Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

Astro · 2010-05-04 00:40:30

Universally, its known that charge q is related to mass M and the magnetic moment μ of a particle by:

$\mu=g \frac{q}{2M}S$

Where S is the spin of the particle. The g-factor is dimensionless also.

In Guassian cgs units the Plancks Charge has a very neat description:

$P_c=\sqrt{\hbar c}$

Note $\hbar c=GM^2$

Where ћ is planks constant, c is the speed of light, and qp is the Planck Charge. Or it can be expressed as

$P_c=\frac{e}{\sqrt{\alpha}}$

Where e is the elementary charge and α is the fine structure constant. The total magnetic moment in a volume V is given by:

$\mu = \int \Phi(r) d(v)$ .

where φ is the magnetization field.

$Ev=1/2\hbar c \omega$

E ~ ground frequency of energy per planck space

w ~ frequency

I first identify what i call the Newtonian Gravigyro Parameter as √Gw. It is seen as similar to the gravitational parameter for a mass GM.

We obtain the gravigryro parameter as;

$\sqrt{\frac{-\hbar \partial_t G}{c}}=\sqrt{G \omega}$

and $GM$ is the gravitational parameter.

This is because of the famous Planck Relation of ћc=GM². The gravigyro parameter can have an appearance in a certain kind of wave equation, given here as:

$\frac{\partial^2 \psi}{\partial x^2}=\alpha \frac{\partial \psi}{\partial t}$

This famous equation has a value for αw as given

$k^2=i \alpha \omega$

(it is interesting to note that k² is also equivalent to μεw² for a transverse wave where ε is the permittivity of free-space. The permeability is usually denoted as μ. The first is an electric constant. The second is a magnetic constant. Remember, Transverse waves can be polarised because the oscialltions are perpendicular to the direction of energy transfer).

With our value for k identified, i issue the equation

$\frac{\hbar^2 k^2}{2M}c \psi=G \omega M^2 \psi$

The quantity on the left as Gw is a magnitude of the ground state of the gravigryo parameter. This means that equation [1 which supposes that per planck space there is a lowest energy of E'v=1/2ћcw.

Knowing this, we take into consideration a wave function this time for the ground state of the parameter as; EvΨ=√ћcwΨ = (√ћ²k²/2M)cΨ [8. But this is a cumbersome expression because of the square root, so we shall continue with the square of this result. Quantizing [8 leads to:

$Ev \psi=(\sqrt{i\hbar \frac{\partial}{\partial t}})^2 c \psi$ [9

Which simplifies to:

$Ev \psi=-\hbar \frac{\partial}{\partial t} c \psi$ [10

It must be noted that this equation is designed for the identity of v=c. For v
If EvΨ=ћwcΨ has a sucessful transition phase from energy to mass, then the v=c term cancels out. For a sucessful cancellation of any v=c term, the equation we will be focusing on for describing inertial mass will be iћ²•∂/∂t•μεw²Ψ=iαћ²w²Ψ. The components of the equation will be described soon.

The equation has an inertial energy E=Mc² and so describes a flux of energy into mass at the square of the magnitude of even a ground state frequency. Analytically, equation [9 as a wave equation has a density over all possible frequencies and polorization states, is given as:

$W=\int \box \phi (\omega) d \omega$

Where $\box$ is the d'Alembertian and so has dimensions of density. The integral is given with a possible restriction of a boundary in the frequencies given, so is a measure of mass [1]. At such a temperature, the gravitational potential gradient φ has a chance in theory to satisfy an appearance of a gravitational mass density. This would be the phase transition i spoke about, and in such a case, the v=c rule cancels out in the equations, and we have only an expression for inertial mass as (ћ²k²/2M)Ψ.

The permeability and permittivity of the vacuum is related to the energy given as:

$-\hbar^2 \frac{\partial}{\partial t} \mu \varepsilon \omega^2 \psi=iaw \hbar^2 (\frac{Mc^{2}}{\hbar}) \psi$

where k²=μεw² and <Ψ|iћ•∂/∂t|Ψ>=ћw known as the energy operator.

Equation 13 would make sense for the inertial mass description since we can invoke the inertial energy description of Mc². All imaginary references are cancelled, so it can be applied to real fields. The equation does not finish there. It has a component left for explanation, and this is the electric and magnetic constants (μ and ε).

