Saturday, February 16, 2019

Lagrangian Versus Hamiltonian -- Orbiting Of Electrons

I will start off with the obvious, and develop this into an insightful thought.  As Anyone knows -- any  given arbitray electron , that is here to exist in a stable atom -- tends to orbit the nucleous of such a said atom, in an elliptical manner.  Aside from the general condition, that is of the charge-based attraction of an electron with a proton, another part of the reason, as to why there is the tendency of what the directional drive of the holomorphic motion -- that is of the activity of any of such individually taken electrons, happens to be over an evenly-gauged Hamiltonian eigenmetric -- as it is here to generally function, in so as to orbit the nucleus of such a said respective atom in an elliptical manner -- is partially due to the Ward-based condition, that the scalar amplitude of the tense of energy, that is most related to the Lagrangian of a correlative Hamiltonian operator -- is then to tend to be analogous if not equal to the scalar amplitude of the tense of energy, that is most related to the holonomic substrate of the self-same corrlative Hamiltonian operator, when multiplied by (-i).  For example:  The Strong Force is related to Euler's Theorem. The Strong Force is most associated with the gluing together of parts of forming nucleons, via what are known of as "gluons," in so as to have nucleons, -- such as protons and neutrons.
Next to be mentioned, is the general condition -- that, when we as people come into contact with a phenomenon of mass -- what we are generally are observing, is the effect of and the presence of eletrons.  Electrons and protons work to bear the opposite charges (Electrons are negatively charged, and protons are positively charged.)  Let's suppose, that we were to initially here to metaphorically call (1+) to be a value that will work to connitate the presence of a proton, - and let's suppose, that we were to initally here to metaphorically call (-1) to be a value that will work to connitate the presence of an electron.
Next -- since the electron is to have a polar-related orbit and spit (with an elliptical orbit), in multiconsideration with the condition, -- that the tense of the energy of the Lagrangian of a Hamiltonian operator, is equal to (-i) times the correlative force of such a tense of energy of the holonomic substrate of the self-same Hamiltonian operator. Let's initially consider the numerical value associated with the basic expression, that is here to both mathematically associate the electron more to the nature of light And to mathematically associate the proton more to the nature of mass. If one were to re-assign the forward-holomorphic direction of the said light, to be propagated relatively straight ahead, then, its one partition-based discrepancy would be around the center of its relative left side (i*PI position).   Yet, given the forward-holomorphic direction is to be re-assigned to be going straight ahead for a fully Lorentz-Four-Contracted mass-bearing superstring, -- its one partition-based discrepancy would be at its relative right side.  (2*PI) position.  Therefore, let's now compare the following:  e^((-1)*((i*PI) )= (i*e^(i*PI)) = i(-1) = -i.  Whereas:--  e^((-1)*(i*2*PI)) = (i*1) = i.
Next:  So we are here relate (-i) to (-1) and (i) to (1), -- to where, if one were to couple the two given multiplets of (-i) upon (i), one would then have: (-)*(i*i) which would equal: (-1)*(-1) =1.  This is then to bear the general Ward-Cauchy-related condition -- that this is part of why electrons and protons have opposite charges, -- and this is, as well, part of why, for atomic stability, there tends to need to be the same number of electrons as protons in an atom.  (The eminent Yukawa Coupling of electron-based force upon proton-based force works to help at unitizing a tense of its energy, and thereby, helping to work to allow for such an atom to bear more of a rest energy.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

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