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Author Topic: Possible Mathematical Description of Photon Flux into Matter using GEM equations  (Read 4464 times)

Offline Mr. Scientist

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Abstract of Idea:

It may be that given a certain energy density, the gravitational field couples with the electromagnetic field and literally fluxes into solid matter. We know in nature this happens all the time so there needs to be a sufficient theory between the gravitational field with is what gives particles their gravitational charge (that is mass) -▼φMg=Fg (from Lecture Notes be Sean Carrol) and that which can transmutate from pure electromagnetic energy ΥΥ → e+e- (two gamma production decay into an electron-positron pair.) 
 
This means that GEM-like equations would need to be considered. In order to do this, i required the following work, in which i think i have succesfully described a plausible evaluation/theory of how the process ΥΥ → e+e- could transpire - in compliments of vern :)

The Mathematical Conjecture of GEM-related/similar Equations

For particles before transmutation or (v = c) we can allow the derived equation (from many hours of contemplation):

p(v/c)=(-▼φ*gtβ) 1

Where φ* is in fact a gradient which measures the energy up to a critical value, so i have also defined it within its own self to have ∂φi=φ(i+1). The critical value or expectation value leads to the flux into mass. If φ* reaches its maximal state which can allow the transmutation to occur, then (v ≤ c) - notice that it is either less or equal. This would mean that the wave function does not necesserily mean that when it reaches the perfect stage for mass-creation that it always will.

Eg(v/c)=(-▼φ*gctβ) 2

Since (c ≠ v) is not true in this form, then the correct way to show the equation is:

Eg(v/c)=(-▼φ*gvtβ) 3
 
So in equation 1, we have a description of the related units p, v, g and t, describing the conjectured interpretation of a massless radiation (or atleast can describe it). Equation 2 strictly forbids massless radiation by the signature of Eg (which is gravitational energy). It has to be gravitational because its under the influence of (-▼φ*).

For equation 1 to flux into matter, the matter which is described by equation 3 depend again on the energy state of density of φ*. To measure the critical density, you can express it as an integral with a boundary condition given as Ω. So the flux equation in its fullest form is provided as:

............<∫Ω|i|>
Eg(v/c)=(-▼∑ V(φ*)gvtβ) 4
...............n=1

Here, it's slightly different, this time V(φ*) relates to the potential energy density , which is required when summation is involved, because nothing is determinate yet. So (φ*) is an energy scalar field and V(φ*) is the potential energy scalar field.

Note also, that the uppercase summation limit has the form of an amplitude statistical probability. It's quite common in physics to use this method when calculating the statistics of any eigenvalue. When it reaches the critical value, summation stops at (∫Ω|i|=n_f) and pure energy turns into matter, because of the two transformations given on the right hand sides of equations 1 and 2, expressioned as:

p(v/c) - describing photon energy to

Eg(v/c) - describing gravitational energy (or also inertial energy due to the weak-equivalance principle)

The two transformations though did depend on the energy density transformation of V(φ*). In effect, V(φ*n) contributes to the feasibility of a mass occuring if it reaches a critical density with a minimal energy expectation of 1022KeV, or expressed by a gamma-gamma interaction ΥΥ. It is conjectured that this is considerable enough to call it a high-energy result within the parameters of φ (the gravitational field).

This would inexorably mean that the energy density of V(φ*) decreases as matter speeds up (M_0c^2) - however, this means that as a test particle slows down as V(φ*) increases. This is the perfect ratio in which demonstrates how the decrease of speed from c to v implies on an inertial mass, in accordance with the summation of V(φ*n), concluded itself as an expectation result.

The work which led me to the hypothesis/conjecture above, derived from the results below. I was investigated possible GEM equations (equations which can succesfully describe dimenionsional relationships between gravity and electromagnetism. I came to this first of all:

E=Fq

F=Mg

rearrange

E=Mgq

where Eg is energy due to gravity and q is charge. Then i dimensionally-configured the equation:

-▼φMgvtβ+(v√ћ(c/G))=√Mgq(E/c-p) 5

From this geometric look, it yielded an inertial energy E_0 since we have the mass due to gravitational acceleration on the left under the field -▼φMg.

