Chapter Ten, Quantum Geometry Summary and Analysis

When working with scales as small at the Planck length, a new kind of geometry must emerge called quantum geometry: a modification of Riemannian geometry, which is the basis of general relativity. Riemannian geometry examined warped shapes, stating the greater the stretching, the greater the variation from the distance on a flat shapes. In other words, there is curvature. In mathematics, spacetime's curvature reflects the distorted distance relations between its points. As an object gets smaller—closer the the actual physical idea of a point—the mathematics more closely aligns with the physics.

As discovered by Edwin Hubble, the universe is still expanding from the Big Bang. If the average matter density exceeds the critical density, then the universe's gravitational force will cause expansion to stop and reverse. Astronomers note the visible matter...