upkiran
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What do you mean by 'multi-dimensional'?
What do you mean by 'multi-dimensional'?
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Welcome to PF!
Hi upkiran ! Welcome to PF!
"multi-dimensional" simply means that a space has more than one dimension.
What is the context? Does this come from a particular book?
Hi upkiran ! Welcome to PF!
"multi-dimensional" simply means that a space has more than one dimension.
What is the context? Does this come from a particular book?
upkiran
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Hi..
I want to know how do you realize multi dimensions. For example when you say that a tesseract is a 4-D object how do you expain its dimensions. what is the base to constructing a tesseract?
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hmm … what's a tesseract? 
ah … one of those … http://en.wikipedia.org/wiki/Tesseract" .
ah … one of those … http://en.wikipedia.org/wiki/Tesseract" .
ok … you can "draw" a 3D version of a tesseract (eg the http://en.wikipedia.org/wiki/File:Schlegel_wireframe_8-cell.png" )
but like a 2D copy of a cube, you lose some information.
In a 2D copy of a cube, some of the lines intersect (in 3D they don't), and the angles between the faces aren't 90º.
Similarly, in a 3D version of a tesseract, some of the faces intersect (in 4D they don't), and some of the angles aren't 90º.
Four dimensions are the minimum necessary to have all the angles 90º, and to have none of the faces or "hyperfaces" intersecting where they shouldn't.
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In spacetime you need 4 dimensions to define a position - 3 spatial and one of time. Extra dimensions, mainly spacial, are posited by string theory. The need for these extra dimensions is controversial and no observational evidence for their existence has yet emerged.
upkiran
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Hi...
Ok now let's go a step further... Consider an object said to have more than 4 dimensions... If space and time constitute four of these dimensions how would you describe the remaining dimensions?
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You just call them "extra dimensions".
(you can give them names if you like … but "what's in a name?"
)
(you can give them names if you like … but "what's in a name?"
)
upkiran
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The name is not important...
I was talking about its existence or characteristics... i mean any dimension other than "THE FOUR" are said to be of the order of Planck length, right.. If so can't those dimensions be explained using only the x,y,z and t coordinates?
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No, they have nothing to do with the x,y,z and t dimensions.
(just like t has nothing to do with the x,y and z dimensions)
(just like t has nothing to do with the x,y and z dimensions
)