Friday, March 21, 2014

Geometric Theory of Mass

General Relativity is a geometric theory of force. As we may remember from high school physics, force and mass are intimately linked. Actually they are proportional, and the proportionality constant is geometric. Of course I am using a spacetime picture of geometry, as Einstein envisioned it, more than a hundred years ago. Four dimensional spacetime.

Recently Terry Tao, from UCLA, has proposed a program, to solve the equations of turbulent flow. Turbulence is circular motion, intimately linked to linear motion. He uses the idea of blowup, as he calls it, or renormalization as is used in physics. In a nut shell; from Jonathan Swift:

"So nat'ralists observe, a flea
Hath smaller fleas that on him prey;
And these have smaller fleas to bite 'em.
And so proceeds Ad infinitum."

The program's purpose is to calculate, with a small universal computer, maybe a cellular automaton, the next flea's metabolic budget.

Dumb implementations of the Navier-Stokes equation, do not give a rule to go from flea to flea, lo-and behold, the eddies blow up, like in an explosion. This reminds me of an old problem in QED. Let's calculate the electron mass, eddies, and eddies give us the wrong value of infinity for the mass which we know is:

9.10938291(40)×10−31 kg

What Tao proposes for turbulence, could work for QED; mmh, that's an idea.

We do have a powerful microscope to look at THE turbulent motion, par-excellence, INFLATION. Closer and closer to the physical singularity which we call, the big bang, B-Modes are amplified by this microscope, a.k.a.,  the Universe, and detected by BICEP2.

No singularity, we just see smaller fleas to bite 'em.

The geometric theory of mass here proposed, is then a solution to the equivalent equation, to Navier-Stokes, maybe Einstein's General Relativity, or its quantized version, the geometric part must tell us, which paths stay until now, and which ones just collapsed. What I have in mind, is something like Kepler's conjecture. Inside a bunch of barriers and holes, some paths can be traversed from A to B, giving us, the masses of the neutrinos, the electron, the muon, the tauon, and quarks. The electron neutrino path say,should be the straightest, this flea, goes from A to B, in the straightest path possible, and beats all other fleas!


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