They are unified in Maxwells equations as the phase velocity of an electromagnetic wave in a free vacuum με=1/c².

This means that the identity of με on the left hand side of equation 14] can be substituted for 1/c²;

$-\hbar^2 \frac{\partial}{\partial t}\frac{1}{c^{2}} \omega^2 \psi=i \alpha \omega \hbar^2 (\frac{Mc^{2}}{\hbar}) \psi$

And so the equation can now also determine the phase velocity of electromagnetic radiation. This equation also has lined up a possible description of the in phase and out phase response, where the permeability is considered as a function of the frequency, and so, can allow a complex description of the permeability to exist.

Last edited by Astro (2010-05-14 06:53:58)

Astro · 2010-05-05 01:44:50

There are skeptics here that post at this forum, is there not?

This place is quite quiet.

Astro · 2010-05-07 04:28:05

ref [1] - I refer you to the Springer Link journal paper, from the Rutherford Observatory, Columbia University, New York, N. Y by L. Motz, published under the Italian
Physical Society, and the summery was thus described;

''Summary In a previous paper (referred to as I in the text) it was shown that the Weyl principle of gauge invariance leads to the relationship $Gm^2 =\hbar c$ for a particle of inertial mass $M$ obeying the Dirac equation, whereG is the Newtonian gravitational constant. Instead of interpreting this equation to mean that $G$ takes on the extremely large value $\hbar c/m^2$ inside a particle like an electron (as we did in I), we now write it in the form $Gm^2/c = \hbar$ and treat it as a quantization condition on the square of the gravitational charge $\sqrt{Gm}$ . We show that this same quantization condition can be obtained from an angular-momentum component in the general-relativistic two-body problem as well as from the Machian definition of inertial mass in a rotating universe by using the Dirac-Schwinger procedure for quantizing charge. From this quantization condition we now deduce that the fundamental particle in Nature (the uniton) has an inertial mass equal to about $10^{-5}g$ . The possibility of using the uniton to shed light on the mystery of the « missing mass » in the Universe is discussed. Other cosmological implications of the uniton are also discussed and it is suggested that unitons can clear up the solar-neutrino discrepancy.''

Last edited by Astro (2010-06-15 17:29:47)

Astro · 2010-05-08 05:26:48

The gravitational charge of a moving particle in terms of its interaction with its respective gravitational field $\Phi$ can be thought of in terms of $F_g=-\nabla \Phi M_{0}g$ where this time, $Mg$ is taken or interpretated as a gravitational charge-mass. Since a photon has no mass, its total gravitational charge (or) the gravitational field acting on the photon must be so tremendously weak. If the photon did have a gravitational charge, it would correspond to an inertial mass of about $10^{-51}$ grams, which is tiny. This is the recent experimental upper-limit for a photon with a mass.

A photon can be effected by gravity however, because it has a momentum associated as $E=pc$ , and so generates its own curvature as it accelerates though spacetime. The curvature it creates can couple to the external gravitatonal field and so can follow bent paths in spacetime.

The subtle interconnectivity of a photon with a gravitational field is one way of stating that the gravitational field potential has no intrinsic mass description for them, and so have no gravitational charge influenced by such a field.

Last edited by Astro (2010-05-08 05:27:26)

Astro · 2010-05-09 12:10:51

$\sqrt{\frac{-\hbar \partial_t G}{c}}=\sqrt{G \omega}$

Is of course the Newtonian gravigyro parameter which covered near the beginning. For interest, other recognized gryo-relations are obtained in physics as parameters. The electron gryo-frequency for instance, which has the form:

$\omega_c=\frac{eB}{M_{e}_{c}}$

Is well-recognized in physics. The form of the Gravigryo charge parameter is given as:

$\sqrt{\frac{-\hbar \partial_t GM}{\hbar}}=\sqrt{\mu_g \omega}$

The gravigryo charge parameter is the frequency of rotation of a charged particle or ion as it interacts with the gravitational field (producing a gravitational charge). Going back to the wave equation which considered the electric and magnetic constants $\mu \varepsilon$ , the identity of $\omega$ can be seen in terms of the gryofrequency, given as $\gamma B$ where B is the magnetic field magnitude.

