I think you already named all the known dimensions in your question. The unknown dimensions, being unknown, don't yet have names. But the usual convention is just to refer to them as 4th dimension, 5th dimension, 6th dimension, etc.
2006-08-19 07:12:06
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answer #1
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answered by PhysicsDude 7
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The final theory of quantum gravity requires 11 dimensions. They are not named after the 3rd of 4th. Of course, the first disclaimer of this post is that experimentally and by observations, we live in a 3+1 dimensional universe. Tegmark was the first to explore the other possibilities of other dimensions and using certain physical arguments and based on the solution space spanned by differential equations, he concluded why our universe should 3+1 dimensional. We know that in the current trend of theoretical physics, M-theory could be the possible theory for quantum gravity, unifying both gravity and the other 3 forces. Hence why we need 11 dimensions? The post is set out to answer many questions raised on this issue. A easy way to think of that, which appeared to be truly obvious, is to look at the gauge group SU(3) x SU(2) x U(1) which is contained in the symmetry group G of the manifold which the theory of quantum gravity sits in. Suppose we wish to choose B as a manifold of minimum dimension with this SU(3) x SU(2) x U(1) symmetry, the question is to ask what is the minimum dimension that can permit this symmetry. We note that for the M theory, the symmetry group would break down to M4(Minkowski) x B, where B is a manifold of some group H. One must note that if H is not an abelian group, the symmetry group G of the manifold is not H but H x H, since the group manifold can be either acted by left or right multiplication. We know the following facts :
a) U(1) is the symmetry of the circle S^1, which has dimension 1,
b) For SU(2), the lowest dimensional space with symmetry SU(2) is the ordinary 2-sphere S^2, hence dimensions of 2
c) In the case of SU(3), things beome more subtle, because the space of the lowest dimension is the complex projective space CP^2, which has real dimensions of 4. Note that CP^2 is a space of 3 complex numbers (I^1, I^2, I^2), and cannot be all zero, with the identification that (I^1, I^2, I^3) = k (I^1, I^2, I^3) for any non zero complex number k. CP^2 can be defined as a homogeneous space of SU(3)/U(2).
So, if we add up the space CP^2 x S^2 x S^1, which contain the internal symmetries of the Standard model, we get 4+2+1 = 7 dimensions. Then, we have 4 non-compact space-time dimensions, so what do we get 4+7 = 11..hence the dimensionality of where the final theory of quantum gravity requires 11 dimensions. Clear as mud, right?
2006-08-19 07:19:14
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answer #2
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answered by Barkley Hound 7
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The number of known dimensions is 1. The '3rd' dimension. All other dimensions cannot be proven and are just theories. '1st' and '2nd' cannot be proven due to the inability to create those dimensions in the '3rd' dimension where everything has a length, width, and height. With everything I have learned, I have come to the conclusion that 'time' does not exist, and if you want to dispute this, try proving 'time' to me. Maybe I have missed something, but I'm pretty sure I know what I'm talking about.
2006-08-22 03:51:23
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answer #3
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answered by Safer S 1
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All we know about are the four dimensions you have named. Saying there are 12 dimensions is really just a theory with nothing to back it up as of yet. Since at this time no other dimensions do exist, calling the remaining 8 dimensions the 5th, 6th..., is actually referring to something that is just not there. This gets really deep. But, if there are additional dimensions that have not been named, could someone please at least decribe them?
2006-08-19 07:23:09
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answer #4
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answered by wader 1
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The answers already given puzzle me. Are we talking about the number of dimensions of space or of the fundmental dimensions.
The fundamental dimensions are mass(M), length(L) and
time(T). The dimension of all other physical quantities can be expressed in terms of these fundamental dimensions.
For example, the dimension of area is L^2, of velocity is LT^-1,of force, which can be expressed as mass times acceleration, is
MLT^-2.
The dimensions of length,width and height are Length.
2006-08-19 07:36:35
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answer #5
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answered by rabi k 2
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12 dimensions exist, only four have been named.
2006-08-19 07:10:35
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answer #6
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answered by ag_iitkgp 7
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