# Even more compact dimensions Re: Re: Compact dimensions and orthogonality

```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
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
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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