# Can extra dimensions be too large to be observable

String theory postulates 6 extra dimension, all too small to be observed. The best description of a small dimension is that of an ant walking on a flagpole: The ant observes that the flagpole allows two dimension of motion (forward/back and left/right). From a very far off perspective, the flagpole seems to only have one dimension; the smaller dimension is too diminutive to be visible.

M-theory adds an additional dimension to string-theory: that got me thinking, is it possible to have a dimension that is too large to be noticeable? Consider the following analogy: to inhabitants Flatland, there are only two dimensions. If Flatland were extended to be the surface of a sphere, it would still seem perfectly flat; they would be living in three dimensional space, but only perceive two.

There are certainly weaknesses in the analogy, but it nevertheless has me thinking about if there could be dimensions that are too large to be naturally observable and what implications that might have in theories such a string/M theory or even if such a dimension were part of an even more ambitious theory that might pick up where M-theory ends.

I'm not enough of a mathematician to know if this is feasible, or to explore the implications myself; but I would love to know if it is possible or impossible, and if anyone has considered this.

• Your analogy makes no sense, because you can also consider Flatland as a hyperplane in 3-space. Mar 12, 2012 at 2:40
• Hi @ChrisGerig, can You write a nice clearing up answer, please ;-)? Reading too many messed up things in the question and in some answers gives me a headache ... Mar 12, 2012 at 10:30
• Relevant: arxiv.org/abs/hep-th/9906064 Jun 16, 2013 at 11:41

have a look at http://en.wikipedia.org/wiki/Brane_world

In your example of Flatworld it's not the size of the 3rd dimension that matters, it's the fact that the Flatlanders are stuck on the plane. The Brane World idea is similar. It suggests that all 9/10 spatial dimensions may be large but we never see them because we're stuck on a brane of only 3 spatial dimensions (+ time).

• That's exactly the crucial point, the "size" of those dimensions isn't even necessarily well-defined. Mar 12, 2012 at 11:59

I think it all boils down to perspective. A dimension is just an aspect of linear extension which we use to measure and coordinate things. Typically, "higher dimensions" are reserved for the universal linear degrees of freedom i.e. they exist everywhere no matter what. Whereas, "extra dimensions" are confined to some entity.

So, can there be large extra dimensions? Well, let's think about the earth and imagine that it's still the age of discovery (16th century). Looking out to sea, we see that the earth expands in two dimensions. You might call waves ripples "extra dimensions" because they wouldn't be observable from far off in the heavens. Much to our surprise though; when we travel to the heavens, the once two-dimensional earth curves in on itself -- revealing a third dimension of the earth. But is this a higher dimension? Or an extra dimension? Does it matter?

Imagine now that earth is actually flat, completely planar, like paper. And we, as humans, are points that can move about the surface. If the surface curls into a cylinder; does it make any difference to us? If we were to rise above the paper, will we have discovered a higher dimension or an extra dimension? Think about that in analogy to space going to hyperspace. Higher dimension or extra dimension?

Honestly, I don't think it matters. It's just a distinction. So, to answer your question; I replace "dimension" with "geometry" and say yes. Is string theory convoluted? Likely so...

Latest work with M-theory operates in eleven dimensions instead of ten, maybe your source of information is outdated.

And some mathematical models from the the vibrating strings that define string theory suggests that there are other vibrating objects out there such as 2-dimensional membranes, 3-branes, and a bunch of other things as well.

The latest research about the shape of our Universe could result in some clues about the extra dimensions out there wich we can't see (either tiny or huge)... if the shape of the universe is spherical or like a "doughnut", it would impact directly on all this dimensions theories.

The big-bang could have created the Universe with many possible shapes... either a huge "soap-bubble", a "ring-shape" (like the one that is created by a person when smoking a cigar) or other shapes.

• "String theory postulates 6 extra dimension" ... "M-theory adds an additional dimension to string-theory" 4 + 6 + 1 = 11 ... nothing outdated there. Mar 11, 2012 at 21:58
• Oh! I see. Sorry then... Mar 11, 2012 at 22:01
• M-theory provides a plausible framework where the 6 micro-dimensions of string-theory might be 10s of orders of magnitude large than Planck length. I have not read a good characterization of what the additional M-theory dimension could be or how it relates to the six Calabi-Yau shaped dimensions of string theory; but it appears that the 11th dimension is not intimately related to the 5th - 10th, as it is not postulated to be part of a 7-dimensional Calabi-Yau+1 shape. Are you indicating that theorists are current considering large scales for the 11th (M) dimension? Mar 11, 2012 at 22:12