HyperGeometrical Universe Theory

 

There is a famous discovery in Science where the Gravitational Lensing played a strong role…J

Of course, I am referring to the Prediction of Gravitational Lensing by Einstein’s General Relativity.

To obtain the predictions of the Hypergeometrical Model for the gravitational refraction of an electromagnetic wave, one has to remember that a Force is represented as a Stress in this model. Acceleration is modeled as a local deformation of the Fabric of Space. This is shown in the equation below:

Where dτ is equal to cdt, that is, it is a dimensionalized time. The momentum of an electromagnetic wave was represented by hk and its mass by this equation:

Light always travels at 45 degrees with respect to the Fabric of Space as shown above. This means that Gravitation only affects the direction of propagation on the Fabric of Space. That cross-section is shown below:

Where

Delta Tau is the de Broglie step in the Hypergeometrical Expansion of the Universe. The angle is given by:

The Force can be written in terms of Gravitational fields as:

Notice that the interaction between an electromagnetic wave doesn’t depends upon velocity since the wave cannot be accelerated or decelerates as a particle could.

The equation of motion for an electromagnetic wave is given by:

At the position of scattering R=Ro yielding:

 

Resulting in the diffraction angle:

Which is the observed Gravitational Lensing.

Q.E.D.

Cheers,

 

MP

 

The Hypergeometrical Force


When I DERIVED the equation for the Hypergeometrical Force – the Grand Unification Force – used a setup with two infinitesimal elements of current (or mass flow).

Here are the equations for Electromagnetism and Gravitation:

                 (1)

Where C1 and C2 are the charges traveling at V1 and V2 and c is the speed of light. R12 is a vector from charge 1 to charge 2.

Similarly for Gravitation:

        

Notice that the only difference is the proportionality coefficient. This means that the interaction is the same – dilaton field-dilator interaction controlled by the Quantum Lagrangian Principle. The proportionality coefficient ratio is given by the ratio of these two angles a₀ and a₁:

R0 is the age of the Universe times the speed of light (15.82 billion light years) and λ1 is the Compton wavelength of a Hydrogen atom. To be precise, this ratio has to be multiplied by an elastic coefficient of the Fabric of Space. This coefficient is the reason why dilaton and Gravitational waves exist.

The humongous (10³⁶) factor is easy to understand by this simple figure. A more detailed analysis can be found in the pdf containing the theory.

This equation can be simplified for the case where there is no rotation and one of the bodies is much larger than the other (Sun and Mercury for instance) into:

This is the first time a force is actually derived from a purely geometrical theory of the Universe, so it took me some time to understand that this equation has to be integrated upon R (distance) to yield the amount of energy that can be shared into Kinetic and Potential at any position.

Adiabatic integration upon R yields the potential

    (3)

This potential is the one used in the Precession of Mercury’s Perihelion problem. Applying it to Lagrangian Formalism yields the more appropriate force formula for physical bodies or charges:

Similarly for F one obtains:

Thus F becomes:

Expanding it in powers of

Neglecting terms above the second order

This means that my Gravitational Force does not contains first order dependence upon v/c and also that is perfectly describes all celestial dynamics. It produces the same formula for the Precession of Mercury or Earth or anything else Perihelion…J

In summary, my formula produces not one but TWO formulas for force. One for constructs that cannot change speed (Light) and another for bodies. They are reproduced without approximations below:

The second formula is used to derive the Gravitational Lensinng (Gerber failed to do so since he only ansatz (guessed) right the first formula).

The more complex formulation for the Force per unit mass (for double jets Black Holes or White Orifices) is given by:

To understand the rest of the Universe, one only need to add the Fundamental Dilator paradigm.

The Fundamental Dilator is a coherence between two deformation states within the 4D spatial manifold. The orientation of the letters in the figure below maps the orientation of the dilator deformation with respect to our 3D Hypersurface. A vertical lettering means that the dilator overlaps minimally with our 3DUniverse (the Fundamental Dilator is quite flat (along the fourth dimension).

 

The Fundamental Dilator can be represented by this diagram:

Figure 1. Balls Diagram for the Proton, represented by a phase of the Fundamental Dilator.

 

Cheers,

MP

 

 

 

The White Orifice

I am sure Stephen Hawking will see the silver lining in the Dark Clouds surrounding this Cylindrical Black Hole…J

It should be an evident truth when one considers the so-called Black Hole with angular momentum that it cannot be an sphere…:) That is, spherical symmetry is not allowed…:) Of course, for different masses and total angular momentum one might have Black Disks…:)

Above a certain mass and angular momentum the obvious Black Hole topology has to be cylindrical..:)

If you remember the correct Law of Gravitation from my Gyrogravity posting:

(3.49d)

(3.49c)

Where C1(m1) and C2(m2) are the charges(masses) traveling at V1 and V2 and c is the speed of light and V2 is the potential at body 2. R points from charge 2 to charge 1.

 

 

Let 1 be a Hollow Cylindrical Black Hole…:) rotating at the speed of light.  

 

 

First let’s consider the matter surrounding the cylinder…:) Let R versor to be perpendicular to the axis of symmetry (rotation). Under those circumstances R.V1 is zero (perpendicular) due to the rotation of the cylindrical mass element 1.

