Alpha Institute for Advanced Studies

415(3): Final Version of the Orbit Equations of m Theory

OK many thanks, I will give this note a final check today n order to find the most general expression for the position vector r bold given the ininitesimal lime element
ds squared = dr bold dot dr bold = dr squared / m squared + r squared d phi squared

In m space r bold is no longer r e sub r. Then I will rework the problem to find the most general result in the kinematic method

415(3): Final Version of the Orbit Equations of m Theory

After a short look on this note I think I will determine the equations of motion from the Lagrangian with the m(r) function in the gamma factor. This should be straightforward (for computer evaluation) and give the same results as from (16,17). The constant of motion (17) should come out.

With this calculation scheme it should even be possible to solve many kinds of cosmological problems, for example the merging of "black holes". We know from Stephen Crothers that cosmologists put a high effort in theses caclulations, but based on a one-body theory (EGR) and classical Newtonian dynamics. Our method is better for miles than that and so simple that it can be evaluated on a desktop computer.

Horst

Am 20.09.2018 um 08:40 schrieb Myron Evans:

415(3): Final Version of the Orbit Equations of m Theory

In this final version the spin connection is incorporated and the orbit equations to be solved simultaneously for the orbit are Eqs. (16) and (17). Horst’s powerful integration algorithm can now be used for these equations.The conserved angular momentum L of the system can be found by numerical integration of Eq. (17). As in UFT190 the orbit is also given by Eq, (18), with the ECE m function (19) in which R is a characteristic distance of the universe. As in UFT108 and other papers it has been shown that m theory produces a shrinking orbit. The Lagrangian is found from Eq. (12) and when it is defined in this way the agreement with the kinematic method of this note is ensured automatically. There are also other ways of developing orbit equations of my theory, for example the simultaneous solution of dH / dt= 0 and dL / dt = 0 where H and L are defined by the Einstein Hilbert action. This was used in a previous UFT paper. The spin connection can be used as an adjustable parameter or it can be introduced by rotating frame theory, which has not yet been used with m theory. Having found the spin connection, the vacuum force can be found and the isotropically averaged vacuum fluctuations found as in previous UFT papers. So themes are being woven together as in the final movement of Mozart’s 41st Symphony, the Jupiter Symphony, to produce a powerful and harmonious theory all rigorously and correctly based on geometry. There are hundreds of checks and cross checks and computer algebra is used whenever possible.

415(3): Final Version of the Orbit Equations of m Theory

Thanks again. I should have the most general expression for r bold ready by about tomorrow. In space of UFT414 r bold = r e sub r in plane polar coordinates, but in m space this is no longer true, making the orbit even more interesting.

415(3): Final Version of the Orbit Equations of m Theory
To: Myron Evans <myronevans123>

When calculating d gamma/dt, terms like d m(r)/dt appear. I replaced these by

d m(r)/dt = d m(r)/dr * dr/dt.

I think this is correct because we do not have a partial derivative here.

Horst

Am 20.09.2018 um 08:40 schrieb Myron Evans:

415(3): Final Version of the Orbit Equations of m Theory

In this final version the spin connection is incorporated and the orbit equations to be solved simultaneously for the orbit are Eqs. (16) and (17). Horst’s powerful integration algorithm can now be used for these equations.The conserved angular momentum L of the system can be found by numerical integration of Eq. (17). As in UFT190 the orbit is also given by Eq, (18), with the ECE m function (19) in which R is a characteristic distance of the universe. As in UFT108 and other papers it has been shown that m theory produces a shrinking orbit. The Lagrangian is found from Eq. (12) and when it is defined in this way the agreement with the kinematic method of this note is ensured automatically. There are also other ways of developing orbit equations of my theory, for example the simultaneous solution of dH / dt= 0 and dL / dt = 0 where H and L are defined by the Einstein Hilbert action. This was used in a previous UFT paper. The spin connection can be used as an adjustable parameter or it can be introduced by rotating frame theory, which has not yet been used with m theory. Having found the spin connection, the vacuum force can be found and the isotropically averaged vacuum fluctuations found as in previous UFT papers. So themes are being woven together as in the final movement of Mozart’s 41st Symphony, the Jupiter Symphony, to produce a powerful and harmonious theory all rigorously and correctly based on geometry. There are hundreds of checks and cross checks and computer algebra is used whenever possible.

