Different number of time dimensions

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SUMMARY

The discussion centers on the implications of varying the number of time dimensions (T) and spatial dimensions (S) in the context of General Relativity (GR) and Quantum Field Theory (QFT). It asserts that while classical GR equations are indifferent to the number of spacelike or timelike dimensions, the path-integral formulation of QFT presents complexities that require further exploration. The user references a paper by Max Tegmark that discusses scenarios with T=0 and T>1, indicating that these cases warrant deeper investigation.

PREREQUISITES
  • Understanding of General Relativity (GR) principles
  • Familiarity with Quantum Field Theory (QFT) concepts
  • Knowledge of path-integral formulation in quantum mechanics
  • Basic grasp of dimensional analysis in theoretical physics
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  • Research the implications of varying spatial dimensions in General Relativity
  • Study the path-integral formulation of Quantum Field Theory in detail
  • Examine Max Tegmark's paper on dimensions for insights on T=0 and T>1
  • Explore the concept of stability in orbits under different dimensional frameworks
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The discussion is beneficial for theoretical physicists, cosmologists, and advanced students interested in the foundational aspects of spacetime dimensions and their effects on physical theories.

Dmitry67
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I am layman, so I can't find an answer on my own.

Suppose, on low energies space is (locally) pseudo-euclidean with the number of spatial dimensions S and time timensions T

In our universe S=3 and T=1

My question: is it possible to 'adjust' equations of GR and QM/QFT to the different S and T? Are there any "no-go" things (like orbit stabilty which, for T=1, is possible only if S=3)? What if T=0 or T>1?
 
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Equations of classical GR do not care about the number of spacelike/timelike dimensions.

For QFT, it's not so trivial. Path-integral equations do not care about that either (at least formally), but that does not seem to be enough.
 
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Not a direct answer, but

http://space.mit.edu/home/tegmark/dimensions.pdf"

might be of help. The cases T=0, T>1 are mentioned as well.
 
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