Friday, February 19, 2016

General Relativity Has Pathological Features In Five Or More Dimensions

General relativity, which is the best known description of gravity that we have right now and about 100 years old, is usually formulated in four dimensions (three dimensions in space and one in time), but it is straightforward to consider its equations in more than four, or fewer than four dimensions.

Real life, of course, can't have fewer dimensions than we observe, so a description of reality in terms of general relativity with one, two or three dimensions cannot be a physically correct description of reality.

A new theoretical analysis of general relativity in five or more dimensions, however, reveals that the theory allows for mathematical pathologies, called "naked singularities" in any version of the theory with five or more dimensions. These pathologies turn up only in rather improbable distributions of matter that might be vanishingly rare in nature even if it had more the four dimensions.  And, these pathologies also might not be present in a five or more dimensional quantum gravity that reduces to general relativity in the classical limit in most circumstances.

But, this finding still buttresses the conclusion that there is something special about a four dimensional universe that may make it the only possibility that can provide a physically correct description of reality, and disfavors beyond the Standard Model theories in which gravity is united with the other Standard Model forces (and allowed to be as weak as it is) in a space-time with more than the usual four dimensions (with five, ten and eleven dimensional options being particular popular alternatives).

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