String thoery - extra dimensions

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String theory requires multiple dimensions to reconcile quantum mechanics with the principles of relativity, with 26 dimensions needed for classical string theory and 10 dimensions when incorporating fermionic strings. The mathematical necessity stems from specific algebraic conditions that only hold true in these dimensions. While the calculations are complex and categorized as advanced mathematics, the underlying physical rationale for these dimensional requirements remains unclear. Many theorists accept this dimensionality and explore methods to compactify the extra dimensions to make sense of the theory. Ultimately, the need for extra dimensions in string theory is a fundamental aspect that continues to provoke discussion and investigation.
kashiark
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Why does string theory need so many dimensions? i know in our 3 it would break special relativity but i don't know why
 
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First of all, note that "classical" string theory in 3 dimensions is no problem at all. The requirement for 26 dimensions only comes when you try to fit in quantum mechanics, i.e. you try to canonically quantize your strings. When you include fermionic strings as well, you "only" need 10 dimensions.

The mathematical reason, although the calculations are usually categorized in "advanced mathematics", can in principle be traced. (If it means anything to you: there is some algebra involving a central term which depends on the dimension d of space-time and only vanishes for a special choice of d = 10, 11 or 26 - depending on the theory you're looking at).
The physical reason why it should only work in that particular number of dimensions is, AFAIK, not so clear. At least I've never really heard any good reason why it is like it is, people just accept it and devise ways around it (e.g. compactifying the extra dimensions).
 

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