Sunday, April 22, 2007

How 3DT is Trivially Anomaly-Free

The Lagrangian for 3DT is the curvature scalar R in 6 dimensions. In my arxiv paper, I show that this curvature scalar is equal to the curvature scalar in 4 dimensions plus all possible matter terms. Therefore, in 6 dimensions, there is no matter, only pure geometry. Anomalies are quantum mechanical violations of conservation laws. Without matter there can be no conservation laws. Without conservation laws, there can be no violations of conservation laws. Therefore, 3DT is anomaly-free.

Sunday, April 15, 2007

How General Relativity is Unified with Quantum Mechanics

The theory of 3DT provides a simple relationship between quantum mechanics and general relativity. I claim that quantum mechanics is the result of waves. For example, the fact that one can not simultaneously determine the position and momentum of a wave leads to the uncertainty principle. This is just a general property of waves leading to the quintessential tenet of quantum mechanics. The waves come from wave equations, which come from a Lagrangian. The Lagrangian is the curvature scalar R in six dimensions. R really does contain all needed wave equations. R is the Lagrangian for general relativity. Therefore, quantum mechanics is contained within general relativity. String theory does not show the relationship between quantum mechanics and general relativity, but it does shed light on the relationship between quantum field theory and general relativity. It does this with extended particles, which 3DT also has.