Many thanks indeed! These are important results and excellently programmed as usual. They prove in another way that ECE2 relativity produces precession of the perihelion, confirming UFT328 and they show the power of the new numerical method we are developing systematically now. Einsteinian general relativity is not only incorrect in many ways, but superfluous. By Ockham’s Razor ECE2 and this method is preferred because it is simpler. The results of this method can be compared with the experimental results on precession of the perihelion of various planets. Congratulations once more to co author Dr Horst Eckardt. We have made significant progress in UFT371 and UFT372 and have shown that classical 3D orbits of the inverse square force law do not precess, but relativistic ECE2 2D and 3D orbits precess, both in two and three dimensions. Classical 3D orbits quantize to hydrogenic wave functions, and we have successfully tested the code for the radial component of the wavefunctions. The relativistic three dimensional orbit quantizes to the relativistic wavefunctions of H. we are also ready to solve the relevant Lagrange quantum mechanics for helium. I would say that for UFT328 the hamiltonian was used in the scatter plot method, but not used specifically to give the energy levels. In papers such as UFT333 and following the hamiltonian was used in a different way.
Sent: 08/03/2017 14:11:53 GMT Standard Time
Subj: Re: 372(4): Relativistic 2D and 3D Orbits and the Relativistic H Atom of ECE2
I programmed the relativistic Lagrange equations. Compared to UFT325/328 the only difference seems to be that we have an additional polar angle coordinate introduced in UFT372. Does the Hamiltonian anywhere go into the calculation in UFT328?
I am sending over some preliminary results. For any reason the plots in the protocol appear tiny so I added them as extra files. For suitable choice of c, we see a clear precession of an ellipse (Fig. 4). I still have to improve the plots. It can alse be seen from Fig. 5 that the non-relativistic constants of motion are not constant any more. Motion is in a plane again, the relativistic terms seem not change the plane of orbit. In so far the results of UFT328 remain fully valid. The equations with polar and azimuthal angle are more complicated, but become simpler when brought into canonical form, see eq. o18.
Am 07.03.2017 um 13:08 schrieb EMyrone:
In this note the new Lagrangian method is applied to the orbits of ECE2 relativity in two and three dimensions, and to the relativistic H atom with fine structure. From work such as UFT328 it is known that ECE2 relativity produces precessing orbits. That paper was based on simultaneous solution of the ECE2 lagrangian and hamiltonian. The method in this note is based on the relativistic lagrangian (1) for plane polar coordinates, and (7) for spherical polar coordinates. It produces precession by using Maxima to solve the relevant Euler Lagrange equations. We have shown over the past decade that Einsteinain general relativity is completely riddled with errors, so this method produces precession without using the Einstein field equation at all. The precession can be compared with data from astronomy for any object m orbiting any object M with an assumed radial gravitational potential. If this assumption is lifted, the orbits become very interesting as shown in UFT371. The relativistic H atom is computed with the same lagrangian method and the result can be compared with the analytical result (42) for the relativistic H atom. Eq. (42) gives fine structure. The Schroedinger equation for H does not give fine structure as is well known.