 

The potential sensed by particle 2 (surrounding matter element of mass) is given by:

Where v1 is a tangential velocity at the Cylindrical Black Hole which is equal to the speed of light…or thereabouts…J

 

Under those circumstances it is easy to see that the force acting upon particle 2 has a radial component and tangential component due to the V1.V2 vectorial product. The tangential component makes the surrounding mass distribution to whirl around trying to catch up with the cylindrical black hole. At the same time the tangential speed increases, the radial force decreases. On the other hand, any mass rotating around in the opposite direction is slowed down until the rotational direction matches the cylindrical black hole…J

 

The fun part happens when we analyze what is happening to the mass flow traveling without any angular momentum right along the cylinder axis. For those particles, V2 is perpendicular to V1 (the tangential velocity of the surface of the cylindrical black hole…) The resulting potential is given by:

Or

This force has the interesting aspect of attracting more strongly the falling matter than the matter being ejected on the other side of the Cylindrical Black Hole…J

 

This means that two collimated jets would arise on each side of the Black Hole…J

 

Cheers,

 

MP

In this blog, I prove that 1+1 is not always 2. I am sure that will be used by some to prove that I cannot count… or as a proof of Godel’s theorem..:)

In fact, on those times where something unexpected occurs, the physics behind an identity failure is surprisingly interesting. When one creates a Gravitational Fundamental Dilator, one adds two Fundamental Dilators (a Proton plus an Electron) such that the ensemble spin is zero.  The creation a spin zero dilator is not unlike the creation of a hydrogen atom.

A hydrogen atom interacts with a charge in a manner extremely distinct than the two separated charges that comprises it. The interaction is reduced by a tremendous factor.  This is still not Gravitation.  Gravitation is the interaction between hydrogen atoms and of course it is 10^-36 times weaker than charge-charge interaction.

Currently Science shows no frugality in the explanation of these two interactions.  It describes them as distinct forces.  The reason is historical.  The two interactions were discovered by different people and at different times.

I put 1+1 together to solve this problem.

It will be self-evident from analyzing how the fundamental dilators interact, that they work as a single unit and the dilaton field emanating from a zero spin ensemble formed by two fundamental dilators is almost identical to the resulting from a single one, differing just by a factor of 1.004145342.Quantum Mechanical reasoning like electron delocalization is allowed by not strictly necessary to understand this paradigm.

In fact, it will not be really self-evident but it will take a tremendous amount of grey cells to understand how dilations add or subtract when in phase or in counter-phase.  Let’s hope for the best, but if you cannot, will not understand it no matter how much you stress up your noodle, please feel free to ask questions.

Cheers,

MP

2.3.6 Electromagnetic and Gravitational Dilators Relationship

 

The archetypal Electromagnetic Dilator is represented by the Proton or Electron coherences presented previously. The Gravitational Dilator is represented by a spin zero Hydrogen Atom shown below:

 

Figure 8. Left panel shows two charge particles interacting. Middle panel show how a spin-zero ensemble (Archetypal Gravitational Fundamental Dilator) is created and how the four phases interact with each other.  The left panel shows the Fundamental Dilator or Archetypal Electromagnetic Fundamental Dilator.

The colored phases are flush with the 3D Universe and controls dilator dynamics through the Quantum Lagrangian Principle.  This means that two opposing charged particles would attract each other in each and every phase.  That would happen normally.  During the formation of a hydrogen atom something different happens.  There is a change in spin and a photon carrying the difference in energy and spin is emitted.

If you consider phase 2, the phase for the fat electron would normally be an antiproton (a negative charge or large local compression of the metric). That phase would be in phase with the corresponding dilaton field from the proton’s equivalent phase (positron).

In the spin zero moiety or normal matter, that phase is a proton (a positive charge or large local dilation of the metric) and it will decrease the intensity of the dilaton field from the proton equivalent phase (positron).  Notice that the constructive or destructive interference depends not only upon the fact that the phase is a dilation or a contraction but also on the position of that dilation or contraction.  The Quantum Lagrangian Principle stipulates that the colored phases are always in phase (constructive interference) with the surrounding dilaton field).   That means that if one changes the tunneling sequence (spin sign) the interaction strength will change.

Remember that the dilaton field is sensitive to the four dimensional volume (4D Mass) of the dilator phase.  This means that the dilaton generated by the positron is identical (almost) to the dilaton field generated by the much larger (in 3D mass or 3D Universe overlapping displacement volume) proton.

This means that in terms of 4D Mass or dilaton field intensity, phases 2 and 4 does not matter in normal Matter..:)

The almost perfect interference is at this point considered to be the reason (culprit) for the 0.004145342 in the 1. 004145342 factor relating a fundamental dilator or fat electron 4D Mass to the Gravitational Fundamental Dilator or Hydrogen atom.  The discrepancy in the cancellation of dilaton contributions in the Hydrogen Atom intermediate states is likely due to different elasticities for compression and dilation or nonlinear effects on metric deformation, resulting in a non-zero contribution for the intermediate states.

Another possibility is that this small discrepancy is due to the fact that the Gravitational Fundamental Dilator is an approximation to Matter in general. Matter in general contains Neutrons and that will affect the ratio.

One should remember that there is 4D volume conservation (Energy Conservation) in my theory, that is, despite of the 3D footprint of an electron being 1/2000 the 3D footprint of a Proton, their 4D volumes should be equal. This discrepancy makes this statement not as precise, if it turns out to the true that the discrepancy is due to physical properties (elasticity) of the Fabric of Space.  That would be an exception the complete geometrical nature of this theory.

Just as a reminder, it should be clear that the 4D Mass (4D Spatial manifold cross-section) is associated with the intensity of dilatons generated by dilators and the 3D Mass is associated with inertia within the 4DSpacetime cross-section.

This is another clear statement detaching gravitational mass from inertial mass.

That is an outrageous statement…:) Please feel free to utter your disagreements…:)

Cheers,

MP