The Gravitational Constant G, Taking The Role Of Poincare Stresses Inside Of Particles With A Radius

[Aethelwulf]

Some physicists take it that the idea of Poincare stresses must exist because if they didn't a single electron would blow apart because of the electrostatic forces. A solution can exist to quell this by saying there is a fine tuning inside of electrically -charged particles like an electron where the gravitational force inside of them becomes extremely large.

 

An electro-gravito-magnetic contribution of energy inside a particle of a radius smaller than the classical radius can be found as:

 

 

[math]E_{GEM} = \frac{1}{2}(\frac{4 \pi \epsilon GM^2}{r_s} + \frac{e^2}{r_s})[/math]

 

Where [math]r_s[/math] is assumed smaller than the classical radius [math]\frac{e^2}{Mc^2}[/math] (but still a sphere, and [math]e^2[/math] plays the role of the electric charge.

 

The inertial mass of a system can be thought of as a charge: In all respects of the math which describes these systems, mass pretty much is a charge [math]\sqrt{GM^2}[/math].

 

The charge I once found can be described using some fundamental relationships, important relationships which are believed to be of importance when describing systems under CGM-physics... (CGM-physics is the idea that the universe somehow can be described by the fundamental constants of nature) - in this equation, we have permitivitty and permeability as a part of the structure of the charge itself.

 

[math]\sqrt{G}M = \sqrt{\frac{\pm \alpha \hbar n}{2 \epsilon_0 \mu_0 c}}[/math]

 

The problem of internal stresses gave rise to what was called the 4/3 mass problem. (You can read more on the the Poincare Stresses in electromagnetic theories of mass which is a very good article by wiki) > Some physicists still talk about mass in such ways.

 

 

 

The way you can solve the [math]\frac{4}{3}[/math] mass problem - is by saying there is a contribution [math]\frac{4 \pi \epsilon GM^2}{r_s}[/math] of the gravitational charge which will play the role of the Poincare Stresses - In essence, we must assume that [math]G[/math] takes on extremely large values inside of the sphere which help cancel the electrostatic forces believed to rip a particle apart. We can assume [math]G[/math] takes on an extremely large value by going back to Motz paper where he once admitted it having a large value through

 

[math]G = \frac{\hbar c}{M^2}[/math]

 

In which he states that the gravitational constant is taken to be very large inside the sphere of a particle. Adopting this equation then allows us to ignore Poincare Stresses. but does raise an important question of fine tuning since the gravitational constant must be large enough to cancel out the electrostatic (repulsive force).

 

 

[some extra equations]

 

In parallel to the electromagnetic theories which where taken seriously by physicists many years ago and some still today, we can rewrite it as gravitational charge analogues.

 

The gravitostatic equation of contribution of energy to mass would be

 

[math]E = \frac{1}{2} \frac{GM^2}{r_s}[/math]

 

This keeps as the gravitational analogue of

 

[math]E_{EM} = \frac{1}{2} \frac{e^2}{4 \pi \epsilon R_{classical}}[/math]

 

The contribution of mass in my equation is found then as

 

[math]M = \frac{1}{2} \frac{GM^2}{r_s c^2}[/math]

 

where [math]GM^2[/math] is the squared gravitational charge (Usually with coefficients [math]4 \pi \epsilon[/math].

 

Now going back to a similar process to Wein (1900), the attraction of the gravitational field can be understood as

 

[math]G \frac{\frac{1}{2} \frac{GM^2}{r_s c^2} M}{R}[/math]

Edited August 2, 2013 by Aethelwulf

[Aethelwulf]

I had to confer with Doctor Jack Sarfatti about how much the gravitational constant would need to be to exactly cancel out the electrostatic repulsion inside the electron. Of course, (a duh moment from me) that it would have to be

 

[math]10^{40} \cdot G(Newton)[/math]

 

I knew that the electromagnetic force field was of [math]10^{40}[/math] magnitudes smaller, but I wasn't sure whether this was actually a product of the same magnitude with the gravitational Newtonian Constant...

[Aethelwulf]

Gravity therefore, (and the charge itself associated to the mass of the particle) must be not only taking a large value inside of the particle, but retrospect of the value given above, we are now saying, it is huge!

