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, [email protected]
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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