This is the geodesic method first derived in UFT416. It shows in another way that the Evans Eckardt equations dH / dt = 0 and dL / dt = 0 are very fundamental and easier to use than the lagrangian method. As in 424(1) a lagrangian can be found to give the EE hamiltonian, and that leads to constraint equations with new information.

## Archive for the ‘asott2’ Category

### 424(2): Geodesic Method of Deriving the Evans / Eckardt Equations

December 10, 2018### Sagnac Effect for Different Platform Radii

December 10, 2018Many thanks for these remarks. A photon travelling around the rim of a Sagnac platform in an optical fibre is affected by the earth’s gravitational field. The Earth has a Schwarzschild radius r0 of 8.9 mm = 0.089 m. So if the Sagnac interferometer is placed in the earth’s gravitational field, the photon traversing an optical fibre loop will be subjected to a correction due to EGR, so the infinitesimal line element is changed to the so called Schwarzschild line element from which the Sagnac effect is calculated using a null geodesic ds squared = 0. As you know this is the result of the Einstein equivalence principle. The radius of the platform is fixed, so dr = 0. The only measurement required is the usual difference in time taken to go clockwise and anticlockwise around the circumference, delta t. This is the usual measurement in a Sagnac interferometer as you know. Steve Crothers and ourselves have severely criticized the Schwarzschild solution, so the results from the Sagnac interferometer will show that it is incorrect. Also, Steve has shown that the standard model mixes ideas – radius and radius of curvature. There is no doubt that the Schwarzschild metric is written with radial coordinate r, so it is an example of m theory with:

m ( r ) = 1 – r0 / r

in the (r , phi) coordinate system. The Sagnac effect in the most general spherically symmetric spacetime is

delta t = 4 pi r squared omega / (m (r) c squared)

and m ( r ) can be measured easily in a Sagnac interferometer. The origin of the ( r , phi ) coordinate system is the centre of the Sagnac platform, so the angular velocity of the rotation of the platform is capital omega = v / r where v is the linear velocity of the rim of the platform. The angular velocity of light traversing the optical fibre is omega = c / r = kappa c because the velocity of the light is c. So the calculations in UFT422 lead to the above result for any m (r). Almost certainly, the experiment will show that m ( r ) is very close to unity, but not identically equal to one because the Sagnac effect is known to be affected by gravity. This is consistent with the fact that the photon of the Sagnac interferometer is affected by gravity, in this case the earth’s gravity. Near a neutron star, in the gravitational field of a very large mass, the Sagnac effect will be completely different from the Sagnac effect on the earth’s surface. In the gravity free conditions on board a spacecraft, I anticipate that the Sagnac effect will be different from that on the earth’s surface.

Sagnac Effect for Different Platform Radii

As far as i know the parameter r in the m function

1 – r0/r

must be the distance from the gravitational centre. It cannot have to do with the radius of the sagnac interferometer.

Another point is whether interferometric measurements give a difference for several hights r. As Bernhard has pointed out, time measurements are changed with c. So it is not possible to measure differences of the Sagnac effect directly at tha place where the interferometer is positioned. I do not know if this is different for interferometry.

Ps: i am out of munich until tuesday, will be back on wednesday.

Horst

Von meinem Samsung Gerät gesendet.

### Daily Weblogs Report Saturday 8/12/18

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### Sagnac Effect for Different Platform Radii

December 9, 2018The Sagnac effect in m theory is modified to delta t = 4 Ar omega / (m (r ) c squared) where m (r ) is to be determined experimentally. Here Ar is the radius of the Sagnac ring and omega the angular velocity of platform rotation of the Sagnac interferometer. In the obsolete Einsteinian general relativity (EGR), m ( r ) = 1 – r0 / r, where r0 is the Schwarzschild radius and r the radial coordinate of the plane polar system (r, phi). Here delta t is the difference in the time taken for light to traverse the perimeter of the rim clockwise and anticlockwise. The effect is measured with an interferogram. The Sagnac interferometer is placed in a laboratory in the earth’s gravitational field, so r0 = 0.09 metres. Here r is the radius of the Sagnac ring. Therefore EGR predicts:

delta t = 4 pi r squared omega / (c squared (1 – 0.09 / r))

Therefore if EGR is correct the Sagnac effect should change with r, where Ar = pi r squared. So experiments are needed with Sagnac interferometers with different platform areas and different r. The usual Sagnac effect is

delta t = 4 pi r squared omega / ( c squared)

