Jun 28 2008

Gravity and the Uncertainty Principle

Published by at 11:42 am under Quantum Mechanics

Earlier it was postulated that the number of turns in an atomic orbital, referenced to the nuclear spin axis of an atom, – or to the nucleus to nucleus axis of a diatomic molecule, is equal to 2n + 1, n being the principal quantum number.  In some instances this may be a little hard to believe, such as when looking at some of the Leighton sketches of Liboff Figure 10.17 [1].  The hydrogen 4F, m = 0, orbital, for example, is one that looks symmetrical with six lobes when sectioned in reference to a plane that includes the z axis of the atom.
Let us say that the electron starts out in the 4F orbital on the negative z axis, which we will also allow to be the negative z axis of the nuclear spin at the same point in time.  It then arcs past the nucleus on its way to the first turn of the orbital where it reverses intrinsic spin orientation as it gives off one or more gravitons.  As the electron spends more time in the areas that show a higher whiteness density in the Leighton sketch, the original -z axis of the atomic nucleus does not have to be aligned with the -z axis of the sketch and the electron spin axis again until the electron enters the 9th turn.  The nuclear spin axis would be allowed to change azimuthal angle back and forth in quantum angular steps.  The electron can be at the original -z location more than once in the course of the orbital, but not at the same instant in time as the -z axis of the nucleus until the last turn.
The raising and lowering operators of the total angular momentum of the state | E0, L, S, J, M>, are known as:
J± | E0, L, S, J, M> = ћ sqrt[J(J+1) – M(M±1)] | E0, L, S, J, M±1>  [2] Chpt. 10, Complement Dx , 3.a.
The operators J± may exist in part to balance the energy so that a steady-state, steady-flow process can occur during the absorption of gravitons by the nucleus and the subsequent release of energy expended by the nucleus in creating a magnetic field that keeps electrons in orbit.  When the electron reverses its intrinsic spin axis at the apex of a turn, it arcs in the opposite direction because its magnetic dipole is reversed, and the magnetic field vector and strength from the nucleus is the same in that locale as just before the turn took place.
From a measurement standpoint En looks stable, however the vector operator M ± 1, with 2l + 1 possible integer values of the magnetic quantum number, ml ([1] Table 10.4, pg 451) , may help keep the energy the same once the uncertainty principle is taken into account.  The shift through integer values of ml, with [Jz, J±] = ±ћJ± ([1] (9.20), pg 358) helps keep the energy of the atom stable.  For example, the energy of the total orbital angular momentum for the D term is 6ћ2/2I ([1] Fig. 9.8, pg 364) through all eigenvalues of Lz, however it cannot be certain at any given instant in time what the value of Lz is for any orbital with higher total orbital angular momentum, L, than the S orbital.
As far as quantum mechanics goes, there does not appear to be anything currently written that will need to change.  For example, take the commutation relations [Jx, J2] = [Jy, J2] = [Jz, J2] = 0  ([1] (9.18), pg 358).  Every soccer match between J2 and Jz will continue to result in a tie score and no one will win, or better yet the game is forfeited before it starts.  That is not to say that nothing will get added.  The wave functions going on inside the electron, and how they interact with the Coulomb potential, can be an additional field of physics.
[1] Liboff, Richard L., Introductory Quantum Mechanics, Fourth Edition, Addison Wesley, 2003
[2] Cohen-Tannoudji, Dui, Laloë, Quantum Mechanics, Hermann, 1977, Paris, France

No responses yet

Trackback URI | Comments RSS

Leave a Reply