$-\hbar^2 \frac{\partial}{\partial t} \mu \varepsilon \omega^2 \psi=ia(-\gamma B) \hbar^2 \frac{Mc^{2}}{\hbar} \psi$

From here i state a relation between the electric charge $q$ and energy given by:

$i\hbar \partial_t=(-\nabla \phi \frac{-\hbar \partial_t}{c^2})q$

Note* the $g$ in $\mu_g$ is dimensionless, it is used to distinguish from the full form of $GM$ .

Last edited by Astro (2010-05-14 06:45:34)

Astro · 2010-05-11 11:43:17

In physics, we like to combine the meaning of certain physical quantities with other quantities in a hope to unify them successfuly, or prescribe them a defined meaning with other quantities. Any equations which have entertained the use of $\sqrt{\mu}$ have been clustered with other terms. The equation $i\hbar \partial_t=(-\nabla \phi \frac{i\hbar \partial_t}{c^2})q$ which describes a relationship between the gravitational potential, energy and electric charge could all be seen to contribute to the total gravitational charge. By simply multiplying $\frac{G}{c^2}$ on the right hand side, we find all of the terms calculate to a magnitude of the gravitational charge:

$\mu^2_g=(-\nabla \phi \frac{-\hbar \partial_t}{c^2}q)\frac{G}{c^2}$

where $F = (-\nabla \phi \frac{-\hbar \partial_t}{c^2})$

So the square root of $(-\nabla \phi \frac{i\hbar \partial_t}{c^2}q)\frac{G}{c^2}$ gives the correct value for the gravitational charge. Also, no longer according to that specific equation, can the electric charge be seen in a seperate light of the gravitational charge; they are both components which are inversely-related. However, it cannot be generally true that the presence of a gravitational charge invokes the presence of some electric charge, because there does exist particles with mass but have no electric charge, so the equation trying to describe gravitational charge and electric charge as two sides of one thing cannot be true. It is interesting to note though that mass does have a relationship with charge given by a very simple equation of: $M=q \phi$ and, in many textooks, $M$ is usually called a gravitational charge of a particle.

Last edited by Astro (2010-05-13 02:33:16)

Astro · 2010-05-14 06:57:01

A quick note which was meant to be written before:

The quantity we had very early on:

$Ev \psi=-\hbar \frac{\partial}{\partial t} c \psi$

can in fact be changed using Poncare's relation for the flux of an electromagnetic wave:

$S \psi=-\hbar \frac{\partial}{\partial t} c \psi$

where $S$ is the flux of the electromagnetic wave, and is equal to $Ev$ for $v=c$ .

Astro · 2010-05-29 20:17:33

In an attempt in previous investigations into how a gravitational charge can possibly be the generator of mass itself; seen as a process where the particles interact with their gravitataional field and in result, the charge is the same manifestation of the mass produced, in similar synchrocity to how a moving particle in an electric field experiences an electric charge.

I became even more interested in the idea as time has moved on, and Higgs Boson still remains ellusive. I ORIGINALLY thought that bringing in another field with strange attributes where the field generated its own mass for one Higgs per space in the field…. I eventually believed that a Higgs Boson was nothing more than a thorn in side of physics, or perhaps even better, completely superfluous. It could be, superfluous in the sense I thought, it was essentially undeeded if we look at the origin of mass as dynamical processes between gravitational fields and bosons, where at some point, a fundmantal process alters the innate nature of massless particles – but how??

Peter Woit’s theory is elegent, but personally, one that is only but. I simply was at a cross-roads. I knew that physics this past decade has become messier and messier – Einstein taught us to keep things as simple as possible… so why are scientists creating theories that cannot be varified alongside them being mathematically dubious and complexicated? Is it the ego, or the search or the belief that some how in the end, the final theory will be so complex, only few will ever understand it?

It must be realized as it has for a long while now, for certain theories in physics to applicate a respectable outcome explaining the world at large, will almost certainly require some strange math – I truly believe this much is inevitable. The uses of mathematical phrases for instance that are dimensionless, wrapped up in an equation which isn’t is one such example. Let me breifly show you an equation I call pompously the ‘’Master Equation’’ which really highlights potential gravitational differences in a massless zero-spin boson for having a possible Phase-Transition from pure energy, to pure inertia (mass).

