GUT Intuitions

If as loop quantum gravity theorists suggest, gravity truly is a function of the geometry of space-time that is different in kind from the particle basis of the other three fundamental forces in physics, then a grand unified theory (GUT) of the other three forces formulated with a version of the particle propagators of the Standard Model particles in a discrete rather than continuous across a quantum space-time grid is a theory of everything. This would have the virtue of eliminating the need for extra dimensions found in string theory/M theory, but not in mere supersymmetry.

Indeed, simply formulating the Standard Model particles and forces in a not precisely local discrete space-time like loop quantum gravity would itself be a grand accomplishment, finally providing a way to unify the Standard Model and general relativity at all.

It also wouldn't surprise me if the pathologies such as magnetic monopoles and proton decay found in many GUTs, for example, the earliest minimal non-supersymmetric SU(5) theories, could be cured if they were embedded in a discrete, general relativistic rather than a continuous Minkowski space-time.

Another particularly nifty speculative stab at unification by Cohl Furey at the Perimeter Institute (flagged by Kea at Arcadian Pseudofactor) suggests that an algebra arising from the combination of the real numbers, R, the complex numbers, C, the quaternions, H, and the octonions, O, might very well be capable of reproducing the Standard Model, with the algebraic limitations of octonions proving particularly useful in inducing non-physical combinations (hence an RxCxHxO model). As the abstract explains:

Unified Theory of Ideals (2010)

Unified field theories try to merge the gauge groups of the Standard Model into a single group. Here we lay out something different. We give evidence that the Standard Model can be reformulated simply in terms of numbers in the algebra RxCxHxO, as with the earlier work of Dixon. Gauge bosons and the fermions they act on are unified together in the same algebra, as are the Lorentz transformations and the objects they act on. The theory aims to unify everything into the algebra RxCxHxO. To set the foundation, we show this to be the case for a single generation of left-handed particles. In writing the theory down, we are not building a vector space structure, and then placing RxCxHxO numbers in as the components. On the contrary, it is the vector spaces which come out of RxCxHxO.

The paper gives just on incomplete example of the process (for left handed first generation particles), but doesn't follow the concept to completion. But, it does show promise.