[Aethelwulf]

So just to write some notation, the resultant equation would be

 

[math] G \approx 10^{40} \cdot G_{inside the radius}[/math]

 

where [math]R < r_s[/math] but still a sphere, so there is an internal structure theoretically we can speak of.

[Aethelwulf]

I just want to write a very simple definition of the Poincare stress from an online source

 

''Non-electric forces postulated to give stability to a model of the electron. Because of the difficulties in regarding an electron as a point charge it is possible to postulate that the electron is a charge distribution with a nonzero radius. However, an electric charge distribution alone is unstable. In 1906 Henri Poincaré postulated unknown non-electric forces, now called Poincaré stresses, to give stability to the electron. Considerations such as these are now thought to be irrelevant(?), as it is accepted that an electron should be described by quantum electrodynamics rather than classical field theory.

 

Read more: http://www.answers.com/topic/poincare-stresses#ixzz2alNC0So2''

 

First of all, the distribution of a charge within a non-zero radius is not invalidated. It has been validated with great success but at the expense of ignoring that particles may actually behave pointlike at a certain threshold. Below this threshold, sphere-like particles which have a radius smaller than your normal classical radius could very well always behave like pointlike particles by those who measure it. A similar rule exists for the 1 dimensionally extended objects of strings (in string theory, these strings are the particles just like an electron). It's sort of not fair to think that a rule exists for string theory particles which clearly are not treated as 1-dimensional objects and that in the more accepted standard model, particles are pointlike and that is the end of the story.

 

I also bolded a misconception in the article quote.

 

''As it is accepted that an electron should be described by quantum electrodynamics rather than classical field theory''

 

Yet there is an overseen problem - that is in physics, we also have semi-classical models. Parts of these models can be described very successfully in non-classical theories, while the same theory can still have elements of it which retain totally classical. So the ''consensus'' that particles in quantum electrodynamics should be described by non-classical means might not be totally the right way to describe nature since you can have very successful theories which mingle classical and non-classical aspects... rather well.

Edited August 2, 2013 by Aethelwulf

[Aethelwulf]

Another problem believing that the electron truly is pointlike is that the equations describing them with a radius going to zero would actually yield an infinite energy when no one is watching the pot boil.

 

The equation which describes this is

 

[math]U = \int_{|r| \leq R} \frac{\epsilon_0}{2} \mathbb{E}^2 d \vec{r} = \int_{R}^{\infty} \frac{e^2}{8 \pi \epsilon_0 r^2} dr = \frac{e^2}{8 \pi \epsilon_0 R}[/math]

 

The equation basically says, if [math]R = 0[/math] then the energy of the electron [math]U[/math] goes to infinity.

 

Infinities are strange things, none have ever been observed in nature, so you may take this to mean that the equation is wrong. But that requires on to be biased that non-classical electrodynamics completely runs the show and that renormalization techniques can solve this problem. Or one can argue, that it is actually indicating particles are not truly pointlike and that is the stance I take in this work.

Edited August 2, 2013 by Aethelwulf

[Aethelwulf]

Is mass the same thing as charge? I approached this question previously.

 

The electric field inside of the electron can be written in terms of the gravitational charge

 

[math]<E> = \sqrt{\frac{3 GM^2}{\epsilon_0 \lambda^4}}[/math]

 

Of course, the gravitational charge has the complete appearance of an elementary charge

 

[math]e = \frac{1}{2\pi} \sqrt{3 \epsilon_0 GM^2}[/math]

 

The electric field then might be part of what we call mass. Only very special cases might we have a mass without a charge, that would be, a mass without an electric charge.

Edited August 11, 2013 by Aethelwulf

[Aethelwulf]

http://scienceforums.com/topic/27053-are-charge-and-mass-the-same-thing/

[Aethelwulf]

What might we mean about an internal degree of freedom noted as the radius [math]\bar{r}[/math] of curvature? A volume of radius is given as [math]\frac{\lambda}{Mc}[/math]. According to [1],

you can relate the Gaussian curvature to the Newtonian Constant [math]G[/math] which assuming, takes on the large value of [math]\frac{\hbar c}{M^2}[/math] and is distributed evenly throughout the volume.