$i\hbar \frac{\partial}{\partial t}\frac{1}{c^2} \sum^{|\infty|}_{j=0} \Lambda^j |\psi^j> - (-\nabla \phi)|\psi>=\mathbf{L}\psi> + (\omega^2 \gamma M_0 c^2(e\frac{i}{\hbar}\hat{H}t))|\psi>$

In this equation, the statement wrapped up on the left hand-side is in fact dimensionless. The addition of the Langrangian term with it, essentially does nothing, yet. First, why the need for this statement? Well, in the statement, we have an inertial matter component $\gamma M_0 c^2$ but it is naturally reduced to zero because of the gamma. The gamma is required for reducing the presence of mass to be zero for a massless spinless boson. It also defines what the right hand side means.
Since the angular spin of the inertial matter $\omega^2$ must also reduce to zero since:

$(\omega^2 \gamma M_0 c^2(e\frac{i}{\hbar}\hat{H}t))|\psi>$ , this means that the energy on the right which describes itself the energy of our said massless boson cannot have an intrinsic spin state – yet. By carefully analyzing an energy perturbative parameter to the order of energy squared $E^2$ , the gravitational potential $\nabla \phi$ case acting instead of the usual potential in Langrangian Mechanics, acts as a gradient on the perturbation. If it satisfies the squared energy condition, then the gravitational field’s potential acts on the magntitude of the bosons energy, creating an innate gravitational charge, a presence of matter, and more importantly, regaining a spin-state, because now the energy cannot be expressed in terms of $\gamma M_0 c^2$ since the gamma term can longer be used, and so the entire statement on the left is no longer dimensionless $(\omega^2 \gamma M_0 c^2(e\frac{i}{\hbar}\hat{H}t))|\psi>$ . Before the boson reaches the energy state required for a gravitational charge interacting with the physical dynamical gravitational field, the original equation can be simple expressed:

$i\hbar \frac{\partial}{\partial t}\frac{1}{c^2} \sum^{|\infty|}_{j=0} \Lambda^j |\psi^j> - (-\nabla \phi)|\psi>= \mathbf{L}|\psi>$

This is simply a Langrangian solution, where the energy in terms of of the boson in addition of the gravitational potential yields the least principle of action in a gravitational field – which is exceedingly small since photons have a permittivity and permeability which is unfoundly different to particles with mass. Basically, a boson will be interactive with a gravitational potential much less pervasive than an electron, or a boson, or any particle with mass.
For the special case where a boson with zero spin interacts with another boson with equivalent non-inertial energy interact, then the langrangian spoke about can be added to the previously dimensionless quantity, if indeed $E^2$ in this respect allows a sucessful Phase-Transition then the Langrangian is now unfied with a particle with inertial matter, one which has a respective quantum angular momentum:

$i\hbar \frac{\partial}{\partial t}\frac{1}{c^2} \sum^{|\psi|^2}_{j=0} \Lambda^j |\psi^j> - (-\nabla \phi)|\psi>= \mathbf{L}|\psi>+( \omega^2 \gamma M_0 c^2( e \frac{i}{\hbar} \hat{H}t))|\psi>$

The strangeness of these equations is quite simply required a block of variables which had absolutely no sense at all from the pure spin-zero boson, that was, until it came apparent those variables were important in describing a theory of a Phase-Transition from energy to matter in a gravitational field…

Last edited by Astro (2010-06-12 14:17:12)

Astro · 2010-06-03 22:54:59

I found that my solutions to trying to explain a possible phase transition is actually equivalent to the Klein-Gorden Equation:

$\frac{1}{c^2} \frac{\partial^2}{\partial t^2} \psi - (-\nabla^2 \psi)+(\frac{Mc}{h})^2 = (\omega \gamma M_0c^2(e \frac{i}{\hbar} \hat{H}t)|\psi>$

where $(\hat{H}t)|\psi>$ is the same equivalance of the orthogonal states in reference to the perturbations. I derived at this from considering a constant force equation:

Assuming quantum mechanics is true about the following statements:

$\hat{H}|\psi>=i\hbar \partial_{t}|\psi>$

In the mathematics of quantum mechanics, the Hamiltonian operator is self-adjoint so it's diagonalisable and all its eigenvalues are real. There is always atleast one family of orthogonal states $|\phi_n>$ that span the state space:

The pertubation of the orthogonal state vector as a function of time is then

$e \frac{-\omega_nt}{|\phi>}$

, so if i went to the equation of the gravitational charge

$\mu^2_g= (-\nabla \phi \frac{-\hbar \partial_t}{c^2}q)\frac{G}{c^2}$

, then we have an electric charge relation to the gravitational charge located on the left of the equation.

