Tuesday, September 18, 2012

The ABC Conjecture

The ABC Conjecture and The Hypergeometrical Universe

The abc conjecture (also known as Oesterlé–Masser conjecture) is a conjecture in number theory, first proposed by Joseph Oesterlé (1988) and David Masser (1985) as an integer analogue of the Mason–Stothers theorem for polynomials. The conjecture is stated in terms of three positive integers, ab and c (whence comes the name), which have no common factor and satisfy a + b = c. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d is rarely much smaller than c.
What could the identity
                                                   a+b=c
where a,b,c have not common factors have to do with a Theory of Everything..:)
a,b, and c are said to be COPRIMES
In number theory, a branch of mathematics, two integers a and b are said to be coprime (also spelled co-prime) or relatively prime if the only positive integer that evenly divides both of them is 1. This is the same thing as their greatest common divisor being 1.
This equation and conjecture reminded me the process I went through when I create my Hyperon Family Assignment.  In the Hypergeometrical Universe Theory, all particles, isotopes are multiples of a Fundamental Dilator intervened by one of a couple of Transmutational Dimensional Notes.  These Transmutational Dimensional Notes map closely to Neutrinos, as the electron antineutrino in the Neutron decay.

For me, the ABC equation (Conjecture) within the Hypergeometrical Universe Theory represents the decay equation for particles. Integer number are represented by multiples of the Fundamental Dilator.

In any other theory where there isn't a single building block (The Fundamental Dilator), this statement wouldn't make any sense.

In the Standard Model, due to the complexity of the ad-hoc quantum number zoo, particles differ too much to be placed in a simple abc equation that regulates the composition of new particles.

Of course, since I am modeling a finite and small number of Hyperons, I didn't have to face the tremendous hard task of proving the ABC Conjecture.  I believe it has a position in the Physical Sciences in the description of Particle Decay or on a positive note, Particle Creation.  All particles should follow the ABC equation and be coprimes in term of Fundamental Dilator Moieties.

Cheers,

MP


Illuminati Puzzle Solution

Life is demanding and I still owe you the equation for all the particles and the solution to the Illuminati puzzle I created on the Verbum Significatium Posting.

A bright fellow/lady discovered the solution to this Illuminate Puzzle below:


The solution is: ENERGY FROM COLD

He asked me if this was some kind of Cold Fusion.  I told him not.

In my theory, Neutrons plays a very important role. They are first excited level of space deformation.

In my theory when matter collapses on itself to form a Black Hole, they form a neutron crystal with finite size and well defined compaction level  The distance between neutrons is defined by the dilaton wavelength (wavelength = Compton wavelength of a Hydrogen Atom).

The "force" that bring particles together (electromagnetism for charge particles), gravitation for neutrons goes to zero when they reached a level of compaction that brings them at distance equal to the Compton Wavelength of an Hydrogen atom.  There isn't any singularity in the interaction between dilators, so there isn't anything that requires the level of speculation that a Black Hole conjures in the impressionable minds of the Relativistic Scientists..:)

Of course, if the crystal is perfect and positions well defined, that means that the entropy within the volume of the "Black Hole" is zero, and all the entropy is in the surface of that neutron crystal.

That should come up as a nice touch considering that that is the expectation from current Black Hole Models.

Like in any other crystal, the Black Hole (made of a perfect neutron crystal) contains domains. In this case, the domains are made up by spin domains, not unlike a ferrimagnetic Yttrium Iron garnet of my childhood..:)

As the Black Hole cools down, the wavefunction of these neutrons extends into opposite spinning domains creating the conditions for annihilation and relaxation of the space.

Matter should simply disappear in a flash of Gamma Rays, leaving no trace other than the kinetic energy freed from the disappearance of the Gravitational Field.

I believe this is the mechanism of Gamma Ray Bursts.  They should happen when neutron domains becomes cold enough to annihilate themselves, leaving just the Gamma Ray (coherence between flat metric and deformed metric states).

Cheers,

MP


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