Hi Richard,

Is there some way, such as reducing the dimensions of
strings to zero, that one can transverse from the world
of extension (the physical world) to that of inextended
experience  or theory?  


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, 14:23:04 
Subject: Re: Compact dimensions and orthogonality 


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. 

Brent 

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