## Discussion of Note 376(5)

Many thanks, they should be precisely the same because the Minkowski force equation is derived from the relativistic lagrangian using the canonical equation for relativistic momentum given by Marion and Thornton in chapter 15, (Eq. (2) of Note 376(4)). It follows immediately that the proper time must be used on the right hand side of Eq. (3), the relativistic Euler Lagrange equation. This leads to the Minkowski force equation (4) of Note 376(4). I first realized this method in Note 376(4). No one has realized that the well known Minkowski force equation (circa 1905 – 1907) gives orbital precession. No one had realized prior to our work that the relativistic lagrangian gives orbital precession. Albert Einstein certainly did not realize it, having no computer algebra of course. We have refuted EGR in many ways, Einstein often made algebraic errors as we al know by now. Minkowski taught at Bonn, Koenisgsberg, ETH and Goettingen and Albert Einstein was one of his students as you know.

To: EMyrone@aol.com
Sent: 03/05/2017 11:31:02 GMT Daylight Time
Subj: Re: Discussion of Note 376(5)

So we have two equations (Minkowski and Lagrange) for the solution of the same problem. The difference seems to be that in the Lagrange version we used

partial L / partial bold r = d/dt (partial L / partial bold r dot)

while for the Minkowski force equation we used

partial L / partial bold r = d/d tau (partial L / partial bold r dot)

(using tau derivative instead of t derivative at the rhs). I can do a numerical calculation with both versions of equations of motion and see if there is a significant difference.

Horst

Am 03.05.2017 um 12:21 schrieb EMyrone:

The relation of the lagrangian to the Minkowski force equation is given in Eqs. (1) to (4) of Note 376(4). As you know, the Minkowski force equation was first used in papers like UFT228 ff., but it was not shown in those papers that the Minkowski force equation gives a precessing orbit. This is a very important result. Notes for UFT376 build on it in various ways. The relation to fluid gravitation is given in Eq. (8) of Note 376(4).

To: EMyrone
Sent: 03/05/2017 10:58:20 GMT Daylight Time
Subj: Re: Note 376(5): Solving the Minkowski Type Orbital Equation

Eqs. (5,6) are different from those we obtained from relativistic Lagrange theory. How are both related?

Horst

Am 03.05.2017 um 11:45 schrieb EMyrone:

A precessing elliptical planar or non planar orbit can be obtained from the Minkowski type force equation (3) of ECE2 relativity by solving Eqs. (5) and (6) simultaneously with computer algebra. This note shows that the field equations of ECE2 gravitostatics produce an expression for the mass density of the source (Eq. (18)), in which X and Y are found from Eqs. (5) and (6). Eq. (18) also gives kappa dot g in terms of X and Y, so knowing g, kappa can be worked out. The quantity kappa is related to the spin connection vector of ECE2 relativity. This spin connection vector does not exist in special relativity, showing that this theory is general relativity. In special relativity, there is no spin connection in its flat Minkowski spacetime.