The Peloponnesian War (Thucydides)

As the diary or blog records, on 27th August 2007 Ray Delaforce expressed his profound anger at the attacks on B(3) by standard model harassers such as Bruhn and Lakhtakia, citing the Objectivist philosophy of Ayn Rand (1905 – 1982), who dealt with group warfare and the politics of envy. Those who are productive and competent in a particular field are subjected to what is now known as hate mailing based on group warfare and the politics of envy. The productive scholars are paradoxically despised for their competence, honesty and integrity, the very qualities that are most needed by humankind in its present perilous condition. The theft of two thousand of my diary entries by a hate group "Fruitcake" has been investigated by DMCA Ltd.,and the Fruitcake site as a whole has been investigated to a small extent by the highest levels of the South Wales Police, and I finally managed to get the stolen postings removed under the DMC Act. The Police were ineffective in doing this because their hands were tied by very weak laws. I will call for an FBI investigation of this hate site, and of WordPress, for allowing it to be set up. I have been advised to do this by the Copyright Office in Washington. I think I will write a short autobiographical book called "The Peloponnesian War" outlining the savage attacks on my colleagues, friends, family and myself by the standard model establishment and condemning those known to be associated with the hate site. The blog records on 10/1/2011 how the harasser Lakhtakia was traced and how the Penn State Police opened an investigation on 5/11/2010. Sparta won the Peloponnesian War and that left the superior Athenian civilization in ruins. Pericles died in a plague The Baconian philosophy and enlightenment has however won the second Peloponnesian war two thousand five hundred years later. The standard model of physics lies in ruins and its methods utterly discredited, for example its use of Wikipedia to try to destroy scientists. Jo McCarthy or Jo Stalin reincarnate.

415(3): Final Version of the Orbit Equations of m Theory

In this final version the spin connection is incorporated and the orbit equations to be solved simultaneously for the orbit are Eqs. (16) and (17). Horst’s powerful integration algorithm can now be used for these equations.The conserved angular momentum L of the system can be found by numerical integration of Eq. (17). As in UFT190 the orbit is also given by Eq, (18), with the ECE m function (19) in which R is a characteristic distance of the universe. As in UFT108 and other papers it has been shown that m theory produces a shrinking orbit. The Lagrangian is found from Eq. (12) and when it is defined in this way the agreement with the kinematic method of this note is ensured automatically. There are also other ways of developing orbit equations of my theory, for example the simultaneous solution of dH / dt= 0 and dL / dt = 0 where H and L are defined by the Einstein Hilbert action. This was used in a previous UFT paper. The spin connection can be used as an adjustable parameter or it can be introduced by rotating frame theory, which has not yet been used with m theory. Having found the spin connection, the vacuum force can be found and the isotropically averaged vacuum fluctuations found as in previous UFT papers. So themes are being woven together as in the final movement of Mozart’s 41st Symphony, the Jupiter Symphony, to produce a powerful and harmonious theory all rigorously and correctly based on geometry. There are hundreds of checks and cross checks and computer algebra is used whenever possible.

a415thpapernotes3.pdf

Note 415(2): The Orbit Equations of Relativistic m Theory

These are equations (18) and (19), which are the orbit equations in the most general spherically symmetric space defined by the infiitesimal line element (1). The conserved angular momentum in m space is given by Eq. (21), which is cross checked with the relativistic Euler Lagrange equations of m space. The m function from ECE theory can be used, as in UFT108, UFT190 and similar papers. The next step is to develop frame rotation theory in m space. This will define the spin connection in m space, and the vacuum force in m space. Knowing the spin connection, the complete field equations can be derived in m space. We also have available the antisymmetry laws of ECE2 theory, and the triple unification of gravitation, electromagnetism and fluid dynamics. All these major advances go well beyond the standard model in a richly woven tapestry of powerful new ideas.

a415thpapernotes2.pdf

415(1): The Lagrangian and Hamiltonian of m Theory

These can be derived straightforwardly by calculating the Lorentz factor from the line element of m theory, Eq. (1). The orbit is obtained by solving the Euler Lagrange equations (13) and (14). The Euler Lagrange equations give the Leibniz equation of m theory, Eq. (29), and the conservation of angular momentum in m theory, Eq. (24). Eqs. (24) and (29) are solved numerically to give the relativistic orbit of m theory in the most general spherically symmetric space. The results should be consistent with previous work on m theory, for example UFT108, in which it was found that a shrinking orbit is given by Eq. (26). In UFT190 it was shown that the m function of ECE cosmology is Eq. (29). So ECE and ECE2 has gone far beyond the standard model in about seven hundred papers and books produced since 2003. ECE Schools of thought exist in essentially all the wold’s best universities.

