## Purely numerical exploration of relative weakness of gravity in S4(1/h)

May 22, 2014 by zulfahmed

Although in the S4 picture, gravity is naturally explained by minimization of an Einstein-Hilbert action over hypersurfaces rather than over all possible metrics with a fixed base space, we assume that the formerly will produce a gravitational field equations approximately equal to the classical one, i.e. ( see here ):

These are Lagrange equations (in the usual functional rather than the S4 functional) for the term

(1)

where the integral is taken over a fixed base with varying metrics. In the S4 physics side, the right cosmological constant should be because this is the term that appears naturally when calculating the Ricci curvature of a hypersurface using the Ricci curvature formula for hypersurfaces with induced metric from .

For exploration, let us consider such that $latex , that is, . Now numerically, and but now we have to insert the value in terms of electron volts, which gives . Using this , we have . Now this figure of is not but rather .

We do not draw any conclusions from the above but note rather, that there are several ways of finding natural relations relative strengths of gravity and electromagnetism in an universe. Either we can normalize the scalar curvature and obtain a relative difference in strength like or we can consider scaling by thought of as the ‘length of fibers’ for electromagnetism even though we are not actually dealing with a fiber bundle but rather the space .

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