I’ve finally managed to write up something short about an idea I’ve been working on for the last few months, so now have a preliminary draft version of a paper tentatively entitled Spacetime is Right-handed. One motivation for this is the problem of how to Wick rotate spinor fields, given that Minkowski and Euclidean spacetime spinors are quite different. In particular, it has always been a mystery why a Weyl spinor field has a simple description in Minkowski spacetime, but no such description in Euclidean spacetime, where the Euclidean version of Lorentz symmetry seems to require introducing fields of opposite chirality. The argument of this paper is that the relation between Euclidean and Minkowski is not the usual chirally-symmetric analytic continuation but something where both sides use just one chirality (“right-handed”). It’s quite remarkable that the dynamics of gauge fields and of GR also has a chiral-asymmetric formulation.
In the ideas about unification using QFT formulated in Euclidean twistor space that I’ve been working on the past few years, it was always unclear why, when you analytically continued back to Minkowski signature, the left-handed Euclidean spin symmetry would not go to the Lorentz boost symmetry, but to an internal symmetry. One goal of this paper is to answer that question.
This past weekend I recorded a podcast with Curt Jaimungal, which presumably will at some point appear on his Theories of Everything site. It includes some discussion of the ideas behind the new paper.