PS: Corrigendum Section 3 of paper 417

Important Results for Superluminal Motion

I will add this diagram to the paper. It shows the generalized gamma factor in dependence of the m(r) values. The curves are parameterized by v/c. gamma can drop below 1 for m(r)>1. It is seen that v/c > 1 is no problem for m theory.

Horst

Am 30.10.2018 um 08:00 schrieb Horst Eckardt:

In the last paragraph of section 3.2 it should read
gamma < 1
instead of
gamma > 1.

I will eventually make an update with an additional diagram of the generalized gamma factor.

Horst

Am 30.10.2018 um 06:44 schrieb Myron Evans:

Fwd: Section 3 of paper 417

Many thanks! This is one of the most important sections in the entire UFT series and a close study is highly recommended. It has many points of interest, for example it shows that the spherical spacetime is in itself sufficient to produce force and energy which is not present in flat spacetime and not present in the classical limit. It carefully defines the conditions for infinite energy from m space and for superluminal motion, and numerically develops the method for finding m(r) from astronomy. It is a great advance over the Einsteinian general relativity because it does not use the Einstein field equation. This means that numerical experimental can be carried out with various m(r) functions. Horst’s numerical work also shows that the spin connection must be a consequence of spherical spacetime and cannot be introduced arbitrarily because conservation of energy and angular momentum may be violated. The Einstein field equation restricts m(r) to 1 – r0 / r. This is wholly incorrect because as the famous UFT88 shows, the second Bianchi identity used by Einstein is changed completely by Cartan torsion. The Einstein field equation is based on incorrect, torsionless geometry. By now this is well known and well accepted as shown by nearly fourteen years of accumulated feedback data. Cartan torsion causes frame rotation which produces the spin connection, and frame rotation and m space theories are interlinked numerically in this section. So concepts are rigorously self consistent. It is shown numerically that some m(r) functions give well behaved results, others do not. use is made of m(r) functions that give orbital shrinking. So in summary the use of equations of motion in m space produces results of major importance. The equations of motion are dH / dt = 0 and dL / dt = 0 where H is the hamiltonian and L the angular momentum, the conserved constants of motion of any orbit in the universe, and of m space dynamics in general. This method can also produce retrograde precession, the Einsteinian general relativity cannot. So we have gone suddenly gone far ahead of the standard model in a major paradigm shift.
Section 3 of paper 417

This is section 3 with three subsections. I hope all is understandable.
The solution of the m function equations in classical limit will go into paper 418.

Horst

Am 29.10.2018 um 18:03 schrieb Myron Evans:

Yes agreed. The velocity of the frame rotation is related to omega by v sub phi = omega r, in the plus or minus direction, and omega is foujnd from the precession

Question for paper 417 To: Myron Evans <myronevans123>

In eq.(61) there is a term v_phi^2 and a term (dr/dt)^2 = v_r^2. Do I
understand it right that v_phi is the velocity of frame rotation which
is predefined, while v_r is the radial velocity component of the orbit.
Then both components are quite differently to handle. Only v_r has to be
determined from the dynamics trajectories.

Horst

Corrigendum Section 3 of paper 417

Corrigendum Section 3 of paper 417

OK thanks.

Corrigendum Section 3 of paper 417

In the last paragraph of section 3.2 it should read
gamma < 1
instead of
gamma > 1.

I will eventually make an update with an additional diagram of the generalized gamma factor.

Horst

Am 30.10.2018 um 06:44 schrieb Myron Evans:

Fwd: Section 3 of paper 417

Many thanks! This is one of the most important sections in the entire UFT series and a close study is highly recommended. It has many points of interest, for example it shows that the spherical spacetime is in itself sufficient to produce force and energy which is not present in flat spacetime and not present in the classical limit. It carefully defines the conditions for infinite energy from m space and for superluminal motion, and numerically develops the method for finding m(r) from astronomy. It is a great advance over the Einsteinian general relativity because it does not use the Einstein field equation. This means that numerical experimental can be carried out with various m(r) functions. Horst’s numerical work also shows that the spin connection must be a consequence of spherical spacetime and cannot be introduced arbitrarily because conservation of energy and angular momentum may be violated. The Einstein field equation restricts m(r) to 1 – r0 / r. This is wholly incorrect because as the famous UFT88 shows, the second Bianchi identity used by Einstein is changed completely by Cartan torsion. The Einstein field equation is based on incorrect, torsionless geometry. By now this is well known and well accepted as shown by nearly fourteen years of accumulated feedback data. Cartan torsion causes frame rotation which produces the spin connection, and frame rotation and m space theories are interlinked numerically in this section. So concepts are rigorously self consistent. It is shown numerically that some m(r) functions give well behaved results, others do not. use is made of m(r) functions that give orbital shrinking. So in summary the use of equations of motion in m space produces results of major importance. The equations of motion are dH / dt = 0 and dL / dt = 0 where H is the hamiltonian and L the angular momentum, the conserved constants of motion of any orbit in the universe, and of m space dynamics in general. This method can also produce retrograde precession, the Einsteinian general relativity cannot. So we have gone suddenly gone far ahead of the standard model in a major paradigm shift.
Section 3 of paper 417

This is section 3 with three subsections. I hope all is understandable.
The solution of the m function equations in classical limit will go into paper 418.

Horst

Am 29.10.2018 um 18:03 schrieb Myron Evans:

Yes agreed. The velocity of the frame rotation is related to omega by v sub phi = omega r, in the plus or minus direction, and omega is foujnd from the precession

Question for paper 417 To: Myron Evans <myronevans123>

In eq.(61) there is a term v_phi^2 and a term (dr/dt)^2 = v_r^2. Do I
understand it right that v_phi is the velocity of frame rotation which
is predefined, while v_r is the radial velocity component of the orbit.
Then both components are quite differently to handle. Only v_r has to be
determined from the dynamics trajectories.

Horst

First results: classical vs. relativistic m theory

First results: classical vs. relativistic m theory

Many thanks, there are several important advances here, and the numerical confirmation of conservation of energy and angular momentum gives great confidence in the results. In general the m theory must be first reduced to flat (Minkowski) spacetime by using m(r) goes to 1 and dm(r) / dr goes to zero. Then well known methods can be applied to reduce the flat space theory to the classical theory. For vacuum force for example, Eq. (6) of Note 418(1), mc squared is multiplied by a factor that includes dm(r) / dr. In UFT417 it was shown that the rest energy in m space is m(r) half m c squared. The relativistic vacuum force is gamma m c squared f(r), where f(r) is the function defined in Eq. (6). The relativistic kinetic energy in flat spacetime is T = (gamma -1) m c squared, which reduces to the classical (1/2) m v squared when v << c. This suggests that a smooth transition from relativstic to classical can be obtained by using the classical vacuum energy F(vac) (relativistic) – m(r) half m c squared. I will have a look at this procedure today. In general however the vacuum force can become very large, in the same way that the famous E = m c squared shows that there is a huge amount of energy in a given mass m because m is multiplied by c squared. The classical hamiltonian (11) of Note 418(1) has been obtained by removing the rest energy m(r) half m c squared. The relativistic hamiltonian is H = m(r) gamma m c squared – mMG / r and the relativistic hamiltonian is very large if the rest energy is not removed from it. The hamiltonian in any relativistic theory is H = T + U + E0, i.e. kinetic energy plus potential energy plus rest energy. A smooth transition to the classical theory is obtained by using H0 = H – E0 = T + U. I think that it was Sommerfeld who first used this procedure to find the quantized Sommerfeld atom. So the same procedure must be used in m theory and I will have a look at this today. Your numerical results are correct, in general the vacuum energy is enormous, so is the rest energy.
First results: classical vs. relativistic m theory

It seems that there is no smooth transition between both theories. in
rel. m theory the equations of motion contain terms with c^2*dm/dr. A
tiny deviation from m=1 generates massive relativistic effects. This is
not the case in the classical m theory where no such terms are there.
The classical m theory approaches the non-relativistic limit much smoother.
Examples:
F0: m function for both calculations (with same initial conditions)
F1: orbit of classical m theory
F2: energies of classical m theory
F3: orbit of relativistic m theory
F4: energies of relativistic m theory

It is seen that energy (and angular momentum) is conserved in classical
m theory but for the same m(r) the results are quite different. In
addition one can play with the "strength" of the relativistic effects by
modifying c in the calculation, but a bigger c (normally reducing
relativistic effects) increases the deviations from ellipses
significantly by the term c^2*dm/dr.