While just recently realizing that Motz had suggested in his paper http://www.gravityresearchfoundation.org/pdf/awarded/1966/motz.pdf that there is in fact a cancelation of the forces. The charge

[math]\sqrt{GM^2}[/math] distributed throughout the volume has a self-energy of order

 

[math]\frac{\hbar c}{\frac{\hbar}{Mc}} = Mc^2[/math]

 

He notes that the electric charge will cancel out the same magnitude recognized as being distributed as [math]\frac{e^2}{Mc^2}[/math]. I independantly came to the idea of the gravitational stresses in the

interior of particles as playing the role of a Poincare stress. I am not quite sure whether Motz was implying such a stress, but it is clear that he saw both the gravitational and the electrostatic forces

to be equal in size. He doesn't seem to point out a problem of fine tuning, but I have said that if this is the case we are surely talking about something which is oddly finely tuned to be in nature.

 

What is interesting is that he proposes an internal degree of freedom for a bound photon particle both traversing a path around a common center. His idea wasn't given in any great mathematical detail, but

he did say it could account for the spin of particles [math]\frac{\hbar}{2}[/math]. A paper which was later written explaining the electron as a photon tied up in a toroidal topology was by a pair of

Glaswegian scientists http://www.cybsoc.org/electron.pdf . Is it possible that all matter is somehow just different forms of trapped light following a curved spacetime inside of the particles? The answer is yes,

but it comes deeper than that. It all comes back to the zitter motion which is found in the quantum mechanics of electrons. This internal degree of freedom has also been associated to an electron clock

http://www.fqxi.org/data/essay-contest-files/Hestenes_Electron_time_essa.pdf?phpMyAdmin=0c371ccdae9b5ff3071bae814fb4f9e9 .

 

In fact, this internal motion could be the presence of bound or free photons. It may answer why the main by-product of annihilating any particle of positive charge with it's antiparticle always reduce to photon

particles. If they are bound in some cases, like the case Motz presumes, then they will follow an orbital path around a common center. They would have defined trajectories simply because they are in a type of

decohered state; for free state photons, we can assume a model like the paper presented previously, where it follows a toiroidal path. The zitter motion of course, can even be something related if not the same thing

as this internal motion. Interestingly, the momentum of the photon [math]\frac{h \nu}{c}[/math] would add to the kind of spin we are dealing with

 

[math]\frac{1}{2} \int \frac{h \nu}{c} d\bar{r} = \frac{\hbar}{2}[/math]

 

where [math]\bar{r}[/math] is the mean radius of transport and [math]\frac{\hbar}{2}[/math] is the sum of the total angular momentum for the photons. In the bound photon model, there is however a fundamental difference

to the free-space case photon following a toroidal topology. The bound pair's angular momentum cancel out and actually give no contribution to the over-all system.

As Motz informs us, that the photon contributes a gravitational mass we should first assume that this is the gravitational charge - a photon in this case will experience a charge if following a curved geodesic.

Since this would simply be the gravitational charge divided by the compton wavelength, this is given as [math]\frac{GM^2}{\lambda}[/math]. Motz notes that this is the same thing as:

 

[math]GM^2\frac{\nu}{c}[/math]

 

he states that since the energy is [math]\hbar \nu[/math] then from the expression [math]GM^2\frac{\nu}{c}[/math] we find the usual relationship [math]GM^2 = \hbar c[/math] and takes this as meaning the gravitational

field inside of the particle is responsible for the existence of the photons. If this is true, the gravitational field [math]\Gamma[/math] must in some way couple to the photons: we would have graviphotons (*) bound by

their respective field. Suppose we have a ''free'' photon, bound in a topological knot, it must couple to the gravitational field by means of following the geodesic topology and it becomes itself simply an

excitation of the gravitational field. However, it will be assumed that the spin of the entire system is important when thinking about how the internal graviphoton field interacts with the external gravitational field.

This assumption is made because when talking about charges and spheres, we usually take for granted that only a rotating sphere experiences an electromagnetic charge.