From here, i defined two values, the first equation takes on a small quantized value (the small value is related to the quantized mass charge of ћ=GM/c in natural units, and the second takes on an extremely large value by rearranging ћc=GM:

(Vћ(c/G))=Mgq(E/c-p) 6

(Vћc)=GMgq(E/c-p) 7

The relation between the electromagnetic force can be given as:

M(M/q)g(E/c-p)=(Eg + v X Bg)Mvћ(c/G) 8

Since the left-hand side of equation 5 given as -ΔφMgvtβ is superficially similar to the equations p(v/c)=(-▼φ*gtβ) and Eg(v/c)=(-▼φ*gctβ) i decided to use them in conjunction of the relative state of φ.
« Last Edit: 29/10/2009 21:57:31 by Mr. Scientist »


 

Offline Mr. Scientist

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A lot of times in this text i referred to equations by numbering them. Some of the text will confuse you because for some reason they never showed up.
 

Offline Mr. Scientist

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There, fixed it.
 

Offline Vern

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I guess I've been out of school a little too long. :) I can't follow the maths.
 

Offline Mr. Scientist

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In theory, something happens to the innate structure of a single quantum of light whenever there is sufficient energy local to transmutate the energy into matter. How the process happens is uncertain, but i can propose a mechanism.

In normal decay processes, we associate the decay of particles to the electroweak force. Gravity is in there somewhere, buts its effects as a force is very small compared to the electroweak unfication, so gravity is often never considered on the scale of particles.

In attempt to show some relation between the transmutation of photon energy into matter with that of which causes matter i.e. the gravitational field given by φ*. The first equation can describe a photon:


Though sometimes when i am in a rush i tend to hurry and make a few mistakes (also when you cut and paste your mistakes and reuse them :) ). Though they are pretty minor:


(-▼φMgtβ)+(v√ћ(c/G))=Mgqc√(E/c-p)

This equation just has components of energy and momentum without being too distracted with the quantum gravitational field. If the radiation is massless, then the equation derived from above:

p(v/c)=(-▼φ*Mgtβ) 1.

Where Fgt=Mgv and M=0 due to v=c.

The idea is that when φ* gets sufficiently high enough, the innate change from photon energy to a gravitational energy can be re-described:

Where normally in relativity we have the relationship: E(v/c)=pc thus:

Eg(v/c)=(-▼φ*Mgvtβ) 2.

So equation two can satisfy the change into a gravitational energy in equation 2 if there is a change in the gravitational field.
« Last Edit: 01/11/2009 19:38:18 by Mr. Scientist »
 

Offline Vern

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Transmutation seems like the magical changing of one thing into another. When I try and visualize that process step by step it just doesn't work. I suspect there is not a moment of magic when one thing becomes another. It is much more simple just to trap a photon in a local pattern and presto; no magic; but we  have mass.
 

Offline Mr. Scientist

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Transmutation seems like the magical changing of one thing into another. When I try and visualize that process step by step it just doesn't work. I suspect there is not a moment of magic when one thing becomes another. It is much more simple just to trap a photon in a local pattern and presto; no magic; but we  have mass.

Not quite by magic. It may seem like that, but all the mechanisms are already there. We know that mass depends on the gravitational field (work by Nordstrom), so the appearance of matter from just a form of energy means that there is a mechanism which is changing the innert properties.

In this case, we are falling towards using the gravitational field itself to manifest longer-lived fluctuations when there is a certain amount of energy involved. The process is no more magical than expecting a fermion electron to decay into a photon and a neutrino.
 

Offline Vern

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Quote from: Mr. Scientist
The process is no more magical than expected a fermion electron to decay into a photon and a neutrino.
A fermion electron; I guess you mean one of the extra massive electrons; need only break the bonds of its trap and speed on its way in a straight line. To me those extra massive electron like particles are simply temporary patterns of energy that almost entrap themselves. But the frequency is not just exactly right for entrapment, so they come unglued. Neutrinos are a prediction of Quantum theory. They probably don't exist.
« Last Edit: 01/11/2009 17:12:36 by Vern »
 

Offline Mr. Scientist

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No just normal electrons; they are from the family of Fermion Particles :)
 

Offline Vern

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I don't know how to get a normal electron to decay without getting it close to a positron. In that case I think you get two gamma ray photons of .510 MeV each. I don't recall a neutrino in the mix.

Edit: Yeah; I guess it would be hard to imagine an electron that was not a Fermion.
« Last Edit: 01/11/2009 18:22:06 by Vern »
 

Offline Mr. Scientist

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I only said an electron decay because i had read this paper recently: http://arxiv.org/abs/hep-th/0312325
 

Offline Vern

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Okay; I see by the paper that they were just making a point and that no electron decay was observed.
 

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