String thoery - extra dimensions

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SUMMARY

String theory requires multiple dimensions to reconcile quantum mechanics with the principles of special relativity. Classical string theory operates without issues in three dimensions; however, the necessity for 26 dimensions arises when attempting to canonically quantize strings. When incorporating fermionic strings, only 10 dimensions are needed. The mathematical justification involves advanced algebraic concepts that indicate specific dimensional requirements, while the physical rationale remains less understood, leading to practices such as compactifying extra dimensions.

PREREQUISITES
  • Understanding of string theory fundamentals
  • Familiarity with quantum mechanics principles
  • Knowledge of special relativity
  • Basic grasp of advanced mathematics concepts
NEXT STEPS
  • Research the implications of 10-dimensional string theory
  • Explore the concept of compactification in string theory
  • Study the role of fermionic strings in higher-dimensional theories
  • Investigate advanced algebraic techniques used in string theory calculations
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Physicists, mathematicians, and students interested in theoretical physics, particularly those focused on string theory and its dimensional complexities.

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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