Innate to the equation, is a force which is basically:

$\vec{F}= (-\nabla \phi \frac{i\hbar \partial_t}{v^2})$

I now note that $\vec{F}= q \phi g= (-\nabla \phi \frac{E\psi}{c^2})$

The orthogonal state we began with, is analougous to perturbation of its equality $|\phi_n (t)>$ where the subscript $n$ dictates the energy level. Applying this to our constant force in the equation

$\vec{F}= (-\nabla \phi \frac{i\hbar \partial_t}{c^2})$

then shouldn't the n'th permutations in the system follow such an equation|?

$\vec{F}_{n}|\phi(t)> = (-\nabla \phi \frac{i\hbar \partial_t}{c^2})(e\frac{-i \omega_nt}{|\phi>})$

This would surely mean that the direction of the potential energy is a residue of variables which tend to remain constant unless acted upon by an external force, so my question is, should this equation has a minimalizing integral, rather than taking a dubious approach into expressing it as a classical langrangian of energy density?

Last edited by Astro (2010-06-03 22:57:12)

Astro · 2010-06-03 23:00:16

If the Klein Gorden equation is indeed completely analogous, then it is equally possible for Klein and Gordens equation to satisfy my energy condition:

$i\hbar \frac{\partial}{\partial t}\frac{1}{c^2} \sum^{|\psi|^2}_{j=0} \Lambda^j |\psi^j> - (-\nabla \phi)|\psi>= \mathbf{L}+( \omega^2 \gamma M_0 c^2( e \frac{i}{\hbar} \hat{H}t))|\psi>$

Which, i think could mean one of two specific things. Either they describe essentially the same thing in the end, or there can be two types of spinless bosons in fundmental nature.

Astro · 2010-06-04 00:40:21

...just testing something

$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$

Its been a while since i typed out a matrix in latex...

$T(a)_{j}=\begin{pmatrix} 1 & 0 & 0 & x \\ 0 & 1 & 0 & y \\ 0 & 0 & 1 & z \end{pmatrix}$

riiiight... got it now...

Last edited by Astro (2010-06-04 01:13:51)

Astro · 2010-06-04 01:22:13

Since the Observer and the Observed can be given a position in the wave function of spaces $|\psi>$ , then it has a translation operator which can be expressed in matrix form:
Iff $T(a)_i \in \alpha_i (\beta_i)$ relation according to $\alpha_i(\beta_i) \in R^4$ where the observer measures the time coordinates in linearity, then there is a special condition in the translation where we are given a specific direction; this could be seen arbitrarily as a manifold:
$T(a)_{j}=\begin{pmatrix} 1 & 0 & 0 & x \\ 0 & 1 & 0 & y \\ 0 & 0 & 1 & z \end{pmatrix}$
proportional to $\beta \in R^3$
Notice how it’s in three dimensions – this is because our observer is not acting on measuring the object, which is why we have reintroduced the subscript $j$ . As soon as why apply the reference principle, we can have a four dimensional manifold, because the mind plays the role of the linearity of time:
$\box T(a)_{j}=\begin{pmatrix} 1 & 0 & 0 & x \\ 0 & 1 & 0 & y \\ 0 & 0 & 1 & z \\ 0 & 0 & 0 & t \end{pmatrix}$
proportional to $\alpha_i(\beta_i) \in R^4$

Last edited by Astro (2010-06-04 18:44:38)

Astro · 2010-06-04 03:54:03

I found this paper right now, which may actually show my idea is not so estranged afterall. http://www.springerlink.com/content/y0164v8651273t23/

Astro · 2010-06-04 17:19:03

Near-extremal black holes are usually performed on by using an energy-perturbation theory around the extremal black hole/singularity/particle, which will be the mathematical foundation of the following theories.; psuedoscientific theories, unfortunately… but still possible.

Some theories involving additional space dimensions predict that micro black holes could be formed at an energy as low as the TeV range. No doomsday scenario can be found though, because the extremity of this singularity cannot gobble matter, no more than it acts like a black hole which cannot emit radiation.

$g_{\mu \nu}=g^{0}_{\mu \nu} + \hbar_{\mu \nu}$

For a spherical body which is not point like on a symmetric metric tensor, and so describes the energy associated to that perturbed singular particle with a structure. The small perturbations reside in the form of $\hbar_\nu \mu$ which then must be analyzed carefully.

