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

2012-10-27 Thread Bruno Marchal


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

2012-10-26 Thread Roger Clough
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 

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

2012-10-26 Thread meekerdb

On 10/26/2012 5:00 AM, 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).


I'm not sure what you mean by 'collapse'.  Do you mean, Is is possible to invent a theory 
which has only a one-dimensional Remannian manifold?  Sure, but I don't think you can 
make it agree with physical observations.


In my view, these are models we invent to try to understand the world; so we need our 
model to be understandable.  That's one of my objections to a lot of 'everything' theories 
like Tegmark's; they hypothesize a model that is incomprehensible in order to 'explain' 
something - it's like God did it and God works in mysterious ways.


Brent

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