### UFT88 Read at Northwestern University

December 9, 2018Northwestern is ranked 29 in the world by Webometrics, 25 by Times, 34 by QS and 25 by Shanghai. It was founded by John Evans and a group of Methodists in 1851 to serve the vast Northwest Territory. It has an acceptance rate of 13% and is associated with nineteen Nobel Laureates, being situated in Evanston, Illinois. There has been a well established ECE School of Thought in Northwestern ever since inception of the theory in 2003, and by now this is true of any university of note, as the scientometrics show. John Evans became the Governor of the Territory of Colorado and helped to found Colorado Seminary which became the University of Denver in which Alwyn van der Merwe is Emeritus Professor. The Nobel Laureate John Pople moved from Cambridge to Northwestern. UFT88 refutes the Einstein field equation by refuting the second Bianchi identity by incorporating torsion. The second Bianchi identity is developed into the Jacobi Cartan Evans identity of UFT313, so the correct use of torsion changes the Einstein field equation completely, showing the the original equation of 1915 is incorrect and meaningless. ECE, ECE2 and m theory develop physics in ways that do not suffer from major geometrical errors. Recently it has become clear that the Einstein theory is refuted by the velocity curve of a whirlpool galaxy, by the orbit of the S2 star and by the Sagnac interferometer when considered in the most general spherically symmetric spacetime of m theory. There are almost a hundred independent refutations of the Einstein theory in the UFT series of about seven hundred papers and books produced since 2003 in English and Spanish translation by Alex Hill. All of these are consulted continuously around the world without objection. Therefore the old system of citation has been overtaken by a system that measures actual consultations.

### Daily Weblogs Report 7/12/18

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### Note 424(1): Derivation of the Lagrangian of m Theory from the Hamiltonian

December 8, 2018The lagrangian is Eq. (19), and is derived from the hamiltonian using the fundamental equation (1) of Lagrangian dynamics. The lagrangian is therefore rigorously equivalent to the hamiltonian and to the Evans Eckardt equations. This is an entirely new physics so a vast amount of new information is given by it. From now on I suggest using both hamiltonian and lagrangian methods. The first thing to do is to derive orbits, superluminal motion, energy from m space, and all previous results of UFT415 ff from the Evans Eckardt equations by solving dH / dt = 0 and dL / dt = directly without using the lagrangian. The rigorously correct lagrangian is now known and the Euler Lagrange equations (22) and (23) will give additional equations which must be equivalent to the Evans Eckart equations. This will lead to several new constraint equations such as (34). The rigorously correct lagrangian (19) reduces to the lagrangian used initially by inspection in the limit m ( r ) goes to one, but not identically equal to one. The Hamilton canonical equations can also be used at a later stage and quantization can be initiated. With the computer, any amount of complexity is no problem.

