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I've seen hyperspace dimensions being discussed in models for superstring theory, where there are 6-7 hyperspace dimensions iirc. But the explanation as to why we don't perceive these extra dimensions are either because they are either compacted into a very small space (such as a calabi-yau manifold) or that our 3-dimensional world is a sub-manifold of a brane I don't quite understand how hyperspace dimensions work, especially in relation to regular dimensions. Basically, my question is, what is the scale of these "extra dimensions"? would they be equivalent to 4, 5, 6... 11-dimensional spaces like regular dimensions, each plane infinitely greater in scale than the other, or does their compactness make their physical value less than that of an infinite 3-dimensional manifold? In short, how would you consider the "size" of an 11D model with 3+1 space-time and 7 hyperspace dimensions, relative to a model with 10+1 space-time? would they be equivalent in scale? I just assume that they must not have the equivalent or comparable scale to our regular 3 spatial dimensions as they are "compacted" and we cannot experience them or are they higher dimensions with physical value infinitely greater than ours? Note: what I mean by "physical value" is in relation to things like scale, size, volume, and mass- as lower dimensions (1D, 2D) have no mass, and higher dimensional objects (4D, 5D...) i assume would have infinite mass if we use the same metrics we apply to 3-dimensional objects (assuming its possible to apply it like this) I may be completely misunderstanding this, as I don't have a lot of knowledge in this area.

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  • $\begingroup$ Im trying to ask how you would compare the "scale" of a model of 3+1 dimensional space-time with 6 hyperspace dimensions like the model of M-theory, to a model of 10+1 dimensional space-time. Would they be qualitatively equivalent in terms of size/scale, as i know higher dimensions are more than infinitely greater in "size" than lower ones $\endgroup$
    – Adithya
    Mar 15, 2023 at 16:25
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    $\begingroup$ Mathematically, how is your measure of "scale" defined, precisely? There are many ways. Physically, what experiment do you propose to probe your question? I know of none, so this isn't really a physics question as far as I'm concerned. $\endgroup$
    – John Doty
    Mar 15, 2023 at 17:09
  • $\begingroup$ Search for "compactified extra dimensions experiments", which gives e.g. arxiv.org/abs/2004.03051, arxiv.org/abs/1008.0765, pdg.lbl.gov/2019/reviews/rpp2018-rev-extra-dimensions.pdf, inis.iaea.org/collection/NCLCollectionStore/_Public/32/053/… etc.. People have both thought about this a lot and they have done tabletop experiments, see e.g. Eot-Wash at university of Washington: npl.washington.edu/eotwash/node/1 . Those guys have built amazing instruments for non-Newtonian gravity at the mm and sub-mm scale. $\endgroup$ Apr 4, 2023 at 22:32
  • $\begingroup$ @JohnDoty Im basically asking, would a 6-dimensional model with 2 compact dimensions, for example, function just like a normal 6-dimensional reality, or would the "compactness" or the hyperspace dimensions make the model basically equivalent to a 3+1 dimensional brane $\endgroup$
    – Adithya
    Apr 6, 2023 at 13:55

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