427(1): Hamilton and Hamilton Jacobi equations for m Theory
Many thanks indeed Excellent computation and graphical presentations. This is another significant discovery in that the results are critically dependent on m(r1). So a very small departure from ECE2 (infinitesimal line element with m(r1) = 1) produces large effects within the Hamilton Jacobi formalism. The m theory is a new and complete system of dynamics, augmenting the Hamilton Jacobi system. As Horst mentions, this is reminiscent of chaos theory.
427(1): Hamilton and Hamilton Jacobi equations for m Theory
The calculations seem to be o.k. I computed the complete Hamilton equations for the inertial system (results o9-o12) and for polar coordinates (o14-o17) and additionally with abbreviation epsilon_1 (o19-o21). The m function appears in addition to the earlier relativistic results as expected.
I also solved the Hamilton-Jacobi equation (37). The resulting diff. eq. is o7 in section 5. This is not analytically solveable with a general m(r1). I graphed two solutions with m(r1)=1 and m(r1)=0.99, see attached figure. For m(r1)=1 the same result as found for UFT 426 comes out. I could simplify the solution method and avoid a quartic equation. For m(r1)=0.99 the results differ significantly, the orbital radius nearly doubles. We find as before that the results depend very critically on the form of m(r1).
Horst
Am 07.01.2019 um 11:09 schrieb Myron Evans:
427(1): Hamilton and Hamilton Jacobi equations for m Theory
This note shows that the Hamilton and Euler Lagrange equations produce precisely the same force from m space (spacetime, aether or vacuum), Eq. (22), which can become infinite under well define conditions as discussed in UFT417. The Hamilton Jacobi equations for m theory are equations (37) and (38), which can be integrated using Maxima to give the radial and angular actions. The quantum of action is h bar, the reduced Planck constant, so Schroedinger quantization of Eq. (37) leads to an entirely new relativistic quantum mechanics, which ought to be able to describe the Lamb shift in the H atom. The spin connection can be found from Eq. (22) as in previous work.