### Measuring the Sagnac Effect

December 8, 2018Dear Bernhard,

Your comments are most interesting, especially the construction of the Sagnac interferometer. UFT421 describes the theory behind the refutation of Einsteinian general relativity (EGR) with the velocity curve of a whirlpool galaxy. The reason is that the observed velocity curve goes to a plateau as r becomes infinite. This was first discovered about fifty years ago and the astronomer who discovered it was ostracized and ridiculed, so must have been on to a good thing. UFT421 first shows that the Newtonian result is Eq. (5), so the velocity goes to zero as r becomes infinite. This is why the astronomer was ridiculed and cast into the outer darkness, down a drift mine. It was thought that Newton (being an idol of the Baconian cave) could not be so completely wrong. The starting point of the Newton theory is the well known Eq. (2). The Newtonian theory also gives Eq. (8). So the key piece of data is the well known velocity curve. The EGR is easily refuted by using the EGR orbit (12) in Eq. (8). As r becomes infinite, Eq. (14) follows. This is the free particle Einstein energy equation (19), so the relativistic momentum at infinite r is Eq. (20) and becomes zero as r goes to infinity. So EGR is refuted entirely because the observed result is a plateau. The fact that the velocity is c / 1000 means that Einstein is very close to Newton, the relativistic momentum is close to the Newtonian momentum, which goes to zero, not the observed plateau. It is also obvious that neither Einstein nor Newton give a Coates spiral orbit. The Coates spirals in a galaxy are obviously visible. Einstein gives a precessing ellipse and Newton gives an ellipse. This failure of EGR was greeted with deafening silence, there were omelettes on eminent faces, and the idea of dark matter quickly cobbled up in order to keep on claiming that EGR must be right after all. We are now told that the universe is made up of dark matter. This is irrational dogmatism. Einstein would have said that his theory was finished and would have started to look for a new one. The S2 star is described in UFT419. In this case it is obvious that EGR is totally wrong because its precession of 0.219 degrees per orbit is not observed experimentally. Within the experimental noise there is zero precession, plus or minus an uncertainty. The constant m theory gives a precession of 0.033 degrees per orbit. Horst discovered that the S2 orbit is an ellipse that can only be described by a constant m. In UFT419 it was shown that the ellipse is not Newtonian. So again Einstein would have looked for a new theory, so would Newton or Leibniz. Now we are told by wiki that EGR is right in S2 because it describes the gravitational red shift. This is despite the fact that EGR is totally wrong because its precession is totally wrong. The m theory of the Sagnac effect is described in UFT422. It starts with the infinitesimal line element of the m theory, the most general spherically symmetric spacetime, Eq. (1). This is given in Carroll. When m ( r ) is defined by Eq. (2), the Einstein theory emerges. So the Sagnac effect is a test of EGR. The former is derived with the null geodesic (3) and the fact that the radius of the platform is constant, so Eq. (4) follows. Rotating the platform is described by Eq (6), the angular velocity of light traversing the Sagnac loop is given by Eq. (8) and the angular velocity of the platform by Eq, (9). Finally use Eq. (15) to arrive at the Sagnac effect (16) in the most general spherically symmetric spacetime. This result can be tested with your very interesting Sagnac interferometer. In EGR

m(r) = 1 – r0 / r

where r0 is the Schwarzschild radius and r the radius of the platform. The latter is placed in a laboratory in the gravitational field of the earth, so r0 is the Schwarzschild radius of the earth, which is 9 mm or 0.09 metres. I anticipate that the Sagnac effect will be the usual one: delta t = 4 Ar omega / c squared so m (r) will be very close to unity. However, it is also known that the Sagnac effect depends on gravity. So actual experimental measurement of m ( r ) will be very interesting. I should think that EGR will not give the experimental result, because the Sagnac effect is well known to be delta t = 4 Ar omega / c squared. So m ( r ) is close to unity, but not exactly one. You ability to construct a precise Sagnac interferometer is most impressive, and this is Baconian science as it ought to be, simple and profound methodology. We do not have to apply for millions in funding to try to prove that a theory that is totally wrong, is after all, totally right.

Cordially,

Myron

Dear Myron

Ok, I see that it will be very difficult to determine not just a constant, but even a function through the experiments we are discussing.

With regard to your theory, so many questions are open to me that unfortunately I can not contribute in this respect. For example:

a) In the Whirlpool galaxy, the stars move almost in circles with very small deviations and maximal speed of c/1000, so it is completely unclear for me, how you can apply Einstein’s theories to it and refute it in this way. (You talk about “a whirlpool galaxy” or “whirlpool galaxies”; I think, there is only one Whirlpool galaxy, see

http://aias.us/documents/numerical/Paper238b-us.pdf

Can this be a confusion with “Spiral galaxy”? )

b) For the S2, an orbital forward precession of 0.2 degrees per revolution is predicted from Einstein theory. What is your computed result and with what for measured values have you compared it?

Carroll’s notes I found here

https://www.preposterousuniverse.com/grnotes/

but not read yet. I’ll probably need some time. 😉

But now back to the experiment:

I have built (not yet complete) a Sagnac interferometer with 1 km glass fiber and 1 m diameter. It should be sensitive enough to determine the rotation of the earth, but perhaps not enough for your purposes. As you suggest already, much more area x windings is needed. This far exceeds my possibilities of self-construction at home. Should I look for a commercial fiber gyro or laser gyro? Unfortunately, such a device is very expensive, and the needed accuracy seems – as I see it – very unknown yet. What kind of further action do you propose?

best wishes,

Bernhard

Myron Evans schrieb am 01.12.2018 um 09:06:

