Many thanks. I think that this is just a matter of notation, it could be clearer to write m(r) so the shrinking function is for example m(r) = 1 – r0 / r + alpha / r squared.

Self Consistency Check with the Geodesic Method

Excellent calculation with the geodetic method.

The only point I have is the use of the m function in form of m(r_1). Since r_1 is defined by the m function itself, this seems to be an infinite recursion. Of course one can use r_1 as an arbitrary parameter for which m is evaluated but it cannot be written in the equations of motion, there this recursion would appear. I am not sure if this is really a problem. Eqs. (27) and (29) seem to be consistent.

Horst

Am 09.10.2018 um 10:57 schrieb Myron Evans:

Self Consistency Check with the Geodesic Method

This is a cross check with the geodesic method, which gives the free particle kinetic lagrangian (16) in the (r1, phi) plane polar coordinate system. The Hamilton Principle of Least Action (21) gives the Euler Lagrange equation (22) and three constants of motion for a free particle, the total relativistic kinetic energy in m space (27), the relativistic free particle momentum p in m space, Eq. (34) and the relativistic angular momentum in m space, Eq. (38). In each case they are the same as the results of UFT415, Q. E. D. For an interacting particle in orbit, the hamiltonian in m space is Eq. (29). The m space plane polar coordinate system must always be (r1, phi), and not (r, phi), so the distance between m and M is r1 = r / m(r1) power half. Clearly, the m sapce curves, so the distance between m and M also curves. Finally the new cosmology is defined by the Euler Lagrange equation (22). The new cosmology is given by Eqs. (40) and (44), the laws of conservation of the hamiltonian and the angular momentum in m space. The Einstein field equation is not used at all of course, because it is totally wrong. The equation dH / dt = 0 gives the force, vacuum force and spin connection. Any new observational results from astronomy, particularly those that refute the standard model, can be explained with this new cosmology, which I propose to name “The ECE2 Cosmology”. The spin connection is the result of Cartan geometry, and the ECE2 gravitational field equations must always contain the spin connection and by implication the vacuum force. As mentioned yesterday Einstein considered the vacuum energy and force in 1931 in a lost paper. The standard model cosmology is in complete tatters because of its neglect of torsion, and its inability to explain the orbit of S star systems and many facts that are rapidly emerging from advanced astronomy.