We will have to investigate this further. I can put together the
equations of motion for direct comparison.

Horst

Section 3 of paper 417

Fwd: Section 3 of paper 417

Many thanks! This is one of the most important sections in the entire UFT series and a close study is highly recommended. It has many points of interest, for example it shows that the spherical spacetime is in itself sufficient to produce force and energy which is not present in flat spacetime and not present in the classical limit. It carefully defines the conditions for infinite energy from m space and for superluminal motion, and numerically develops the method for finding m(r) from astronomy. It is a great advance over the Einsteinian general relativity because it does not use the Einstein field equation. This means that numerical experimental can be carried out with various m(r) functions. Horst’s numerical work also shows that the spin connection must be a consequence of spherical spacetime and cannot be introduced arbitrarily because conservation of energy and angular momentum may be violated. The Einstein field equation restricts m(r) to 1 – r0 / r. This is wholly incorrect because as the famous UFT88 shows, the second Bianchi identity used by Einstein is changed completely by Cartan torsion. The Einstein field equation is based on incorrect, torsionless geometry. By now this is well known and well accepted as shown by nearly fourteen years of accumulated feedback data. Cartan torsion causes frame rotation which produces the spin connection, and frame rotation and m space theories are interlinked numerically in this section. So concepts are rigorously self consistent. It is shown numerically that some m(r) functions give well behaved results, others do not. use is made of m(r) functions that give orbital shrinking. So in summary the use of equations of motion in m space produces results of major importance. The equations of motion are dH / dt = 0 and dL / dt = 0 where H is the hamiltonian and L the angular momentum, the conserved constants of motion of any orbit in the universe, and of m space dynamics in general. This method can also produce retrograde precession, the Einsteinian general relativity cannot. So we have gone suddenly gone far ahead of the standard model in a major paradigm shift.
Section 3 of paper 417

This is section 3 with three subsections. I hope all is understandable.
The solution of the m function equations in classical limit will go into paper 418.

Horst

Am 29.10.2018 um 18:03 schrieb Myron Evans:

Yes agreed. The velocity of the frame rotation is related to omega by v sub phi = omega r, in the plus or minus direction, and omega is foujnd from the precession

Question for paper 417 To: Myron Evans <myronevans123>

In eq.(61) there is a term v_phi^2 and a term (dr/dt)^2 = v_r^2. Do I
understand it right that v_phi is the velocity of frame rotation which
is predefined, while v_r is the radial velocity component of the orbit.
Then both components are quite differently to handle. Only v_r has to be
determined from the dynamics trajectories.

Horst

paper417-3.pdf

Question for paper 417

Yes agreed. The velocity of the frame rotation is related to omega by v sub phi = omega r, in the plus or minus direction, and omega is foujnd from the precession

Question for paper 417To: Myron Evans <myronevans123>

In eq.(61) there is a term v_phi^2 and a term (dr/dt)^2 = v_r^2. Do I
understand it right that v_phi is the velocity of frame rotation which
is predefined, while v_r is the radial velocity component of the orbit.
Then both components are quite differently to handle. Only v_r has to be
determined from the dynamics trajectories.

Horst

417(7): Role of m(r) in the Classical Lagrangian and Hamiltonian

417(7): Role of m(r) in the Classical Lagrangian and Hamiltonian

Many thanks! I would say that the rest energy in m space is modified by the fact that m(r) is no longer one, so the rest energy is E0 = m(r) half m c squared. The famous Minkowski space rest energy E0 = m c squared is obtained from a work integral : integral F . dr = T2 – T1 where F = dp / dt and p = gamma m v. This procedure gives the Minkowski space relativistic kinetic energy T = (gamma – 1) mc squared = E – m c squared. There is nothing in this method that asserts that E0 must be constant, and as soon as we depart from Minkowski spacetime the rest energy depends on m(r). This is one of the startingly new features of the m theory. At the obsolete Schwarzschild radius the rest energy disappears entirely because m(r) = 0 at r = r0 when m(r) =1 – r0 / r. The m(r) function in the quartic is actually x squared, so your protocol already gives the answer, m(r) = x squared, and there is no need to take square roots. So we can simply plot the four m(r) roots to see how they behave, whether they are real valued or complex valued. If they are complex valued we can use square root (m(r)m(r)*) as is the usual practice in physics.

