Gary,
Thanks for the score & post which I've responded to. I've read yours again. My maths isn't adequate (I prefer dynamic geometry) but I do think I like scalar values for time, and I'm sure there's really no co-incidence but an important physical truth. May it be hiding in the windings of toroid pairs (3D helices when in relative motion) and the Gottfreid-Jackson angle?
Refreshing my thoughts on Quaternions I delved back and came across these passages. I wonder if you can make any sense of them?
"As reality is 3D, complexity may increase by the cubic function. Quaternions are non-commutative continuous field potential functions of two compound parts, real scalar and 'imaginary' 3D vector. We suggest that the 16 symmetry sets may be a handed hierarchy, seven (x2) rotational, one (x2) quasi-translational. Quaternions and Octonians may aid description of the evolution of the dynamic rotations and translation of complex 3D systems.
and; .."The coherent kinetic power of a (twin vortex, single) toroid translating in air as a 'pressure gradient' form is significant and can knock down buildings, as this video.i But we must also consider from the torus rest frame, where buildings, EM waves and other forms, including complex toroids approach and interact. We suggest such interaction may be valid candidates to consider alongside quantum electron orbitals and 'shells for modelling collisions and particle 'decay' or perhaps rather 'transmutations'. Full 3D vector fields may be theoretically modelled using multiple quaternionic wave functions; s2 +x2+y2+z2 =1 (see 6.8). But we wish to focus here on the conceptual framework of obtaining the classical from the quanta, so need a slightly different approach and thought experiment; Consider the toroid bubble in motion at v through the water. We must always remember that the water may be a stream or flow, a la Fizeau, itself moving in relation to a nearby body of water or a riverbank, but here we only consider the local case. An emitter at rest in the water sends a one second EM signal towards the torus. The DFM predicts that there will be both a temporary trivial propagation velocity D, (at ~ANY orientation), and a permanent propagation angle rotation which is dependent on the lateral vector of the torus. The one second period will then also be changed, which is equivalent to wavelength being Doppler shifted and also to the signal time period being dilated or contracted. This change is purely kinetic and not accounted for in current interpretation."