Obviously, many of the results in the paper are familiar.
However, the restriction to a purely geometric
approach focusing on the properties of vectors has some
interesting consequences. For example, spin and particle/
antiparticle solutions already appear at this level, indicating
that these are simply different ways to build vectors
in space and spacetime. Therefore, the spinor part of
the wavefunctions arising from the Pauli-Schrodinger and
Dirac equations are directly related to the properties of
vectors and not necessarily a consequence of (relativistic)
quantum mechanics. In particular, spin can be viewed as
allowing vectors with a negative norm, such that a particle
traveling in the negative momentum direction with a
negative norm produces the same four-momentum. This
is not a rejection of wave mechanics. In this paper, it is
assumed that the four-momentum (or the energy and the
momentum) can be given a certain value at a particular
point in space and time. In quantum mechanics, momentum
and energy are replaced by operators and their
values are ”stored” in the wavefunction. This aspect is
beyond the scope of the current paper which restricts
itself to a description in terms of vectors.
There was some discussion of this concept many years back when this fellow worked out the math for creating this massive theoretical mulit-dimensional geometric object.
As an amateur faceter (it's hobby), this is very interesting indeed. To be able to take a bit of quartz or topaz or beryl or corundum, and cut it in such a way as to produce a "light cage" that is a thing a beauty has its allure. To think that the universe is based in its core upon such creations ... well, you made my day.