Tuesday, November 27, 2018

general relativity - Might local gaps in spacetime suffice to leave its infinity and eternality incomplete?


At https://arxiv.org/pdf/1403.1599.pdf, Vilenkin, in 2014, used the Borde-Guth-Vilenkin theorem's premise that the "bouncing" local universes of an expanding or contracting multiverse would necessarily be geodesically incomplete either to the past or to the future, using General Relativity without the one assumption added to it by Einstein and Cartan, which was an assumption that fermions have spatial extent. That extent would be submicroscopic, but nevertheless greater than the Planck length, and the addition of it is said to have left relativity more complicated mathematically, but still able to meet all of its experimental proofs. 


The math and physics notations in Vilenkin's paper are beyond my comprehension, but I'm assuming that they reveal some gap in space, and, consequently, in the time that's integral with it. It appears to me that the totality of that space which is occupied by fermions might correspond to that gap, if there is one.


One factor that might bear on the answer would be the use of "parallel transport" in Einstein-Cartan theory, which seems to be required in circumstances resembling some of those where geodesics, or affine geodesics, are used in GR.




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