Browsing this fascinating site, I have come across many speculations on higher dimensions and quantum matters and particle spins that may relate to something I have been working on for some years. I would like to outline it here to see if forum members can either find faults in the reasoning or ways forward with it. I welcome criticism or collaboration with equal enthusiasm.

1) The following paper makes the case that the entire universe has the geometry of a Glome type hypersphere or 3-sphere.

(see https://www.specularium.org/hypersphere-cosmology)

2) Quantum physics appears incomplete to say the least, and quantum field theory looks like an increasingly tortuous conceptual mess of ad-hoc hypotheses and questionable maths.

3) If a hyperspherical geometry applies to the entire universe then perhaps it also applies to the quanta and fields which compose it.

The Quantum Hypersphere idea starts with a model of the neutrino, the seemingly simplest of the matter quanta or fermions.

A four-dimensional object can rotate in two different planes simultaneously. See a doubly rotating tesseract/hypercube here: -

https://en.wikipedia.org/wiki/Rotations ... dean_space

This gives a visualisable picture of such a double rotation.

If we imagine the ‘inside out’ rotation as occurring in the wz plane with z also representing the direction of propagation, then the xy rotation corresponds to the ‘roll’ around the z axis.

If the double rotation is not isoclinic but has xy rotating at only half the rate of wz then perhaps this accounts for the spin ½ spinor.

Reversing the direction of the propagation z axis also reverses the direction of the xy spin. Thus, a neutrino coming from the opposite direction appears as an antineutrino and we get the observed parity violation, i.e. no right handed neutrinos or left handed antineutrinos.

I hope to show that all fermions have a basic neutrino ‘skeleton’. Electrons and nuclear particles can have extra spins* as well that do not reverse with inversion of the z axis of spatial propagation, thus allowing for both right- and left-handed electrons and positrons for example.

(* I suspect this involves extra dimensions, possibly imaginary time dimensions which may have a pseudo-spatial Minkowski signature.)

Anyway, I look forward to your comments on the basic idea of spinors from a non-isoclinic double rotation in four spatial dimensions.

Regards, Pete.