Last edited by Astro (2010-06-05 15:06:18)

Astro · 2010-06-05 15:55:14

Proposal 1: Particles have a structure since extremal bodies like electrons have a curvature. To state they are pointlike is totally erroneous and contradictory.
Postulation 1: How can zero-dimensional systems even exist in a three-dimensional vacuum? It makes no sense to why nature could allow this.

THE FOLLOWING

Production of micro black hole requires that the concentration of mass or energy corresponds to its Schwarzschild radius. These micro singularities are analogous to a micro black – but there are two cases we can consider – there is also a near-extremal case scenario for a black hole – in theory, they should state that an electron contains observables which would mirror singular pointlike systems.

Near-extremal black holes are usually performed on by using an energy-perturbation theory around the extremal black hole/singularity/particle, which will be the mathematical foundation of the following theories.; psuedoscientific theories, unfortunately… but still possible.

Some theories involving additional space dimensions predict that micro black holes could be formed at an energy as low as the TeV range. No doomsday scenario can be found though, because the extremity of this singularity cannot gobble matter, no more than it acts like a black hole which cannot emit radiation.

$g_\mu \nu=g^{0}_{\mu \nu} + \hbar_{\nu \mu}$

If we make a bold assertion that the metric itself $g_\mu \nu$ is equal to that of the Hamiltonian $\hat{H}|\psi>$ , then we can by theory perturbate $\hbar_\nu \mu$ in the orthogonality of state around the singular structure, by the identity of relations $|\phi_n>$ . The reason why, and how, will come soon.

From similar gravitational relativistic equations, we have for a Langrangian: $S=\int L \sqrt{-g} d^4 x$ which satisfies a structural system for a particle because it has a density which can only be attributed to a volume $\rho= \nabla^2 \phi$ , thus the curvature is the mass and the structure is the proposition that can be obtained, even in a Least Action of Density.

For a spherical body which is not point like on a symmetric metric tensor, and so describes the energy associated to that perturbed singular particle with a structure. The small perturbations reside in the form of $\hbar_\nu \mu$ which then must be analyzed carefully.

These following derivations are the only way I can describe such a theory in terms of geometrical relativity:

$i\hbar \partial_t |\psi >=\hat{H}|\psi>$
And knowing $g_{\mu \nu}=g^{0}_{\mu \nu} + \hbar_{\nu \mu}$

Then my relation which is quite an assumption is $g_{\mu \nu}|\psi> = \hat{H}|\psi>$
If this is true, then it follows the perturbations of Orthogonality States $\phi>$ , so calculating it in terms of a minimalizing integral:

$\delta \int \hat{H}|g_{\mu \nu} |\psi> = g^{0}_{\mu \nu} |\psi> + \hbar_{\mu \nu}_{0}|\psi>$

There are many meanings here. It means that the perturbed state of $g_{\mu \nu}$ on a singularity/particle in spacetime is expressed as the ground state of $\hbar_{\mu \nu}_{0}|\psi>$ WHICH JUST STATE that the perturbation are as small as they can get, and $g^{0}_{\mu \nu}$ escalate to produce the lowest energy, but is the reason why $\hat{H}|\psi>$ for $g_{\mu \nu}$ is small, is because of a limiting condition found in Fermi-Energy Levels.

The final equation if I have done this right, should state:
$\delta \int <\psi|E_n+g_{\mu \nu}|\psi_n> = <\phi_n|g^{0}_{\mu \nu} + \hbar^{\mu \nu}_{0}|\phi_n>$

Last edited by Astro (2010-06-11 15:48:17)

Astro · 2010-06-06 15:49:24

$I_M=M \frac{G}{c^2}$ where $I_M= \mu$

If left is defined as an inertial matter, then there must be an inertial energy (WHICH will be shown soon as being equivalent to the energy sqaured boundary.

The gravitational charge corresponds to $\mu_g$ . From here, we find solutions by algebraic manipulations:
$I_M=GM=\mu$ thus multiply the distance out and then simplify for:

$I_M d = M \frac{G}{c^2}_0 \frac{1}{2} a t^2$

Taking the potential we have

$I_{M} dg =e^{i}\partial_{i} (M {G}{c^2}_0 ) \frac{1}{2} a t^2$

Using an Einstein summation for $-\nabla \phi$

Simplifying $I_{M} dg= e^{i}\partial_{i} {M \frac{G}{c^2}_0 \frac{1}{2} a t^2$

Leads to $I_{M} dg= (-\nabla \phi) \mu_g \frac{1}{2} at^2$

The charge located on the left can be identified specically with an inertial mass.