Experimental Confirmation that Gravity affects the Sagnac Interferometer

Many thanks to Bernhard for these interesting remarks. The answers to any question in dynamics and orbit theory are always contained within equations (10) and (11) of Note 420(2), the equations of motion in m theory of all dynamical systems in the plane polar coordinates (r, phi). These can be developed in any coordinate system. As you probably know, they have been integrated numerically by Horst as in UFT417 ff. to give many very interesting results. The function m(r) is not known a priori because we are not using the Einstein field equation to constrain it to the Schwarzschild 1 = r0 / r. In Note 420(1) the Einstein theory is completely refuted using the velocity curve of a whirlpool galaxy, so it should no longer be used. In UFT419 the Einstein theory is completely refuted (by a factor of a hundred) using the S2 orbit. So it can be any function of the general spherical spacetime as defined in Carroll’s free online notes to “Spacetime and Geometry: an Introduction to General Relativity”. To answer any question about dynamics or orbit theory, the system to be solved is defined (for example the pendulum) and the equations of motion solved. It seems that the Sagnac effect has indeed been used to measure gravity, which is all that is needed. The Sagnac effect is simply changed to delta t = 4 Ar omega / ((m(r) c squared), which means that it is affected by gravity as observed experimentally. In the Einstein theory m(r) = 1 – r0 / r, but in m theory m(r) can be any function of r. In fact m theory is based directly on the well known infinitesimal line element of the most general spherical spacetime. I am not sure what is meant by a zero area Sagnac interferometer, or ring laser gyro. We need the opposite, a very large area made up of tens of thousands of windings of a thin optical fibre in order to maximize the area of the interferometer, and to maximize its sensitivity.

Dear Myron

I am glad that you like my idea. But, to be honest, this idea came just from the joke with the cuckoo clock. I think, before ‘my invention’ a lot of inventors and physicists had similar or much better ideas to measure the gravity – mostly without a built-in cuckoo. 😉 Of course, the method is practicable, but for precise measurements it is better to drop a mirror in a vacuum vessel and use a laser interferometer for directly determining the acceleration. Here for example an industrial manufactured device:

http://microglacoste.com/product/a10-outdoor-absolute-gravimeter/Your search text leads, among others, to

https://arxiv.org/pdf/1808.08653.pdf

Is this what you mean? From ‘zero-area’ Sagnac interferometers I read already. Obviously this devices are insensitive for rotation, but why they should be sensitive to gravity is unclear to me yet. I will look for more infos.One problem persists – from my point of view – similar to the measurement of a time using a clock at the same position as the experiment:

Using a gravimeter, we measure the gravity at this special location. Because the earth is neither an exact sphere nor an exact ellipsoid of revolution, we cannot compute an expected value and then compare it with the measured value. Therefore, I see no way to separate the measured value – internally a light runtime, an interference shift, a pendulum period, a spring expansion – into the ‘real’ part directly proportional to the gravity, and a ‘deviation’ part caused by m(r). We should have access to a measuring method independent from m(r) and another method with the wanted dependence.

A question about your theory: As far as I know, in many theories some unknown constants occur. For example, after finding the proportionality ‘force proportional M m / r²’ one can define a constant G with ‘force = G M m / r²’, what directly leads to a measurement method for this constant: Measure the force and compute G = force r² / (M m). Surprisingly for me, the m(r) is a unknown

functionand not simply a constant. Why the function is not derivable from the theory?best wishes,

BernhardMyron Evans schrieb am 28.11.2018 um 07:52:

Many thanks for this idea of the pendulum and atomic clocks. By all means go ahead and try the experiment. The overall aim is to measure the m function, so any method will be interesting. I don’t think that it is necessary to measure the run time itself, but I think it will be necessary to maximize the precision of any method used. If one googles “gravitation and the Sagnac effect” or similar it is found that the Sagnac effect has been proposed for measuring gravitational waves. In the commercial Sagnac interferometer or ring laser gyro, delta t = 4 Ar omega / c squared as you know. The m function simply changes delta t to delta t / m. The area Ar can be maximized by using many turns of a fibre optic and the angular velocity capital mega can be maximized by spinning the platform to high speeds. If m depends on gravity it will be different at sea level and at high altitude in an aircraft or satellite. In conditions of zero gravity on board a spacecraft, the effect is maximized. So if m is gravity dependent then delta t should change slightly with gravity as in UFT145 to UFT147. In the Sagnac interferometer the timing is measured with interferometry, and not with atomic clocks, so there is no problem. The m theory would have to be applied to pendulum theory to see how it changes the equations of the pendulum. This can be done with the lagrangian or hamiltonian. So this is very interesting.