 

(*) I say they are effectively a graviphoton, because the gravitational forces are responsible for the existence of the photon, the gravitational field is extremely large so the photon must have a gravitationally-induced

flux.

 

This means, to try and get a complete picture of the model, that the graviphoton has a dynamic property which connects it to the gravitational field - the charge happens because the entire system is rotating. It is

analogous to the definition of electric charge: that is, that particles like an electron only experience a charge when motion is present. Well I think the same needs to be required in this model.

 

The geodesic spoke of in which our gravitationally-induced photon is moving in, can be thought of a line element (Weyl). Motz recognizes how important it is to talk about a charge if a photon is following a curved path in

space http://www.gravityresearchfoundation.org/pdf/awarded/1966/motz.pdf . The line element is

 

[math]ds^2 = \frac{dr^2}{(1 - \frac{2GM}{c^2 r}) + \frac{G}{c^4} + \frac{e^2}{r^2}}[/math]

 

The path of a photon is well-known to be [math]ds = 0[/math] but for a bound system, you would get two values of the inverse radius. In our single photon model, albeit simpler, we must understand then in our former case.

In this case, it is also much easier to think of it trapped in a toroidal topology. A toroidal structure is given by a length

 

[math]\bar{r} = \frac{\lambda}{4 \pi}[/math]

 

The internal wavelength of the particle should have a correction order [math]\frac{\alpha}{2 \pi}[/math] when appropriate. A coupling of the system to the gravimagnetic forces are achieved by a cross product

 

[math]\sqrt{G}M\frac{v}{c} \times \frac{2 \omega c}{\sqrt{G}} = \sqrt{\frac{e^2}{4 \pi \epsilon_0}}\beta \times \frac{F}{\sqrt{G}M}[/math]

 

You get the coupling field [math]\frac{2 \omega c}{\sqrt{G}}[/math] by obtaining the Coriolis field [math]-2M(\omega \times v)[/math] and dividing it by the gravitational charge [math]\sqrt{G}M[/math].

 

The average of the electric field is obtained from recognizing there being motion attributed to the system, where we have the gravitational charge divided by the product of the mean transport of radius and

the permittivity of the internal degree's of freedom. This has a very important physical meaning, the permittivity is responsible for the resistance there is to form the electric field by the photon toroidal topology.

The result is of course, the average of the electris field inside of the particle

 

[math]<E> = \sqrt{\frac{GM^2}{\epsilon_0 \frac{\lambda^4}{4 \pi}}}[/math]

 

Keep in mind that the mean radius of transport is in fact taken as the analogue of a geodesic found in General Relativity, the topology is the toroidal structure characterized by the length

[math]\bar{r} = \frac{\lambda}{4 \pi}[/math]. It is from here one might if bold enough make some assertions, others a bit easier to imagine than the other ones. As Motz first realized, the source of the gravitational field

for a particle of mass was the gravitational charge [math]\sqrt{G}M[/math]. The electric field inside of the particle is dynamically-related to the distribution of the charge [math]\sqrt{G}M[/math] throughout the length parameter.

 

Effectively one can say, that if the gravitational charge goes to zero, then so does the resulting internal electric field. We no longer would have a photon in a toroid bound by the gravitational field. Just as before however, we must

assume that the average electric field inside our particle

 

[math]<E> = \sqrt{\frac{GM^2}{\epsilon_0 \bar{r}^4}} = \sqrt{\frac{GM^2}{\bar{r}^4(\mu_0 c^2)^{-1}}}[/math]

 

Also takes on very large values for [math]G = \frac{\hbar c}{M^2}[/math]. The electric field inside the particle just becomes another side of the gravitational field which is induced by the motion of our photon following a tight

curvilinear spacetime. There is no question that the Newtionian Constant remains a constant at this magnitude inside of the particle, but there is far as I am aware no reason why different topological knots in spacetime can occur.

