Hello James,
On the time scale of time 10^9 y and distance 1 ly, the planets are viscous liquid droplets moving on their orbits around the sun in a planar radial gravitational force field 1/r^2 and a magnetic dipole field with its axis on the orbit parallel to the dipole axis the sun.
In the radial vicinity near the static orbit, the radial gravitational field is the field of an harmonic oscillator. All external forces induce vibrations where only the lowest frequencies induce continuous, ever lasting vibrations.
The higher-frequency parts die out exponentially through the diffusion of the angular momentum via the pair interaction in the planetary system, the energy via the internal viscosity and by thermal electromagnetic radiation.
Seen as a problem of long time intervall random time observation, that is observing slow motion nearly constant observalbles only, the planetary system mimics a quantum system of light spin-droplet systems moving in nearly circular orbits around a stationary heavy nucleus.
The orbits in a potential -1/r + L^2/r^2 are orbits of minimum energy. The orbits becom circular by angular momentum diffusion via pair scattering. They constitute the known long-term stable configuration with a stable radial harmonic series.
From the algebraic similarity to an atomic system, we know that in planar radial coordinates, the spectral eigenstate system consists of radial oscillator states around the orbit, with spin-spin coupling.
For particles with spin 1/2, electrons, the coupling of spin angular momentum and magnetic moment is 100%, i.e. 2* ( spin 1/2 + orbital angular momentum) is the integer ladder of the square of the total angular momentum (L +1/2 s)^2 with the 2-axis moment 2 m varying in the odd integers -2L-1 , 2L+1.
Now we get to the point: the paraxial moment, parallel to the Sun's external field on the orbit, gives rise to a series of oscillator states, with the series of eigenstates being the positive integer ladder to infinity for spin and angular momentum parallel.
If the spin orbit is antiparallel, the ladder is finite up to the value where the total angular momentum is zero. A particle with a retrograde spin greater than the orbital angular momentum is an impossible state in quantum mechanics. In mechanics, it will likely spread the liquid droplet over the orbit, in other words, in a local rotating system, the centrifugal forces exceed the oscillatory forces that keep the liquid droplet on its orbit.
These considerations may seem a little "philosophical", but they rest on some rock-solid foundations: the Fourier analysis of orbital motion introduced by Gauss for the Moon's orbit, the second law of thermodynamics of energy diffusion in any Hamiltonian degree of freedom, and finally the 1-electron system in 2-dimensional systems with a 1-form A magnetic potential producing a 2-form F magnetic force.
Albeverio had developed these ideas of similarity between quantum and stochastic systems in the 1970ties.
The 2d systems have been an intense subject of research since von Klitzing's observation of the quantum Hall effect in the interface of planar epitaxial semiconductors, which has the rigid identity of electric charge, spin, and orbital magnetic field and the integer energy, spin-orbit, angular momentum, and oscillator ladders of eigenstates, such that now units of electric charge and Bohr magnetons are now expressed by the steps of the integer quantum Hall resistance (and the Josephson voltage).
Apologies for attempting a compression of about four or more Advanced Mathematical Physics courses. But I think there is no explanation on a simpler scale of ideas.
Disclaimer:
This text has been written in English, translatwd into German and back into English by, thanks, translate.google.com and as such is an GPT-lectored original text by Roland Franzius.
Kind regards, Roland Franzius
