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Extra Dimensions in String Theory 
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#91
Apr1208, 10:08 AM

P: 13

Ok I understand, for the better part, that this topic is dead but I need to explain something for those who read over it.
String theories ,mainly the SuperString theory, use a scale of 10 dimentions to describe locations of strings (and to allow for the existance for fermions and bosons in the theory) The idea of 10 dimentional strings in our "4 dimentional" (3 space and 1 time) worldline is difficult to grasp, as seen. What happens is the extra 6 dimentions are, ideally, wrapped in a ball/coil/ring/whatever someone decides eventually upon at every point in the 4 dimentional worldline that we live in. We cannot detect them due to their size of less than that of strings (which are theoretically 10^33 cm... which is very very beyond our power to comprehend). Interesting fact: In the 1920's Kaluza and Klein came up with the Compactification theory. (and here comes my lazy factor ^^ ) "In the original work of Kaluza it was shown that if we start with a theory of general relativity in 5spacetime dimensions and then curl up one of the dimensions into a circle we end up with a 4dimensional theory of general relativity plus electromagnetism! The reason why this works is that electromagnetism is a U(1) gauge theory, and U(1) is just the group of rotations around a circle. If we assume that the electron has a degree of freedom corresponding to point on a circle, and that this point is free to vary on the circle as we move around in spacetime, we find that the theory must contain the photon and that the electron obeys the equations of motion of electromagnetism (namely Maxwell's equations). The KaluzaKlein mechanism simply gives a geometrical explanation for this circle: it comes from an actual fifth dimension that has been curled up. In this simple example we see that even though the compact dimensions maybe too small to detect directly, they still can have profound physical implications."  John M. Pierre So I hope i may have cleared up some things. And in my opinion, I believe that the dimentions are real and are just too small and difficult to detect that we cannot actually prove they exist. 


#92
Nov2311, 11:12 PM

P: 1

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Using that definition, then dimensions beyond four (including time), appear to create a paradox that a given point within extra spatial dimensions has to be both within and outside of the first four dimensions, and that is why it is difficult or impossible to visualize extra dimensions.



#93
Dec3011, 10:43 PM

P: 1

Since this old thread was bumped up just a month ago, I'll add my two cents.
Arivero settled it in the latter part of post #76. As the original questioner's thought on the subject evolved, it became clear to me that he has been led to believe that extra dimensions of space as theorized by strings are not only unreal in that they do not refer to anything that physically exists, but, as mere mathematical conveniences, they were never even MEANT to refer to real spatial dimensions in the first place. The jury is out on the first half of the statement. The second half is emphatically wrong. The stringy math predicts extra dimensions. According to the math, they are spatial and they are, in theory, real, at least in so far as the three we are all familiar with can be called "real." Now, whether or not these extra spatial dimensions exist is another question altogether, but I do not think that was the original poster's question, received, as it may have been. His was much more fundamental. 


#94
Dec3113, 03:05 AM

P: 1

A dimension is simply the measurement of movement.
The movement that we as humans are aware of is Up and down or Height Back and forth or Length Side to side or Width By this definition, physically we live in a three dimensional world. So wouldn't a higher dimension have to have more ways of movement in order to be higher? If so what would they be? 


#95
Jan614, 12:08 PM

P: 11

I red full post of yours and its quite awkward but I am junior than you in age but I am very intrested In this theory
for ur question "  are the "higher spatial dimensions" of string theory mathematical abstractions only? " thats a very gud thing that u tried to compare this theory with mathematics but all these dimensions are not just the abstractions in mathematics also there are multidimensional structures are there for example boy's surface which is nothing but a 23 d manifold and as we know a manifold is nothing but and n number demensional surface comming to string theory the extra spartial dimensions are also from polyakov manifold and as we know each and every manifold follows certain equation for their particle's path of trajectory the extra spartial dimensions are derived or coined by polyakov equation under polyakov action in the string theory the strings follows only 4 dimensions ie 1d 2d 3d 4d that is time but in superstring theory the string follows 4 dimensions + 7 extra spartial dimensions I hope what I stated above may help u 


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