A toroid just appears to be a very convenient model but it could be one of many different kinds of geometry. This would mean that the electric field varies for different sizes of particles since it is proportional to changes in the

geodesic path! The changes could account for the heirarchy of mass - that is that the gravitational charge created by the photons toroidal topology would occupy more space for an increasing radius and so should increase the

volume in which the internal electric field contains inside of our system. This is common sense if we thought about inertial energy being equal to the mass of a system and see a relationship in

 

[math]\Delta E = 2 \pi f \Delta \lambda[/math]

 

Where a change of the overall energy depends on changing the length (or geodesic of our photon).

 

Different sizes of particles would then just be different photon paths in extremely confined spaces where it's observed inertial mass is really just the motion of the

particle/particles involved (Not to confuse the reader, but we are talking about a single-particle state. Bound states may even occur in nature).

 

There really isn't anything wrong either assuming that an electric field can be proportional to the gravitational charge. Even in the special case of the Neutrino, Motz can model it as a bound pair of photons in a strong gravitational field.

 

There is however a constraint on the mean radius of transport - that is, that the maximal radius is [math]\frac{\lambda}{2}[/math] yet we have to use a correction parameter

 

[math]\frac{\alpha}{2 \pi}[/math]

 

where [math]\alpha[/math] is the fine structure constant. Using the relationship [math]GM^2 = \hbar c[/math] (which is the quantization of charge), we know that the uncertainty between the internal energy of the system is related to time as

 

[math]\Delta E t \leq \Delta E \Delta t \leq \frac{\hbar}{2}[/math]

 

so that

 

[math]\Delta E \leq \frac{\hbar}{2t} \leq \frac{\hbar c}{2 \ell}[/math]

 

which implies a relationship

 

[math]\Delta E \leq \frac{GM^2}{2\ell}[/math]

 

A correction to this inequality must be made then where the length can be considered [math]\frac{\lambda}{2}[/math],

 

[math]\Delta E \leq \frac{GM^2}{\lambda}[/math]

 

The physical meaning of this is that the internal energy flux is bound by the maximal uncertainty in the mean transport of radius (defined by the compton wavelength/2) but we have a correction order. As the paper http://www.cybsoc.org/electron.pdf recites, the limitation

of the speed of light means that only paths within the radius can provide a contribution of inertial energy (mass) to the system. The uncertainty relationship of

 

[math]\Delta E \leq (\frac{GM^2}{\lambda} = \frac{GM^2}{\alpha \lambda_C})[/math]

 

Shows us that the energy depends on the varying uncertainty of the compton wavelength up to a maximal radius of transport. The energy is also therefore conserved through the fine structure constant if one applied the correction [math]\lambda = \alpha \lambda_C[/math] ref: http://www.cybsoc.org/electron.pdf. So not only does the electric field vary proportional to changes in the geodesic of the confined photon's path but also the energy of the system is proportional to the path(s) also.

Edited August 12, 2013 by Aethelwulf

[Aethelwulf]

Now... to zitter motion. As it was said in the first intelligible paper of a photon model of an electron (ref 1.) http://www.cybsoc.org/electron.pdf states that there are striking analogies of the Dirac solution of equations describing zitter motion (whom later) David Hestenes showed that it could be considered an ''internal dynamic'' clock. The instantaneous velocity eigenvalues [math]\pm c[/math] can be pictorially imagined as the two interlooping path which the photon takes in the toroid. They are actually light-like helices of [math]\frac{\lambda}{2 \pi}[/math] which defined the maximal degree of freedom for the mean radius of transport. I found a way we can talk about it mathematically.

 

The system of coupled equations describing a particle system comes in the form

 

[math]\dot{u} = \frac{1}{r} + \frac{q}{M} F \cdot u[/math]

 

[math]\dot{p} = F \cdot u + \nabla \phi[/math]

 

[math]\dot{S} = u \wedge p + \frac{q}{M} F \times S[/math]

 

As Hestenes points out in his paper http://www.fqxi.org/data/essay-contest-files/Hestenes_Electron_time_essa.pdf?phpMyAdmin=0c371ccdae9b5ff3071bae814fb4f9e9 the zitter motion radius is given as

 

[math]r^{-1} = (\frac{2}{\hbar})^2 p \cdot S[/math]

 

where the beautiful mathematics is revealed where one notices the potential depends on the charge to mass ratio

 