a415thpapernotes1.pdf

414(9): Equations of Motion and Multiple Self Consistency Checks

This note gives a rigorous self consistency check for the free particle hamiltonian (6) using the ECE2 infinitesimal line element (1). This is a baseline calculation before embarking on m theory in UFT415. It is found that the relativistic equations (40) and (41) give r(phi) as in Eq (31), derived in two different ways giving the same results. This means that the numerical integration of Eqs. (40) and (41) must give the orbit (31). This provides a check for the numerical method. The orbit (31) is integrated to give Eq. (53) for the relativistic free particle in plane polar coordinates.The non relativistic free particle is described by Eq. (56). The m theory with m = 1 – r sub 0 / r gives the obsolete Einsteinian general relativity (EGR), and introduces additional terms in Eq. (17). Here r sub 0 is the obsolete Schwarzschild radius. It is known that m theory gives a shrinking orbit, so will be merged with the relativistic orbital theory of UFT414 in UFT415. So I will now proceed to writing up UFT414.

a414thpapernotes9.pdf

The correct rel. kinetic energy

Subject: The correct rel. kinetic energy
To: Myron Evans <myronevans123>

Thanks again for this meticulous numerical checking. The lagrangian used in Note 404(4) was the complete lagrangian as defined in Eq. (17) and in Marion and Thornton chapter (14.113) of the third edition. This was one of two methods used to derive the relativistic Leibniz equation (29) and the relativistic angular momentum (31). The two methods gave exactly the same results. The Euler Lagrange variables were r and phi. The calculations are given in Eqs. (21) to (29). The relativistic angular momentum L is given in Eq. (31) and dL / dt gives Eq. (34). Eq. (29) derived in this way as as shown to be the same as Eq. (7), derived from the very fundamental kinematic equation (5). So to obtain the kinematic equation the complete lagrangian (17) must be used with Euler Lagrange variables r and phi. Eq. (7) can be transformed into Eq. (44) using Eqs. (37) and (38). Eq. (44) is the usual form of the relativistic Newton force as given for example in the problem section of Marion and Thornton, third edition, chapter fourteen, problem 38. The new insights given in Note 414(4) are Eqs. (37) and (38). Then Note 414(5) gives a triple cross check using the hamiltonian method. The complete relativistic hamiltonian H must be used, Eq. (1). This is a constant of motion so dH / dt = 0. This gives Eq. (6) of Note 414(5). When this is used in the relativistic force (7), the realtivistic Newton force Eq. (11) is obtained in a third way. so there is a triple cross check. The relativistic force equation has been derived in three ways, each giving the same result:

F = m gamma cubed dv / dt = -mMg / r squared.

As you know, we have used this equation in Cartesian coordinates in several previous UFT papers to give many interesting and original results. Finally the rotating frame method was applied to this equation, giving the relativistic version of paper UFT413. So a whole pile of new physics has emerged.

T = – m c^2 / gamma

or

T = (gamma-1) m c^2 ?

I obtain different results for both. In the second case an additional factor 1/gamma^2 seems to appear in the baseline calculation.

The results in the first case are

and in the second case:

The first case can be simplified with re-inserting gamma.
I will have to check this further.

Horst

Relativistic Spin Connection due to Frame Rotation

Many thanks for such a fast response! I rechecked my calculation and agree. This is all most interesting, and have a very good holiday!

Relativistic Spin Connection due to Frame Rotation

It seems that there is a term -1/r missing i the relativistic spin connection. It should read:

For the numerical calculation I have to compute the equations from the definitions directly because they have to be resolved for r dot dot and phi dot dot at one side. Will see if I can do this today. Tomorrow I am going on holiday.

Horst

Am 10.09.2018 um 11:46 schrieb Myron Evans:

Relativistic Spin Connection due to Frame Rotation

This note calculates the relativistic spin connection by assuming that the frame rotation applied to the relativistic Newton equation produces the spin connection and vacuum force. The result is that simultaneous solution of Eqs. (21) and (22) gives the orbit. It will be very interesting to see whether or not this is a shrinking orbit.

414(7).pdf

Relativistic Spin Connection due to Frame Rotation

This note calculates the relativistic spin connection by assuming that the frame rotation applied to the relativistic Newton equation produces the spin connection and vacuum force. The result is that simultaneous solution of Eqs. (21) and (22) gives the orbit. It will be very interesting to see whether or not this is a shrinking orbit.

a414thpapernotes8.pdf