Since August 2008 when I first found a method of showing that that a static universe must be compact (exploiting Gaussian upper bounds on heat kernels in noncompact riemannian manifolds) leading to a scaled 4-sphere model to late 2012 when I was first able to show a sharp match of redshift using the S4 model thereby showing that the redshift can be easily explained in a static model which provided impetus for static compact models for the universe, the most important recent results in this direction has been an extremely simple explanation for the weakness of gravity in S4 models based on fundamental geometry, or more precisely the fundamental geometric difference of gravity from other (gauge) forces: in four space dimensions the Yang-Mills functional is conformally invariant while the gravity action (integral of a scalar curvature) is not. Indeed, the size of the universe explains the weakness of gravity. In S4 theory the size must be fixed to the length equivalent of , and the weakness of gravity is (if gravity is modeled as integral of scalar curvature over hypersurfaces) or if it is modeled on the entire S4 universe. The first is the preferred model where electromagnetism (and the nuclear forces) propapagate in all four space dimensions but gravity is localized to the three dimensional ‘physical’ hypersurface. In fact more can be said about the behavior of electromagnetism in this model, which is that S4 acts as a sort of ‘total space’ of a bundle formally but is actually not quite. Although every point of a three-dimensional hypersurface has a unique ‘normal geodesic’, these intersect and one does not have a perfect total space. Electromagnetism can still be defined as a 1-form on the total space. Yang-Mills theory is mathematically well-understood based on the work of many geometers and physicists — for example, the instantons had been fully solved by the ADHM construction in the late 1970s. With the preliminary explanation of the Lamb shift in an S4 universe, we have a simple and powerful unification model that concretely opens up the space for study of objective metaphysics. The approach allows us to begin with an *explanation* of quantum phenomena not as simply empirical phenomena but as phenomena which are consequences of the global geometry of the universe.

## Weakness of gravity revisited

June 8, 2014 by zulfahmed

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