Dear Myron

As it looks like, you suggest the use of a Sagnac interferometer instead of a circulating light pulse. Of course, this interferometer uses circulating light too, but it measures only a difference between two times (or run lengths) via interference and not the run time itself. If the goal of the experiment is measuring the run time in dependence of the gravitation, is it not much easier to measure the time instead of the difference of two times varying in the same sense?

But the main problem – from my point of view – is not solved yet: If we use an atomic clock for measuring the time the light needs to travel, and if we put the experiment together with the atomic clock in a different gravitational field, how can we ensure that only the orbital period changes, but not the running of the atomic clock?

By the way, your joke with the cuckoo clock brings me an idea for a gravimeter: This revolutionary device consists of an atomic clock and a high precision cuckoo clock (the cuckoo may be omitted, but the pendulum is essential). Both time displays are compared to each other. Because the pendulum depends directly from the gravity, and the atoms nearly not, the comparison immediately gives a measurement of the gravity field. 😉

best wishes,

BernhardMyron Evans schrieb am 27.11.2018 um 10:41:

The Gyrogravimeter from m theory

Dear Bernhard,

This is very interesting. The relevant equation is Eq. (14) of the attached, the Sagnac effect in m theory, where m can be any function of the distance R0 to the centre of the earth (UFT145 to UFT147). It is the basic equation of an instrument that I referred to as the gyrogravimeter. It simply needs a conventional, high accuracy, Sagnac interferometer, made up of as many loops as possible of a fibre optic wire, so the area is maximized and the instrumental accuracy maximized. For example ten thousand loops increases the area by a factor of ten thousand and increases the time difference by a factor of ten thousand for a given angular velocity of platform rotation. Then this portable and compact gyrogravimeter can be used at sea level and top of high mountain such as the restaurant at the top of the Jungfrau in Switzerland. Your clocks will be more accurate than a cuckoo clock. In general m can be any function of R0. The Einsteinian general relativity uses the function (15). So this experiment can test the Einstein theory, which is known to be completely obsolete. The portable gyrogravimeter can be used to measure the gravity at any point on earth or space, and is useful for geology, prospecting, and so on. The Einstein theory fails completely in a whirlpool galaxy as is well known. This is shown quite simply in UFT420(1). It has just been shown to fail completely in the S2 star, by a factor of a hundred. So this would be an important experiment.

I am not sure if Swiss restaurants are equipped with cuckoo clocks, so your timing devices would be orders of magnitude more accurate.Myron

Dear Myron

Some weeks ago, Horst asked me about the construction of an experiment you suggested. As I understood, the time taken for a light ray to orbit around a ring (or a polygon constructed of mirrors) is to be measured, depending on the distance to the center of the earth, that is, on the strength of the surrounding gravitational field. More general, it seems to be about different physical processes whose timing could be dependent on the gravity.

Of course, I am happy to help with the project, to create the design and to set up and execute the experiment. I have some cesium atomic clocks; maybe their accuracy is sufficient.

However, I have a question about this:

According to Einstein, the run of the clock (the time itself) is dependent on the strength of the gravitational field too, and also depends on the speed of movement, which increases in mid-latitudes with the height above the ground. Therefore, the orbital period of the light in the experiment can not be measured at all using a clock located near by the experiment – unless your theory predicts a different behaviour. The only thing that comes to my mind is to just move the experiment to different locations, but always leave the clock in the same place. For the measurement then a radio connection would be necessary. What is your suggestion?

best wishes,

BernhardPS: Do you need some more animations for astronomical or other purposes? (See our previous correspondence below.)

### Section 3 of UFT 420

December 8, 2018Many thanks! This is another excellent Section 3 by Horst, showing that the critical terms in the lagrangian and hamiltonian are essentially the same. It will be very interesting to develop H , L and dH / dt = 0 and dL / dt = 0 in quantum mechanics for example and apply them to all kinds of problems in classical dynamics. This is my intention for UFT424. Finding the right lagrangian is also an important problem. In fact the lagrangian L is related to the hamiltonian H as described in the equation following Eq. (14.114) of Marion and Thornton third edition:

L = H – sigma sub i v sub i p sub i

and this is worth investigating further.

Added today

Dave

On 12/7/2018 11:37 AM, Horst Eckardt wrote:

> I finished section 3 which contains various calculations of equations

> of motion. It results that the differences between Hamiltonian and

> Lagrangian method are less significant than thought.

>

> Horst

### Daily Weblogs Report 6/12/18

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