Bonaya Samuel's unified field theory based on the law of relativistic charge can be used to account for the physics at Planck's scale.
for the purpose of the present discussion and for the sake of new viewer's I will briefly derive it using the concept of a unit space vector of a complex Hilbert space, since the electron/ charged sub-particle is dependent on space and time. The energy of the electron/ charged sub-particle is given by E=e^2/(4pEo)gradu' =(-ih/2p)du'/dt
where u'=unit space vector or
e^2/4pEo=hv/2p, -------------------(1)
or e^2=2hvEo -----------------------(2a). substituting the specific charge relation in (2a) we obtain the relation:
(s^2)(m^2)=2hvEo -----------------(2b)
where P=pie Eo=permitivity of free space,
Similarly the gravitational energy of a quantum mechanical system is given by:
E=Gm^2gradu'=(-ih/2p)du'/dt where u'=unit space vector or:
Gm^2=hc/2p ------------------------(3)
or Gm'^2=hc/2p ---------------------(4a)
where m'= Planck's mass.
0r, m'=sqr[(hc)/(2pG)---------------(4b)
Substituting 2b into the De Broglie relation,we obtain velocity- wave relation for a quantum electromagnetic system:
(v^3)w^2=h(s^2)/(2Eo) ------------(5).
Substituting 4b into the De Broglie relation , we obtain the following velocity wavelength-relation for quantum gravity:
c^3w^2=2phG -------------------------(6).
There exists in this case an analogous relation between the two velocity-wavelength relations, just as is the case for coulomb's law and law of universal gravitation. In planetary motion this relation simplifies to Kepler's third law of planetary motion.
For the purpose of my present analysis I will introduce two unified field identities. the first one I called a unified field space identity interrelating electromagnetic and gravitational waves that is
(v^3w^2)/hs^2/2Eo)=(av)^3w^2/(2pGh)=1
from this identity
a^3=4pGE/s^2 where a= unified field space correlation coefficient.
(av)^3w^2/(2pGh)=1 can be reduced to Kepler's third law of planetary motion when the De Broglie relation substitutes for h and a^3w is substituted by 2pRps where Rps= distance of planet to star.
it reduces to Rps.v^2/(Gm)=1 or (f^2)(R^3)=Gm/(4p^2).It can be shown that the period of oscillating pendulum is according to Kepler's third law of planetary motion.
From this space identity we can also obtain the following electromagnetic wave relation:
a^3w^2=2pGh/c^2. The importance of this relation is the fact that each electromagnetic wave is associated to a particle antiparticle pair associated with a a particular specific charge. This means the electron and positron pairs are associated with a particular electromagnetic wave assuming the definition of a particle as one having specific charge.
the above space identity can be used to establish the refractive index relation below:
n=c/v=w''/{w' (Er)^1/2) or Ur=n^2/Er where w''= wavelength of electromagnetic wave in free space w'=wavelength in medium Er= relative permitivity and Ur= relative permeability.
the second unified field identity that I will introduce is a mass identity
m^2/(2hvEo/s)=m^2/(hbv/2pG )=1 where b= unified field mass correlation coefficient.
from this relation b=4pEoG/s^2 .
The relation below is obtained from the identity:
m=[(2hEv)^1/2]/s=[(hbv)/(2pG]^1/2. This relationship derived is really a quantum unified field relativistic law of mass and the one derived in special relativity is only an approximation of it.
These relations establish the fact that at quantum levels electromagnetic forces are more dominant than gravitational forces. (This second identity can be used to derive the generalized Bohr Mosley's wave number relation I previously Presented.
When bv=c or v/b=c m=mp where mp= Planck's mass or
m=mp=[(hc)/(2pG)^1/2. This is the quantum gravity relation.
when we put h=2pmvr into this Planck's mass relation we obtain the relation:
GMp/r =c^2. This is a quantum black hole relation where r becomes Schwarzschild radius or r=Rs. This radius is the distance from singularity to event horizon. The gravitational energy of this quantum black hole is quite different from that of the singularity singularity.
Assuming a singularity having specific charge of a proton. the following information about Planck's mass:
velocity of the singularity=3.707533654*10^44
Energy of the proton singularity=2.9886083*10^81.
converting this to mass using the Einstein's mass energy relation, this is mass of 3.82573368*10^64. This is the energy of 1.7*10^34 solar sun's.
Mass of singularity =2.1767128*10^-8kg.
Radius of singularity=1.307584446*10^-71m.
Schwarzschild radius =1.616041706*10^-35m.
Gravitational energy of black hole=1.221003813*10^19Gev.
Gravitational energy of singularity=2.417932143*1043j.
Big bang force= 2.285722444*10^152n.
Frequency of singularity=4,510453593*10^114Hz.
Magnetic flux density of singularity=9.416714906*10^106 T etc.
After the bang the Planck's mass and the energy of the singularity would fractionate in the super clusters, clusters, galaxies according to some Gaussian distribution curve that is :
i=1Sn M/Mp=1 and i=1Sn E/Ep=1.
The Planck's mas is the crystal seed of particle's.
The universe had three main orders. In it's zero order no matter existed. the was only the logos, the intelligence,the little hallo of light that played at the Father's door. since M=sqr(2hEv)/s. at this order v=o and m=o but the spun of the universe in this order was infinite. in this order there was no time it was all eternity in this intelligence.
At time t=o The Planck's mass was born as a crystal seed from the intelligence and it carried all the genetic blueprint of the present visible and invisible universe and the seed singularity had the instructions to bring fort according to the commandments of the logos. This seed had the potential and instructions to generate mass using the vast resource. In this form space collapsed to the Schwarzchild radius. The big bang which scattered this energy and mass to the present space instantaneously because of the high velocity potential pf this particle. The velocity calculated accounts for the horizon problem of cosmology. This seed carried the code of superconductivity, gravitation,electromagnetism,particle spectroscopy,the five fourth law of cooling etc. Cosmological redshift could be accounted for by continuous interaction of electromagnetic radiation with space charge, resulting in loss of energy by radiation.
Let me say it is not possible to start with special relativity to derive quantum gravity since the two are irreconcilable though it is possible to play a maths game and introduce a hypothetical space that will cancel special relativity and plant quantum gravity such a space would have no significance but its error will be manifest because of inability to climb high to explain other phenomena of the same.
I will end here for now with more comments later.
Yours,
Samuel Bonaya Buya