417(7): Role of m(r) in the Classical Lagrangian and Hamiltonian

This is a remarkable note, giving new experimental methods for determining the function m(r).
Definition (32) for H_0 first seemed a bit arbitrary to me because a non-constant term is subracted from H, but the results are self-consistent.
It should be possible to set up Euler-Lagrange equations for this classical approach of spherical spacetime. The Lagrangian obviously is (35). What has to be inserved for v^2 here? I guess the definition from plane polar coordinates as in (36):

v^2 = r dot^2 + r^2 phi dot^2.

The four solutions of the quartic equation (62) are extremely complicated (see attachment) and it is not clear which square roots give real valued results. It might be better to use a numerical solution method like Newton-Raphson and start with m(r)=1.

Horst

Am 25.10.2018 um 10:40 schrieb Myron Evans:

417(7).pdf

PS: Re: Circuits for Infinite Energy from Spacetime

Circuits for Infinite Energy from Spacetime

This is an excellent result, a modification by Horst Eckardt of the infinite energy condition found by Russ Davis. The m theory gives both superluminal motion and infinite spacetime energy from the same basic equations so goes far ahead of the standard model. This is an excellent group discussion.
Circuits for Infinite Energy from Spacetime

2nd try

PS: This is an m function which is quadratic for r<a and of type 1/r^2 for r>a. I had to play a bit with the constants so that the transition at r=0 is continuous and differentiable. In the graph it is a=1/2.

Horst

Am 22.10.2018 um 19:24 schrieb Russell Davis:

Horst,

Perhaps I missed something in the recent papers and notes, but isn’t the salient requirement only that m(r) –>1, so that the spin connection expression UFT415 eq.44 reduces to UFT414 eq. 54 ? However, is there a minus sign typo between these two equations?

Isn’t the more stingent requirement, m(r) –> 1 for r–> infinity, only needed for certain cosmological-scale features that you were modeling?

-Russ

PS: Re: Circuits for Infinite Energy from Spacetime

Circuits for Infinite Energy from Spacetime

This looks like another useful result, and as can be seen there are many ways of cross correlating concepts and ideas of energy from spacetime. The principles of physics are well established and there are many ideas available for the engineers.

Circuits for Infinite Energy from Spacetime

PS: This is an m function which is quadratic for r<a and of type 1/r^2 for r>a. I had to play a bit with the constants so that the transition at r=0 is continuous and differentiable.

Horst

Am 22.10.2018 um 19:24 schrieb Russell Davis:

Horst,

Perhaps I missed something in the recent papers and notes, but isn’t the salient requirement only that m(r) –>1, so that the spin connection expression UFT415 eq.44 reduces to UFT414 eq. 54 ? However, is there a minus sign typo between these two equations?

Isn’t the more stingent requirement, m(r) –> 1 for r–> infinity, only needed for certain cosmological-scale features that you were modeling?

-Russ

Circuits for Infinite Energy from Spacetime

I would say that the maximum value of force and energy from sapcetime can be found by finding the well behaved maximum value of a function by differentiation, and that the parabolic result is one possibility. In the limit m(r) goes to one the Minkowski spacetime is retrieved as is well known. In the general spherical spacetime m(r) is any function of r (Carroll chapter seven). It looks as if the most important need at this time is for a big industrial / academic effort to feed back the output into the input.

Circuits for Infinite Energy from Spacetime

Russ,

the limit m(r) –>1 should hold for large r because we expect non-relativistic behaviour in the far field. For m(r)=0 we have a singularity, therefore it should always be

0 < m(r) <= 1.

m(r) > 1 is possible for rotating frames as described in UFT 417(6), but this is more an exception. For me it seems most plausible that the sought form of m would rise as r^2 for small r and then recurve to a constant value. Then we would have big spacetime energy transfer for small radii.

Horst

Am 22.10.2018 um 19:24 schrieb Russell Davis:

Horst,

Perhaps I missed something in the recent papers and notes, but isn’t the salient requirement only that m(r) –>1, so that the spin connection expression UFT415 eq.44 reduces to UFT414 eq. 54 ? However, is there a minus sign typo between these two equations?

Isn’t the more stingent requirement, m(r) –> 1 for r–> infinity, only needed for certain cosmological-scale features that you were modeling?

-Russ