Last edited by Astro (2010-06-18 22:42:34)

Astro · 2010-06-09 01:27:34

Final Thoughts

From a rational perspective, we must for now, assume Relativity is correct. The idea I’ve encapsulated on has produced a bizarre, perhaps even pseudoscientific notion of viewing the spacetime manifold. The fourth dimension of space, is not truly of time, but a static dimension of space itself, like the mathematical lingo goes, this leaves the foliation as necessary hypersurface solutions, leading to solutions so unique, the static dimension of space is interchangeable at the will of the knowledge of an observer.

Locally, static spacetime looks like a standard static spacetime, which is inexorably the focus of some attached Lorentzian warped product $RXS$ which has a metric of the form $g <t|x>=(-\beta <x|t>))dt^2+g_{S}(x|t>)$ .

[1]
In such a local coordinate representation the Killing field K may be identifies as and so the S-manifold are of K-trajectories, may be conceptualized as a 3-space of stationary observers – in my case, the killing field must involve the perturbation of the Phase Transition. If λ is the square of the norm of the Killing vector field, λ = g(K,K), both λ and $g_S$ are independent of time. It is from the latter fact that a static spacetime obtains its name, as the geometry of the space-like slice $\sum$ does not change over time.

[1] - where R is the real line, $g_S$ is a (''positive definite'') metric and β is a positive function on the Riemannian manifold S.See Wikipedia for [like-information…] now, the static dimension depends verily on the direction in which observers inside the universe perceive an experience of time. This time is frozen, yes, but from our frames, it is not, meaning that the human experience cannot be biased about the worlds it inhabits… solipsism looses its meaningfulness if it cannot describe essentially why we seem to observe and experience entering my body from the outside.

Last edited by Astro (2010-06-09 07:47:13)

Astro · 2010-06-09 03:12:49

...

Last edited by Astro (2010-06-09 07:48:23)

Astro · 2010-06-09 03:14:35

....

Last edited by Astro (2010-06-09 03:15:26)

Astro · 2010-06-10 21:29:11

same as below

Last edited by Astro (2010-06-18 22:45:42)

Astro · 2010-06-12 23:26:38

going to be modified

Last edited by Astro (2010-06-18 22:45:04)

Astro · 2010-06-19 04:15:23

During the writing of these equations, and the postulations brought forth, it seems like the Higgs Field Theory is failing in every respect conceptually to reconcile why there should actually be 5 different Higgs Bosons - if one wasn't enough. I started in this work with the more simpler Higgs Model where we vision a single type of Higgs, but attention to this have suggested otherwise:

http://www.theregister.co.uk/2010/06/15/higgs_bosons/

It seems that perhaps the standard model on how it views energy should be looked at again? It's true that in all of these things i write, that i have some confidence that a Higgs Field sounds ridiculous, because not only can it require many more types of Higgs, there is nothing to suggest why there is not more than 5. Even more puzzling is that its use in string theory is pretty much a messy theory when looked at by the professionals such as Dr. Sheldon Glashow, who once commented he did not understand why there should have been an explanation for gravity in string theory models. As far as he was concerned at the time, don't know if his opinion has changed, but he was already confident on the workings of gravity, from a classical and to the more acccurate General Theory of Relativity.

Einstein said we had to keep things simple... why have we stred down this path where physics is no longer about simplicity, but mathematical complexity usually beyond most peoples imaginations? The standard model has become messier and messier, and i think (even if my approach does not suffice) it is time it was looked upon again, this time from a new light.

Last edited by Astro (2010-06-19 04:19:19)

Astro · 2010-06-24 17:31:41

On Spectral Energies in the Perturbative parameter in accordance to the Density in a given Volume.

$F_i= \sum^{3}_{j=1} \sigma_{ij} A_{j}$ eq 1.

Which is the stress-energy tensor, or also known as the ''pressure of density. Since $\sigma=\rho$ , then it can be expressed from the Nordstrom relation.

