Apr 01 2008

## Wave Function Transfer, Rev. A

The wave function of a free graviton can be written in the form

E_{0} sin (kx-ωt) or B_{0} sin (kx-ωt)

where the wave number k = p/ћ, and the electric and magnetic field components are in phase with each other.

The momentum of a free graviton, which we will now call p_{g} for purposes seen later, is written as p_{g} = h/λ_{g} = 1.671 x 10^{-19} kg-m/s. The fundamental charge, termed *e*, that of an electron or a proton, is 1.602 x 10^{-19} C. Linear momentum from a free graviton must be transferred into angular momentum as it is absorbed by an electron in a quantum atomic orbital.

In terms of energy, with the numerical value of p_{g}^{2}/*e*^{2} at 1.088, generally we have

p_{g}^{2}/*e*^{2} = (Const._{1}) _{S}∫ B^{2}∙n dA

The rotational wave function of a graviton as an internal component of an electron may be of the form:

Ψ_{rot} = (Const._{2}) exp [i2πα(*e*B/p_{g})ct],

which would be orthogonal to a corresponding standing wave function.

In Ψ_{rot} , p_{g} is the same momentum of the graviton when free and traveling at the speed of light, B is the internal magnetic field of the electron that is perpendicular to a plane that passes through the center of the electron and is perpendicular to its spin axis, and α is the fine-structure constant. Once released again however, the free graviton likely has no rotational component. In fact, it must not if a graviton is to be absorbed by an electron in either of two spin orientations.

The imaginary component of the complex wave function of an absorbed graviton will be large enough so that it takes several gravitons to make a full charge. Additionally, not all the graviton energy will go into charge contribution; some will contribute to the mass of the electron.

Not including spin energy, the equation E^{2} = p^{2}c^{2} + (mc^{2})^{2} represents the relationship between total energy of a particle, the electron in this case, and its linear momentum and rest mass. It is fortunate that the numerical value of p_{g}^{2}/*e*^{2} is greater than 1 so that we can be more confident that there is an uptick in both mass and linear momentum for an electron in a quantum atomic orbital when a graviton is absorbed. An interesting concept here is that the electron gains linear momentum in the opposite direction, within a certain conical angle, that the free graviton was traveling.

The rotational energy of an electron was estimated in my April 2007 paper as being 3.06 x 10^{-9} J, and elsewhere on this blog the number of gravitons in an electron was roughly estimated as 3.06 x 10^{-9} J / 5.011 x 10^{-11} J = 61. Using the reciprocal of the dimensionless fine-structure constant, the average number of gravitons in an electron, in an atomic orbital at the face of the earth, could possibly be 137/2 = 68.5.

I apologize for the way pi and alpha transfer from my word processor documents into this blog. Pi can look like an n, and alpha can look like an a, and be misread if not compared to n and a elsewhere.

Apr 14 2008, Rev. A: Added a subscript “g” to the representation of the momentum of a free graviton after first mention, and also to the wavelength of a graviton. Added the paragraph “Not including … was traveling.”