On Thu, Oct 25, 2012 at 2:23 PM, meekerdb <[email protected]> wrote: > On 10/25/2012 10:49 AM, Richard Ruquist wrote: >> >> On Thu, Oct 25, 2012 at 1:43 PM, Stephen P. King<[email protected]> >> wrote: >>> >>> On 10/25/2012 11:52 AM, meekerdb wrote: >>> >>> On 10/25/2012 4:58 AM, Richard Ruquist wrote: >>> >>> Stephan, >>> >>> Since yesterday it occurred to me that you may be thinking of the 10 >>> or more dimensions of string theory as being orthogonal because they >>> were so before the big bang. But the dimensions that >>> curled-up/compactified went out of orthogonality during the big bang >>> according to Cumrun Vafa. I'll look up that reference if you are >>> interested. >>> >>> According to Vafa 2 dimensions compactified for every single space >>> dimension that inflated. In over simplified terms, 2 dimensions >>> (actually in strips of some 10,000 Planck lengths) to be compactified >>> lined up say in the east-west space dimension so that space in an >>> orthogonal direction could expand. So some semblance of orthogonality >>> exists in the compactification process, but it is clear that the >>> compactified dimensions become embedded in 3D space for inflation to >>> occur. >>> >>> >>> It's implicit in the definition of dimensions of a Riemannian manifold >>> that >>> there are as many orthogonal directions as dimensions. Compactified >>> dimensions are just small; they're small, not infinite, because they have >>> closed topology. That property is completely independent of having >>> orthogonal directions. >>> >>> Brent >>> >>> Dear Brent, >>> >>> Compactness and orthogonality are not the same quantities. Yes. But >>> my >>> point is that the compact structures in string theories (super or not) >>> are >>> orthogonal to the dimensions of space-time. Maybe we need all take a >>> remedial math class on linear algebra and geometry! >> >> I am still waiting for the explanation of how you know that to be true- >> that the compact manifolds are orthogonal to space dimensions. >> Richard > > > If they weren't orthogonal then a vector on them could be represented by by > a linear combinations of vectors in 3-space - and then they wouldn't provide > the additional degrees of freedom to describe particles and fields. They'd > just be part of 3-space.
They are just part of 3 space once the extra dimensions are compactified. I do not know about what happens to the extra degrees of freedom. Richard > > Brent > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