This mean eq 1. which is of course a famous equation, can now be given as:

$F_i= \sum^{4}_{j=1} (\nabla^2 \phi)_{ij} A_{j}$ [1]*

This means that the pressure or force acting on the 3-tensor of stress energy is one associated to the gravitational potential.

[1]* note the summation of spacetime now. This is because we are now using a four dimensional approach, by applying the four-dimensional de'Alembertian.

To state more clearly the force is associated to the gravitational potential, could be given i suppose as a more pictorial approach by giving:

$F_{i}(-\nabla \phi) = \sum^{4}_{j=1} (\nabla^2 \phi g)_{ij} A_{j}$

where $\nabla^2$ is the de'Alembertian.

A total density can be classically seen as $\Delta \rho = \sum \frac{F}{A}$

where $A$ is the area. Since we can work in infinitessimal planck units of space and time, it should still work as an approximation to amount of energy spectral densities a system can undergo.

So in this case, i refer us back to the energy-perturbative equation for a spinless field, massless field:

$i\hbar \frac{\partial}{\partial t}\frac{1}{c^2} \sum^{|\infty|}_{j=0} \Lambda^j |\psi^j> - (-\nabla \phi)|\psi>= \mathbf{L}|\psi>$

It is not, just to remind the reader, until atleast $E^2$ is satisfied, can we approach a two photon collision state, where matter undergoes the phase transition.

If this is true, then it seem that the best approach to understanding the Hierarchy model would be to assume that energies greater than $E^2$ will almost certainly create particles with different rest energies. Such an approach, would be to take a taylor expansion as an approxomation, but in this case, we will still show it as a case from the classically-based idea:

$\Delta \rho = \sum \frac{M}{V}(1 + \frac{1}{2}(\beta^2)+\frac{3}{8}(\beta^4)...)$

Here, $\beta$ is a trigonometric function equal to $\frac{v}{c}$ .

Last edited by Astro (2010-06-24 22:09:02)

Astro · 2010-06-24 18:15:26

The equation has an inertial energy $E=Mc^{2}$ and so describes a flux of energy into mass at the square of the magnitude of even a ground state frequency. Analytically, as a wave equation has a density over all possible frequencies and polorization states, is given as:

$W=\int \nabla^2 \phi (\omega) d \omega$

This non-classical approach will be systematically-relevent to the polarization and probability states for a phase transition which will play an important part in the nucleosynthesis of matter itself.

Last edited by Astro (2010-06-24 18:16:16)

Astro · 2010-06-24 21:40:51

In general relativity, the gravitational potential is provided by a metric tensor $g_{\mu \nu}$ - it is itself a 4x4 matrix. It's only when the gravitational potential reaches the components of the metric with $00$ as the index of $g$ does it couple to some external energy density.

This is perfectly sound, since the perturbation of the energy equations provided thus far, can arbitrarily use this to show how perturbations in a gravitational field can couple to some external energy; and if this is true, then we may have the direct requirement for the model suggested ~ a gravitational field, self-consistent in providing particles with mass with a lowest energy expectancy of $E^2$ .

Perturbing the state of the gravitational field aka. the Newtonian Potential $\phi$ , we would normally have:

$g_{00} = (1+2 \phi)$

This equation hopefully should have some major importances with my equation of the Gravi-gyro charge parameter, through the recognition of the Newtonian Gravitational Parameter.

In our modern convention, we find that most would say that fundamental systems that make up a rotating body have their inertial mass, but this is equivalent to a kinetic energy term $E_{K}_{0}$ , so we say it contributes to the gravitational field. If we have learned anything from General relativity, that is that curvature, mass, gravity and spacetime are interconnected so very much, that removal of one of these components would utterly destroy their meanings, as they mathematically define each other. In some sense, they are much different fascets of the same manifestation.

Since there seems to be something special about these relations, would it now be so audacious to state that the gravitational field took a similar role for fundamental systems?

The equations so far, and the postulations of general relativity work well as an approximation at best, rather than an equality, however we seem to find ourselves not interested in how the gravitational field interacts with particles... just a little speculation here... but since gravity is so weak on the fundamental level, doesn't mean it cannot interact intrinsically with the struture of the particle itself providing mass, given the correct energy-conditions. Next, we will look at this from the degenerative states of perturbation - which would seem to fit the model best.

Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

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An Equation Describing A Particle Field in terms of Permeability

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