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Someone asked about proof of higher dimensions. But discounting time as a dimension, along with the hyper-dimensional GUTs/Supersymmetry theories, has this possibility been tested and what did the results suggest?

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    $\begingroup$ Test in collider context put limits on the size of compact extra dimension. $\endgroup$ – dmckee --- ex-moderator kitten Jul 7 '16 at 0:46
  • $\begingroup$ It is being tested extensively and all tests, so far, have come up empty. For my taste the most obvious ones, for now, are the searches for non-Newtonian gravity. See e.g. the work of npl.washington.edu/eotwash/sr, but there are other groups trying similar experiments. $\endgroup$ – CuriousOne Jul 7 '16 at 1:01
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    $\begingroup$ What counts as evidence? My computer works, which is evidence of electromagnetism, which is consistent with the predictions of Kaluza-Klein theories. If "evidence" is an observation consistent with the predictions of a theory, this counts. If you have a more restrictive definition of evidence, then it's hard to answer your question without knowing what that definition is. $\endgroup$ – WillO Jul 7 '16 at 2:54
  • $\begingroup$ WillO, I am talking about experimental data that is consistent with predictions of a theory. Particularly a theory that there is an Orthogonal Universe that impinges on the one we can observe. $\endgroup$ – Mr X Jul 8 '16 at 5:20
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The reason the whole idea of 11 spacetime dimensions came about is because the equations of string theory without these extra dimensions have "quantum anomalies"...namely, the creation and destruction of energy, which is obviously kind of a problem. But, with 11 spacetime dimensions...voila! Problem solved.

Then, of course, people were like, "but why don't we experience these extra dimensions?" And string theory physicists responded with the Kaluza-Klein idea...in a nutshell, they're curled up so small we can't see them. Which is kind of hard to picture$^1$, but it explained it.

So, then, what would constitute as experimental evidence of these extra dimensions? There are three things that would provide evidence (according to Brian Greene's book The Hidden Reality, page 94-95):

  1. Gravity: Basically, because space is the medium for gravity, more dimensions provide more space for gravity to spread through. The idea is that the strength of gravity becomes diluted as it spreads through the additional dimensions (this offers an explanation of why gravity is so weak). If we could measure gravity's strength over distances smaller than the extra dimensions, we should find it's strength to be stronger. The problem? Measurements on scales as short as a micron haven't found any deviation.
  2. Missing Energy: If the extra dimensions exist and are much smaller than a micron, they will be "inaccessible to experiments that directly measure gravity's strength." The LHC provides another route, namely looking at collisions between speedy protons and the debris left behind. Why? The debris could be squeezed into one of the tiny dimensions, thereby carrying away energy, which would be recorded.
  3. Mini Black Holes: Anything can become a black hole if compressed sufficiently. So, if there's extra dimensions that result in gravity being stronger when acting over short distances it should be easier to create baby black holes (i.e., two protons slammed together with enough force might be able to create a tiny black hole) which would then disintegrate into particles that could be recorded.

Again, it should be noted that none of this has been found, though scientists are looking for it.

Hope this helps!

$^1$It might be easier to picture this idea if you think of a really, really, really tall straw (taller than the Empire State Building). Up close, you can see it has all three dimensions, right? But from a distance, it just looks one dimensional. Now imagine that straw was smaller in diameter than an atom's nucleus...

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  • $\begingroup$ One can argue, though, that it doesn't take string theory to have compact hidden dimensions, or, to use a string theorist stereotype about super-symmetry "We take it, if it's there, but we don't need it, if it isn't.". $\endgroup$ – CuriousOne Jul 7 '16 at 1:15
  • $\begingroup$ Sure, but the same possible experiments still apply. In this case, these experiments would provide good evidence for multiple dimensions in or out of the string theory context. I was merely providing the string theory framework to explain why the idea was brought back into the mainstream, so to speak. $\endgroup$ – heather Jul 7 '16 at 1:43
  • $\begingroup$ @MrX, is this answer acceptable to you, or is there something I didn't address? $\endgroup$ – heather Jul 8 '16 at 20:35
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In principle this could be tested in the near future, but it could be perhaps a million years ahead. The problems is that these dimensions seem to be rolled very tight, with dimensions much smaller than an atomic nucleus. However there is another twist in the opposite direction: Holographic principle. The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region, that is a two-dimensional surface. This theory has not yet been proved to be correct, but if it happens to be correct, we could say that we actually live in two dimensions, rather than 3, and that the 3rd dimension is only an illusion of our senses.

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    $\begingroup$ Out of curiosity, how do we eat then? Wouldn't food just split us in half? (In terms of the Holographic principle.) $\endgroup$ – heather Jul 7 '16 at 0:59
  • $\begingroup$ @heather you do not seem to understand the equivalence between formal systems $\endgroup$ – Wolphram jonny Jul 7 '16 at 1:11
  • $\begingroup$ I probably don't understand that (to be honest I've never even heard of it); I was just curious as I don't know much about the holographic principle. I'll google it. $\endgroup$ – heather Jul 7 '16 at 1:13
  • $\begingroup$ @Wolphramjonny Even assuming the validity of the holographic principle, this would by no means imply that the universe consists of fewer than 3 spatial dimensions. In particular there is plenty of arguments in biology and chemistry showing that, for the elements to interact and compose as they do, the universe must consist of at least 3 spatial dimensions. $\endgroup$ – gented Jul 7 '16 at 9:00
  • $\begingroup$ @GennaroTedesco the holographic principle does not say that we are a literal two dimensional projection, like 3D straight to a flat screen. It say that you can have a two dimensional formalism that is equivalent to our 3D formalism. In the holographic surface we do not even need to be localized, but the predictions are the same. For instance, a knot in the 3D description corresponds not to a 2D knot, but to some valid structure that, when translated into the 3D formalism, it results in a 3D knot. $\endgroup$ – Wolphram jonny Jul 7 '16 at 23:42
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I can define it very easy from a math point of view (the hypercube construction example), even we can apply real models based on the mathematical principles, but there is no practical way to measure/test that, not with current capabilities.

As a note, a Black Hole may be the clue we're looking for. All that compressed and stored energy could manifest itself in another dimension, with little effect on the known 3. But again, we cannot practically measure this.

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