Spinor Space with a temperature gradient to explain its twice revolution enigma

Spin space is usually viewed as a space in which the usual vector "flag pole" is enriched with an orientation (directed 2-space elements) defining flag. A spinor state is specified by 4 real parameters and a sign r, θ, φ, α . That sign is indicative of an orientation being specified and thus we can think of Spinors as polarised (pseudo-)vectors that in embodying an orientation have a "greater" awareness of the space that they exist in. The identity operation is not equivalent to rotating through 360 about a fixed axis.

Dirac's belt and Feynman's plate scenarios describe an apparent necessity to revolve a system through 720 degrees in order for it to return to its initial configuration (identity operation). Dirac's belted object distinguishes an identity operation from a 360 rotation rotation about an axis by realising an entanglement of belts with the embedding space in the latter. A rotation around some fixed axis by 360◦ cannot be continuously deformed to the trivial motion, but it can be deformed to a rotation by 360◦ around any other axis (in any direction). Only is a rotation by 720◦ deformable to the trivial one. While a composition of two motions (that in themselves) are not deformable to the trivial one, gives a motion that is deformable to the trivial.

Can think of spin space alternatively as a connected spherical space with a temperature gradient in which at the centre the temperature is cooler and as such that measuring rulers are half the length they are at the circumference. Such a continuous temperature gradient is equivalent to defining a Weyl gauge through the 3-sphere. The sphere while isotropic is not homogenous as lengths measured differentially along radius. As such C/r will be 4pi instead of 2pi.