Date: Thu, Feb 22, 2018 at 8:38 AM

Subject: Re: 402(3): The Generalized Momentum

To: Myron Evans <myronevans123>

There seems to be an intricate point with the gamma factor: according to eq.(11) of the note, gamma contains the velocity component v_i for each generalized coordinate q_i. This is different from using the modulus of v in all component equations.

Horst

Am 19.02.2018 um 15:44 schrieb Myron Evans:

]]>This Eq. (6.151) of Marion and Thornton, third edition. the term as introduced in Kelvin and Tait, "Natural Philosophy" (1867). It is the origin of the Lagrange equations of motion, and also the origin of the relativistic lagrangian. The relativistic momentum as used by Einstein is derived from the conservation of momentum. Horst has found that the relativistic Newtonian force, the time derivative of the relativistic momentum, gives retrograde precession, a major discovery because EGR fails to give retrograde precession.

Date: Tue, Feb 20, 2018 at 3:43 PM

Subject: Re: 402(4): The Vacuum Fluctuations for a Precessing Planar Orbit

To: Myron Evans <myronevans123>

This looks similar as I am preparing for UFT 401. Will finish the section the next days.

Horst

Am 20.02.2018 um 11:11 schrieb Myron Evans:

]]>The mean square vacuum fluctuation responsible for a precessing planar orbit is given by Eq. (16), in which the orbital velocity v for small precessions is given by the Newtonian (17). The angular frequency of fluctuations for any planar orbit is given by Eq. (19). These results are a straightforward result of the relativistic Newton equation (1) used with the ECE2 force equation (3). The orbital precession is obtained as in UFT377 by numerical integration of Eq. (1) with given initial conditions. This theory can be used with any coordinates system. This calculation is to second order in the tensorial Taylor series as in UFT401. The aim is to use this theory to obtain complete agreement with experimental data.

Date: Mon, Feb 19, 2018 at 12:17 PM

Subject: Self Consistency problem with relativistic Newtonian force

To: Myron Evans <myronevans123>

To my understanding the resulting inconsistency is quite clear. Lagrange theory gives relativistic equations of motion from the relativistic Lagrangian. If the equations of motion are derived from another equation directly, in this case

F = m d(p_rel)/dt = gamma^3 m dv/dt,

this is an INDEPENDENT approach, and it cannot be expected that both methods give the same result a priori. For the results to be identical, it must be

p_rel = partial L / partial bold r dot,

and this is obviously not the case. Nevertheless the Lagrangian gives the relativistic angular momentum as a constant of motion. But there is no prescription that the above first equation contains the same p_rel as obtained formally from the Lagrangian. To my knowledge the approach

p_rel = gamma m v

comes from generalization of relativistic dynamics based on the Lorentz transform which only holds for constant relative motion. Perhaps this is the problem.

Horst

Am 18.02.2018 um 13:21 schrieb Myron Evans:

]]>There is freedom of choice of proper Lagrange variables, but the review just sent over seems to be the only way to achieve complete and rigorous self consistency, and in this sense the method is unique. The formal Euler Lagrange equation using a proper Lagrange variable vector r is rigorously correct but if and only if it is correctly interpreted and correctly expressed in any given coordinate system. The formal equation to my mind is elegant and economical.

Date: Sat, Feb 17, 2018 at 6:53 PM

Subject: Re: 402(1): Origin of Retrograde Precession

To: Myron Evans <myronevans123>

I think that constructing a vector equation from a scalar equation is not unique, see my other emails from today.

Horst

Am 16.02.2018 um 13:46 schrieb Myron Evans:

]]>It is shown that the lagrangian that gave retrograde precession in UFT377, Eq.(1), must be interpreted as Eq. (4), which splits into Eqs. (10) and (11). In retrograde precession, the relativistic Newtonian force is used as in Eqs. (12) and (13). Forward precession is given by Eqs. (28) and (29), which are found from the same Eqs. (10) and (11) as retrograde precession, but without the specific use of the relativistic force. The vector form of the relativistic force, Eq. (24), is found from its magnitude, Eq. (15) in the development from Egs (15) to (24). So the retrograde precession is given by the relativistic Newtonian force, which accounts for relativistic conservation of momentum (Marion and Thornton, chapter 14) because the relativistic velocity is deduced from conservation of momentum in special relativity. ECE2 relativity is essentially special relativity in a space with finite torsion and curvature. TRhe latter are missing completely from ordinary special relativity. The retograde precession equations (25) and (26) therefore take account of conservation bothf of relativistic energy and linear momentum but the forward precession equations (28) and (29) consider only the lagrangian and conservation of relativistic energy (relativistic hamiltonian). So the retrograde precession theory is more complete. Both retrograde and froward precession obey the laws of the Hamilton Lagrange dynamics. By changing initial conditions, retrograde precession may become forward precession, and vice versa.