_high_life_ said:
how do u kno we have 11 dimensions(got it right this time:D)how do u kno there arent sences than perceive completely different matter,space and time??
i still hold on to my belief that there wouldnt be dimensions without senses to percieve them and give them purpose.
everything has a purpose.
ah but they do have a purpose
I'd just be paraphrasing this..and im lazy and cbf to write my own
Hi all,
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.
yours sincerely,
Bernard Leong
Cavendish Laboratory
Now, chances are you dont understand all of this..pick the parts you dont get and i'll go through it with you
i'll come back and write a more simplified explanation in a couple of days. Brain isnt firing right due to the w/e if you catch my drift
