaginary, are be the laws that are formulated on more than actual number of dims. Inverse Square law is already formulated based upon real observations of correct number of spatial dims. – kpv Oct 02 '18 at 15:25
  • @kevin: Let us leave this discussion here as you are trying to stay open and safe and I have taken a stand, so we are not going to agree. – kpv Oct 02 '18 at 15:28