Hi Brent, What happens -- or is it even possible -- to collapse the dimensions down to one (which I conjecture might be time), or zero (Platonia or mind).
Roger Clough, rclo...@verizon.net 10/26/2012 "Forever is a long time, especially near the end." -Woody Allen ----- Receiving the following content ----- From: meekerdb Receiver: everything-list Time: 2012-10-25, 15:27:47 Subject: Re: Compact dimensions and orthogonality On 10/25/2012 11:47 AM, Richard Ruquist wrote: > On Thu, Oct 25, 2012 at 2:23 PM, meekerdb wrote: >> On 10/25/2012 10:49 AM, Richard Ruquist wrote: >>> On Thu, Oct 25, 2012 at 1:43 PM, Stephen P. King >>> 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. No, that's incorrect. I don't know much about string theory, but I wrote my dissertation on Kaluza-Klein and the additional dimensions are still additional dimensions. KK is simple because there's only one extra dimension and so compactifying it just means it's a circle, and then (classically) the location around the circle is the phase of the electromagnetic potential; quantized it's photons. Being compact just means they're finite, it doesn't imply they're part of the 3-space. If they were they couldn't function to represent particles 'in' 3-space. > I do not know about what happens to the extra degrees of freedom. If you lost them then you'd just have 3-space, possibly with different topology, but you couldn't represent all the particles which was the whole point of string theory. Brent -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. 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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