[math]\frac{e}{M} S \cdot F[/math]

 

What is interesting to note here, is that the fine structure constant can be defined as

 

[math]\sqrt{\frac{e^2}{4 \pi \epsilon GM^2}} \alpha[/math]

 

which is a deeper way of understanding the potential involving the elementary charge as a ratio to the gravitational charge

 

[math]\Phi = (\sqrt{\frac{e^2}{4 \pi \epsilon GM^2}} \alpha) S \cdot F[/math]

 

 

To note, [math]F[/math] is the chosen notation by Hestenes describing the electromagnetic field which in mathematical jargon, is a bivector. You can see this from his work on spacetime algebra http://geocalc.clas.asu.edu/pdf/ZBWinQM15**.pdf .

Edited August 12, 2013 by Aethelwulf

[Aethelwulf]

In the toroid model of ref 1. the fine structure is written as

 

[math]\alpha' = (\frac{q}{M})^2 \alpha[/math]

 

we will state

 

[math]\alpha^{\dagger} = \sqrt{(\frac{q}{M})^2} \alpha[/math]

 

which means the potential can be rewritten as

 

[math]\Phi = \alpha^{\dagger} S \cdot F[/math]

Edited August 12, 2013 by Aethelwulf

[Aethelwulf]

The ability to see the potential of zitter motion as dependant on the fine structure constant [math]\alpha^{\dagger}[/math] should not come at a surprise since I have stressed previously that

 

[math]\frac{e^2}{c} = \pm \alpha \hbar[/math]

 

as suggesting that the angular momentum is conserved through the fine structure constant, as we see here

 

[math]\alpha^{\dagger} S \cdot F[/math]

 

The spin vector [math]S[/math] is also conserved through the fine structure constant. Not to forget that generally-speaking, the charge itself is made from the fundamental ingredients

 

[math]e = \sqrt{\frac{2 \alpha \pi \hbar}{\mu_0 c}}[/math]

 

from this, one can speculate the fundamental ingredients which makes the inertial gravitational charge

 

[math]\sqrt{G}M = \sqrt{\frac{\alpha \hbar}{2 \epsilon_0 \mu_0 c}}[/math]

 

also conserved the angular momentum component in such a way.

[Aethelwulf]

In the proper frame, the phase of both the orbital rotation and the internal photon is incidently

 

[math]\phi = \omega t_0[/math]

 

ref. http://www.cybsoc.org/electron.pdf

 

where [math]t_0[/math] is the proper time where

 

[math]t_0 = \gamma(t - \frac{vx}{c^2})[/math]

 

The phase of the internal photon can be written as

 

[math]\omega t_0 = \omega \gamma(t - \frac{vx}{c^2})[/math]

 

The gravitational coupling of the geodesic path of the internal confined photon is related to the phase and the gravitational fine structure constant as

 

[math]\alpha_G = \frac{GM^2}{\hbar c} = (\omega t)^2[/math]

 

thus naturally

 

[math]\sqrt{\alpha_G} = \sqrt{\frac{GM^2}{\hbar c}} = (\omega t) = 2 \pi f \gamma(t - \frac{vx}{c^2})[/math]

 

Therefore the phase of the photon appears as a form of the gravitational coupling constant.

Edited August 12, 2013 by Aethelwulf

[Aethelwulf]

Is there actually a direct relationship such that

 

[math]\alpha_G \equiv \omega_C t_0[/math]

 

... ? Yes the phase of the photon can be attributed to a special case where the revolution of the compton angular frequency occurs within planck time scales. We might even expect this special case to exist as you confine the photon to smaller and smaller spaces. Doing so, you are restricting the time in which a quantum action can take place.

Edited August 12, 2013 by Aethelwulf

[Aethelwulf]

Finding relationships like this with the fine structure constant can be insightful, telling us that there is a deep meaning behind the dynamics at work and even helps us see hidden meaning in some dimensional analysis.

