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Take for instance a arbitrarily chosen 2-dimensional rectangle, having a length of $x$, a width of $y$ and height of 0. (Or take for instance a 1-dimensional line. Or take for instance a 0-dimensional point.) It would have a total volume of 0. Without any volume, it would not only be impossible to perceive but also contain no mass. Does this mean that lower spatial dimensional objects do not actually physically exist in our universe?

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    $\begingroup$ Define physically exist. $\endgroup$ – ACuriousMind Nov 20 '14 at 14:11
  • $\begingroup$ Can be measured and proven to exist. Not sure how to elaborate. $\endgroup$ – martin Nov 20 '14 at 14:14
  • $\begingroup$ First, we do never prove anything that is a statement about the real world. Second, do things like "the line through two points" exist in our world for you? If not, as I suspect, do quarks exist although you cannot ever detect a single quark? Existence is a slippery notion, far more than you'd expect. $\endgroup$ – ACuriousMind Nov 20 '14 at 14:24
  • $\begingroup$ That's true. One can take it further and ask if the notion of spatial dimension even exist or if the universe simply contains a single infinite curled up dimension. $\endgroup$ – martin Nov 20 '14 at 14:31
  • $\begingroup$ possible duplicate of If I squeeze something really hard, will it ever become two-dimensional? $\endgroup$ – Kyle Kanos Nov 20 '14 at 14:32
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It could exist in the sense I believe you are thinking. It will not exist based on what we know about physics, or made of the particles we already know. But it is possible to imagine a parallel 2D universe that for some reason collides with ours (some people define universe as the whole, so in that case it would be part of our universe, but just initially separated from our 3D region). The details will depend on "if" and "how" its particles interact with those in our universe. So the 2D objects can be there, but they could be invisible or not, depending on how they interact with our electromagnetic field, in other words, on speculative yet unknown laws of physics.

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