Title: A testable variation on the linearized general relativity containing the symmetries of the standard model
using quaternions and hypercomplex numbers in the action
>
Abstract
The Maxwell action of electromagnetism is rewritten using the noncommutative division algebra of quaternions.
The potential in the electromagnetic action is rewritten with the weak force gauge symmetry SU(2), also known
as the unit quaternions. The potential can be recast again with electroweak symmetry as the product of U(1) and SU(2)
symmetries. The conjugate of one electroweak symmetry times another for the potential in the action is enough to
account for the strong force symmetry SU(3). A 4D commutative division algebra is constructed from the hypercomplex
numbers modulo eigenvalues equal to zero. The action is rewritten again with the hypercomplex multiplication rules
in a gauge invariant way. Like charges attract for the hypercomplex action based on an analysis of spin of the
field strength density, the spin in the phase of the current coupling term, and the field equations that result
by applying the Euler-Lagrange equation. The field equations of the hypercomplex action contain Newton's law of
gravity paired with a time-dependent term and thus are consistent with special relativity. There is also an Ampere-like
equation so that a 4-potential theory can account for bending of both time and space caused by gravity. It is shown h
ow the Rosen metric is a solution to the field equations, and thus passes weak field tests of gravity to first-order
Parametrized Post-Newtonian (PPN) accuracy. The proposal is distinguishable from general relativity at second-order PPN accuracy.
The lowest mode of wave emission for this simple field theory is a quadrupole. The final rewrite of the action has
gauge-dependent electromagnetic and gravity field strength densities where the two gauges cancel out, leaving a gauge-independent
unified action. Since the Higgs mechanism is not needed for this unified field proposal, it is predicted no Higgs boson will be found.
Links
Technical paper on GEM (various formats)
The paper as one would expect to see it.
The same paper, ported to Mathematica, with math confirmed. Much more detail, like all the terms in the Lagrangian.
The same notebook, as a pdf.
Talks on YouTube
A 90 second description of the approach
13th Eastern Gravity Meeting
An explanation of the t-shirt
Tensors and quaternions
Unified feild theory and the current coupling term
Short video on real, complex, quaternion and hypercompex number theory
Other research
Doing Physics with quaternions Yes Virginia, there is more one can do with quaternions than 3D rotations.
VisualPhysics.org Think analytic geometry, animated. Lots of cool, odd stuff.
Fun to own
The GEM t-shirt Note: $5 discount for all physics Ph.D's (grad students included)!