 

For instance, the ratio of the electromagnetic force to the gravitational is given as

 

[math]\frac{\alpha}{\alpha_G}[/math]

 

by working in natural units, [math]4 \pi G = c = \hbar = \epsilon = 1[/math] the constants become

 

[math]\alpha = \frac{e^2}{4 \pi}[/math]

 

and

 

[math]\alpha_G = \frac{M^2}{4 \pi}[/math]

 

This results in the famous charge to mass ratio

 

[math]\frac{e^2}{M^2}[/math]

 

We can actually find this importance all throughout physics. A particular one of importance is the identity

 

[math]F = Mg + e\mathbf{E} + ev \times \mathbf{B}[/math]

 

The acceleration of a vector [math]a[/math] is just [math]\frac{F}{M}[/math] which results in an equation of motion

 

[math]a = g + \frac{e}{M} \mathbf{E} + \frac{e}{M} v \times B[/math]

 

You can perhaps see why I chose this particular equation of motion, it has the mass to charge ratio as coefficients to the electric and magnetic fields.

 

In a loose kind of way, you can call it a square root of the fine structure

 

[math]a = g + \sqrt{\alpha}( \mathbf{E} + v \times B )[/math]

 

(You've gotta be careful to tweak the right units) but you'll get the just. Even the ratio [math]\frac{v^2}{c^2}[/math] can be attributed to the fine structure constant!

Edited August 12, 2013 by Aethelwulf

[Aethelwulf]

Suppose we can talk about the electric flux and magnetic flux inside a particle of an area enclosed by a sphere (also known as the horizon of the mean radius of transport) we might have

 

[math]\Phi_e = \frac{e^2}{\epsilon_0}[/math]

 

and

 

[math]\Phi_m = \frac{\phi_{0}^{2}}{2 \mu_0}[/math]

 

knowing that

 

[math]c = (\sqrt{\epsilon_0 \mu_0})^{-1}[/math]

 

[math]\hbar = \frac{\phi_0 e}{2 \pi}[/math]

 

and the relationship describing fine structure

 

[math]\alpha = \frac{1}{2} \frac{e}{\phi_0} \sqrt{\frac{\mu_0}{\epsilon_0}}[/math] (1)

 

One can meld these equations together to reach two interesting relationships

 

[math]\alpha = \frac{1}{2 \sqrt{2}} \sqrt{\frac{\phi_e}{\phi_m}}[/math]

 

and the square of the gravitational charge

 

[math]GM^2 = \frac{\sqrt{2}}{2 \pi}\sqrt{\frac{e}{\epsilon_0}\frac{\phi_{0}^{2}}{2 \mu_0}} = \frac{\sqrt{2}}{2 \pi} \sqrt{\phi_e \phi_m}[/math]

 

Let's just quickly explain what the electric [math]\phi_e[/math] and magnetic flux [math]\phi_m[/math] are. Doing so might make us realize that the gravitational charge is manifestly an electromagnetic property (something we have been hinting at for quite a bit now).

 

In short and simple terminology, the electric and magnetic flux is the amount of electromagnetic field which penetrates a given area... in our case, we are assuming a fundamental length of transport within an area.

 

The point however of the two equations obtained revealing the fine structure constant and the gravitational charge is that to solve for them in terms of [math]\phi_e[/math] and [math]\phi_m[/math] that the ratio and the product become independent of unit representation. According to the author

in the reference below (1), he claims that this is a verification that both [math]\phi_e[/math] and [math]\phi_m[/math] have the same dimensions.

 

However, the author may not have sufficiently known the full interpretation of his equations since there is no mention of the gravitational charge through equivelance [math]\hbar c = GM^2[/math]

 

[math]GM^2 = \frac{\sqrt{2}}{2 \pi}\sqrt{\frac{e}{\epsilon_0}\frac{\phi_{0}^{2}}{2 \mu_0}} = \frac{\sqrt{2}}{2 \pi} \sqrt{\phi_e \phi_m}[/math]

 

Thinking of the gravitational charge as something to do with electromagnetic flux is not a new approach in this work, since we have attempted to describe the electric field as related proportionally to the gravitational charge before. But thinking of it in terms of the fluxes is a new approach.

 

 

 

(1) - http://arxiv.org/vc/hep-ph/papers/0306/0306230v2.pdf

Edited August 12, 2013 by Aethelwulf