Far out cosmology: space time right-handed (Introduction)

by David Turell , Tuesday, October 24, 2023, 22:45 (185 days ago) @ David Turell

Shown by mathematics:

https://www.math.columbia.edu/~woit/righthanded.pdf

"Abstract
The relation between vectors and spinors in complex spacetime is conventionally defined so
that Minkowski spacetime is related by Wick rotation to the standard Euclidean four-dimensional geometry. There is a different chirally asymmetric possibility, using purely right-handed spinors, in which Minkowski spacetime gets Wick rotated to a four-dimensional geometry with a distinguished direction. This right-handed spinor geometry also gives self-dual two-forms that can be used to get chiral formulations of the Yang-Mills and general relativity actions.

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The Standard Model quantum field theory is not well-defined in Minkowski spacetime
without some further information, with analytic continuation from Euclidean spacetime one
way to accomplish this. Defining the theory this way allows one to exploit the symmetries of
the Euclidean spacetime, and in [10] we described a speculative proposal for understanding
the symmetries of the Standard Model in terms of the geometry of the Euclidean version of
twistor space. Such a twistor space description is inherently completely chirally asymmetric, with points in spacetime corresponding to spinors of one chirality. The most unconventional part of the proposal is that the part of the Euclidean rotation group that acts on the other chirality could physically correspond not to a spacetime symmetry but to an internal symmetry. The main goal of this paper has been to understand the possible origin of such a counter-intuitive phenomenon. Note however that mixing between Euclidean rotational symmetry and an internal symmetry has been seen in other contexts, in particular in the twisting used to define topological quantum field theories.

The conventional way of relating Euclidean and Minkowski spacetime spinors is by a
chirally symmetric analytic continuation which takes Euclidean spacetime symmetries to
Minkowski spacetime symmetries for both chiralities. In this paper we have proposed a
different relation, which uses just one chirality. Spacetime (both Minkowski and Euclidean)
can be said to be “right-handed”, and we see that this goes beyond the spin 1/ 2 matter degrees of freedom, with Yang-Mills and gravitational dynamics also described using right-handed spinors...This proposal is set in Minkowski spacetime.

Comment: All of the complex calculus equations are omitted. Chirality of spacetime is an interesting concept. Does it mean there is another left-handed universe for symmetry or is it like biochemistry where mechanisms are always one way or the other without balance.