Sunday, August 19, 2007

Hypergeometrical Covariance


Hypergeometrical Covariance or Shadow Physics

It should have been patently clear when I corrected Newton's Second Law and Grand Unified Gravitation with Electromagnetism, but maybe I didn't emphasized enough the importance of the diagram shown above.

It shows two cross-sections of a Hyperspherical Lightspeed Expanding Shock Wave Universe. Not unlike the Universe of Shadows on the Cave Walls in Plato's Allegory (right panel) and Reality (left panel).

One can consider reality the left panel diagram (RXYZ). Anything that happens, happens without any qualifiers on that cross-section. A change of velocity would change the local normal to the Fabric of Space. That same change in velocity would have a corresponding change in the Shadow Universe (TauXYZ).

This is what I am loosely calling Hypergeometrical Covariance, that is, any law applying to anything in the Universe should have both representations. That is valid for the Four-Momentum and for "Force" in both panels.

The Hypergeometrical Newton's Second Law, redresses F=mdv/dt as
F= mdtan(theta_tau)/dtau where dtau is cdt.

If you replace m by a projection of a 4D unitary volume and introduce a Stress=volume*Strain law for both cross-sections you will recover Grand Unification.

Well, it is slightly more complex since one has to add to it the Hypergeometrical Standard Model (or Fat Electron) to deal with electromagnetism.

I used words to express the 3D projection of a complex 4D spinning dilator. It should suffice but only if you really stretch your brain a little.

Grand Unification depends upon assigning a one atomic mass unit to an electron. The same mass one assigns to a Proton. That is a proportionality reasoning since one is not measuring masses in the RXYZ cross-section but one needs to know how many dilators one get within a Kg of 4D Mass or Charge.

Grand Unification is achieved by using a single interaction (single "force").

Gravitation and Electromagnetism differs because the one and only interaction is being applied to different moieties (zero and half spin moieties).

Details of the Grand Unifcation argument are in the paper and in the blog. Specially relevant are the Hypergeometrical Newton's Second Law.

F=m.a is a nice equation but it leaves F to be determined. The Hypergeometrical Universe equivalent is Stress_RXYZ=Stress_TauXYZ leaves nothing undefined and provides the guidance to the derivation of a Grand Unified F from first principles.

Sometimes I state as being self-evident some conclusions of my theory. They are certainly self-evident to me, but the positivistic defying position is also an attemtp to raise a polemic, a discussion and to make sure that at least one Homo Sapiens can fully understand the theory - before I drop this subject.

Cheers,

MP





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