  I show how the isomorphism between the Lie groups of types $B_2$ and $C_2$
leads to a faithful action of the Clifford algebra $\mathcal C\ell(3,2)$ on the
phase space of 2-dimensional dynamics, and hence to a mapping from Dirac
spinors modulo scalars into this same phase space. Extending to the phase space
of 3-dimensional dynamics allows one to embed all the gauge groups of the
Standard Model as well, and hence unify the electro-weak and strong forces into
a single algebraic structure, identified as the gauge group of Hamiltonian
dynamics. The gauge group transforms between phase space coordinates
appropriate for arbitrary observers, and therefore shows how the apparently
arbitrary parameters of the Standard Model transform between mutually
accelerating observers. In particular, it is possible to calculate the
transformation between an inertial frame and the laboratory frame, in order to
explain how macroscopic laboratory mechanics emerges from quantum mechanics,
and to show how to write down a quantum theory of gravity that is consistent
with quantum mechanics, but is not consistent with General Relativity.
