Abstract
String theory developed as an attempt to integrate gravity into the standard model of particle physics. However, this really boils down to a problem with the logical concept of the point, which the gravity of general relativity exasperates. While substituting strings for points has its advantages, string theory has led to a secondary problem with the definition of a point: Sub-divisions of space-time can only be probed so far. At very small scales, space-time is so warped by a potential probe's energy, it forms a black hole and loses its meaning. In effect, small strings have doomed space-time. Theoretical physicists are reluctant to give up on string theory, though, because string interactions don't occur at a point, but are spread out, thus avoiding many problems with particle interactions at a point. Yet, a still bigger problem is that some think that neither string theory nor particle theory are background independent theories. In their view, particle theory requires a background, but, in general relativity (GR), mass warps the very background that the particle or string theory needs. Given these problems, some theorists have sought a background independent theory called Loop Quantum Gravity, coming at the problem from the standpoint of GR, rather than that of particle physics. However, in all of this theoretical struggle, no one has attempted to solve the problem of the definition of the point itself. Instead of attempting to ignore it, or substitute strings for it, or devise a spin network or a spin foam with it, perhaps we should be seeking a new definition of the point itself. This essay introduces a new approach to do that, by considering 3D space/time vibrations, where the point is defined as the boundary between the two "directions" of a given physical dimension. This opens the door to discretizing both space and time, without contradiction.
Doug Bundy