A Status of large higher dimensions

Anne Ross
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The second Randall-Sundrum model was based on a large as opposed to compactified dimension. Has the possible existence of large higher dimensions been eliminated and what evidence rules them out?
 
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Recently, Spergel's group have written a paper based on last year's widely discussed neutron star collision which was detected using both EM as well as GW astronomy. The measurement experimentally constrains the amount of spacetime dimensions to 3+1 and it has therefore ruled out models based on the hypothesis that gravitational leakage occurs into large extra dimensions (which would explain the relative weakness of gravity), such as 3-brane models embedded in higher dimensional spaces.
 
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That is great Auto-Didact. Just what I needed.
 
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I came across the following paper by Mir Faizal, Lawrence M Krauss, Arshid Shabir, and Francesco Marino from BC. Consequences of Undecidability in Physics on the Theory of Everything Abstract General relativity treats spacetime as dynamical and exhibits its breakdown at singularities‎. ‎This failure is interpreted as evidence that quantum gravity is not a theory formulated {within} spacetime; instead‎, ‎it must explain the very {emergence} of spacetime from deeper quantum degrees of...
How would one build mathematically an infinite number of spatial dimensions theory? I can concieve mathematically an n-th vector or ##\mathbb{R}^{\infty}##, I had done so in my Topology course back then. But obviously it's not empirically possible to test. But is a theory of everything ought to be "finite" and empirical? I mean obviously if there are only 4 interactions (currently known); but then again there could be more interactions around the corner. So to encompass it all seems to me...

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