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.

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.

Advantage #7 of 3DT over String Theory

3DT is finished. The theory was completed and appeared in 2005, the 100th anniversary of the appearance of Einstein's three famous papers of 1905. String Theory has not been completed and there is no end in sight.

Advantage #6 of 3DT over String Theory

Another point of similarity of 3DT with relativity is that both are theories of gravitation. Thus, 3DT continues the 300+ year old tradition started by Newton and continued by Einstein of placing gravitation in the position of highest importance. In 3DT the electromagnetic, weak and strong interactions are aspects of gravitation in six dimensions. String theory does not focus in on gravitation as the most important force and so does not share in this tradition.

Advantage #5 of 3DT over String Theory

Another point of similarity between Three Dimensions of Time (3DT) and general relativity is that both have the curvature scalar as their Lagrangian. 3DT's curvature scalar is in six dimensions and includes all known and predicted matter fields. This means all matter is just part of the geometry of a six-dimensional world. In other words, in six dimensions there is no matter, only geometry. This is the achievement of Einstein's dream of describing everything in terms of the "marble" of geometry alone, without the "base wood" of fundamentally different matter fields. This is in contrast to String Theory, which has ad hoc matter fields.

Advantage #4 of 3DT over String Theory

There is a precedent for Three Dimensions of Time (3DT). Adding dimensions of time has worked before - when Einstein added one dimension of time to the three of space. 3DT finishes the job Einstein started of adding dimensions of time to make time symmetrical to space. There are three dimensions of time because there are three dimensions of space. This is in contrast to string theory, which was invented to explain the strong interactions. Here it lost out to QCD (quantum chromodynamics). Using a failed theory of the strong interactions to explain everything is faulty.

Advantage #3 of 3DT over String Theory

The theory of Three Dimensions of Time (3DT) achieves quark confinement by leaving out the free-quark terms from the Lagrangian. How can free quarks exist in the world if there are no free-quark terms in the Lagrangian to describe them? In 3DT the free-quark terms have to be zero. String theory does not have a method for producing quark confinement. The standard model does, but it requires supercomputers for its calculations. 3DT's method is much simpler than this because it requires no calculations. For the details, go here.