On 26 Oct 2012, at 14:00, Roger Clough wrote:

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).

Yes it is more zero, or zero^zero (one). In my favorite working theory.

Bruno





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

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