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The Word Dimension 
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#1
Dec1312, 04:18 AM

P: 149

I have some difficulty understanding the exact connotation of the word "dimension" as used in string theories re "extra dimentions".
Are these extra dimensions really meant to be dimensions of space or are they simply extra parameters that need to be integrated mathematically into the description of reality proposed by these string theories? It sometimes seems to my lay mind that the word "dimension" is not used in a specific, rigourous way... IH 


#2
Dec1312, 04:54 AM

PF Gold
P: 6,120

the extra dimensions in string theory are dimensions exactly as you think of the 3 dimension we observe, it's just that they are somehow tiny or "curled up" or something that makes them not observable to human senses. Yes, it's weird.



#3
Dec1312, 05:01 AM

P: 149

Thanx...I guess the notion of "curled up" also does not lend itself to clarity. Unobservable/unperceivable is much better. To my mind, anything labelled as spatial "dimension" also has a connotation of infinite extent. It's difficult to conceive of a dimension as being spatially nestled within three others. Perhaps it's more a semantic problem that we face here than a physical one? Would there be a more accurate term to attach to string theories' "extra dimensions"? IH 


#4
Dec1312, 03:28 PM

P: 292

The Word Dimension
The word dimension has a number of meanings in Physics and Mathematics. In this context the number of dimensions is the number of independent basis vectors that span the vector space.



#5
Jan1413, 02:41 PM

P: 11

If you want to describe the position of a point on a carpet, you can use a coordinate
(x,y, d) where (x,y) describes the position of a curled carpet hair and d is the distance on that hair. String Theory contains 10 dimensions, the regular 4 dimensions (x,y,z,t) plus 6 more, curled in a geometry of Spacetime called the CalibiYau manifold. String Theory posits that the smallest bits of matter are not pointlike particles but vibrating bits of string forming either loops or open strands. Vibrating in different ways corresponds to different particles of nature. Even our more powerful microscope which is the Large Hadron Collider probe reality at too high spatial scale to empirically prove that there are more than the four regular dimensions. The other 6 are like the hairs of the carpet seen from afar. I do not believe this theory but this is roughly how I understand it. 


#7
Jan1513, 12:45 AM

Sci Advisor
PF Gold
P: 9,381

In mathematics, a 'dimension' is merely a degree of freedom.



#8
Jan1513, 01:18 AM

Sci Advisor
P: 2,193




#9
Jan1513, 01:52 AM

Sci Advisor
P: 5,366

Note that compactification in this sense des not require embedding in a higherdim. flat space; therefore the compactified dimensions of String theory are not embedded in a larger space. Look at the garden hose example: it's a two dim. manifold with one large and one small (circular) dimension. In differential geometry it's possible to describe this manifold w/o referring to the three dim. embedding space! We use it for visualisation, but mathematically it is absent. 


#10
Jan1513, 01:21 PM

P: 5,632




#11
Jan1913, 03:32 PM

P: 11

I think that Islam was not about the validity of sting's theory. I thought he was simply interested to know what the word "dimension" means in the context of this string theory.



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