Clifford Tetrads, Null Zig Zags, and Quantum Gravity∗

Quantum gravity has been so elusive because we have tried to approach it by two paths which can never meet: standard quantum field theory and general relativity. These contradict each other, not only in superdense regimes, but also in the vacuum, where the divergent zero-point energy would roll up space to a point. The solution is to build in a regular, but topologically nontrivial distribution of vacuum spinor fields right from the start. This opens up a straight road to quantum gravity, which we map out here. The gateway is covariance under the complexified Clifford algebra of our space-time manifold M, and its spinor representations, which Sachs dubbed the Einstein group, E. The 16 generators of E transformations obey both the Lie algebra of Spin-4, and the Clifford (SUSY) algebra of M. We derive Einstein’s field equations from the simplest E-invariant Lagrangian density, Lg. Lg contains effective electroweak and gravitostrong field actions, as well as Dirac actions for the matter spinors. On microscales the massive Dirac propagator resolves into a sum over null zigzags. On macroscales, we see the energy-momentum current, ∗T , and the resulting Einstein curvature, G. For massive particles, ∗T flows in the “cosmic time” direction—centrifugally in an expanding universe. Neighboring centrifugal currents of ∗T present opposite radiotemporal vorticities Gor to the boundaries of each others’ worldtubes, so they advect, i.e. attract, as we show here by integrating Lg by parts in the spinfluid regime. This boundary integral not only explains why stress-energy is the source for gravitational curvature, ∗This paper gives the derivations of the results I reported at the PIMS conference entitled “Brane World and Supersymmetry” in July, 2002 at Vancouver, B.C. It also contains new results on spin-gravity coupling, on how a topologically-nontrivial distribution of vacuum spinors removes singularities and divergences, and how the amplitude of the vacuum spinors determines the gravitational constant and the rate of cosmic expansion.