Russ,

Doug introduced the Hodge dual to hide certain information and to obtain simpler expressions for curvature tensors. I have to discuss this with him in detail. It has to do with the fact that the essential information in Cartan geometry is contained in the antisymmetric parts of the connection.

Referring to paper 439, you can compute the Hodge duals of all tensors but this is not necessary in the path from the tetrad to the force field tensors. The Hodge duals of the connections were computed in that paper. From the examples it is seen that they are not necessarily simpler than the original connections. Theoretically you could compute the dual torsion from the Lambda connections and then identify with the E, B fields in the dual representation of the F tensor.

Horst

Am 26.10.2020 um 18:13 schrieb Russell Davis:

Hi Horst,

I’m glad the blog is back up and operational. I also like Myron’s original blog format (template) that Sean was to implement; it’s provides a pleasant visual continuity with all the past blog posts.

Doug also sent me a draft copy of his new paper (which you refer to on your latest blog post), in which he develops Hodge dual simplifications that capture the information of the tensor formulations. Can Doug’s approach be used in relation to your paper 439 to establish an even more handable equation set pathway for calculating or analyzing the features of a particular physical system?

-Russ

In this paper, my plan was to link Einstein to ECE at the Riemann tensor level, in so doing obtaining the Einstein field equations (first Bianchi identity).

In the next paper, I would introduce the tetrad and spin connection and have torsion and curvature respecified, with the limitations, determined in this paper, placed on the metric connection. The second Bianchi and Maurer equations, etc. would be added to the mix as I think you are suggesting.

To summarize my reasoning steps in this paper – all of this on a Riemann-Cartan manifold.

Part I. If torsion is assumed to be totally antisymmetric, then there are four and only four scalars, each one associated with a basis element the base manifold.

Part II. The hodge dual of a totally antisymmetric tensor is a vector which satisfies the requirements of Part I.

Part III. Torsion is equal to twice the value of the antisymmetric connection component, whether we look at it as a rank 3 tensor, or as a dual vector.

Part IV Assuming that the metric connection is antisymmetric as given by the commutator’s antisymmetric nature then there is an array ( don’t know if it is a tensor) with possible non-vanishing diagonal entries only. This is the most general symmetric component , given the antisymmetry of the commutator .

Part V. Sums along the diagonals of the symmetric connection generates three one forms, of which two are equal (and equal to the four dimensional gradient of a scalar that is a function of the metric). The third one is related to the other two with the difference being the 4-divergence of the metric.

Part VI A Ricci-like rank two tensor can be made by applying the results of Part V above to the curvature tensor. This entity (not proven to be a tensor) is composed of an antisymmetric part, a symmetric part with vanishing diagonals, and a purely diagonal (symmetric) component. Taking the Hodge Dual of this reduced curvature generates a relatively simple vector based expression – the symmetric part disappears. A scalar curvature which follows is also quite simple. Both of these expressions carry non-linear terms in the vector for the antisymmetric connection (or torsion).

Part VII Reduction to Einstein – in the limit of torsion vanishing, this becomes the Einstein equation including a wave-like disturbance in a function of the metric. (something I gather Einstein’s original relativity did not)

Part VIII Einstein with Torsion – A linearized version of the equation including torsion looks like the Einstein-Cartan-Sciami-Kibble equation. The non-linearity terms in torsion that were neglected were not discussed.

I will spend some time this week considering a totally covariant torsion, and see how that propagates through the paper.

Thanks

Doug

Horst

Am 28.09.2020 um 20:55 schrieb Horst Eckardt:

]]>This is a corrected version, there was some confusion in tables and figure captions.

Horst

Am 28.09.2020 um 18:14 schrieb Horst Eckardt:

Dear all,

My colleague Bernhard and I dealt in great detail with the dynamic simulation of pendulums and the so-called Würth gear. There is a claim from the environment of the Milkovic pendulum that additional energy should be released. We looked at a calculation made by an anonymous author and found errors in it. According to classical mechanics, such a pendulum cannot accelerate itself. However, there are alternative mechanisms, e.g. from the ECE theory, which could theoretically make this possible. That would explain claims by various authors, but they have so far failed to provide scientific, public evidence.

Bernhard made beautiful animations for the pendulum and Würth gears, which we will present on occasion.

Please check the paper. Then it will be published on the AIAS web site (in 2 languages).PS: the paper was largely translated by Google Translator from the German version. Please check the quality of translation.

Regards,

Horst

I found a few minor typo’s in the paper,

page 3 line 1 – eigenvector -> eigenvalue

just after Eq 13 coeefficients -> coefficients

just prior to Eq 16 requesting -> requiring

first line after Eq 20 sentence structure error – This implies certain mathematical properties of A and B. For example if the matrices are Hermitian then the eigenvalues must be real.

last line of section 2 – In this case the matrix elements… ( a suggestion only )

Take care of yourself. All is well with me and my family.

Doug

> On Aug 27, 2020, at 1:20 AM, Horst Eckardt wrote: >

> Dear Workgroup,

>

> I finished a paper on a computational method, which allows computing properties of elementary particles. I developed this essentially last year when we worked on m theory. Therefore, m theory is basically used for setting up a scheme which is represents an eigenvalue problem. Implementing this would be a good master or doctoral thesis for a student. > Pleas check the paper, before I will publish it on the AIAS web site. >

> Horst

>

yes, a constant m(r) is primarily assumed for photons travelling through vacuum. Near to massive stars, there is also vacuum but the function m(r) of the gravitational field impacts the m value of the photon in vacuum. If we assume that both values are additive, it comes out that for m(r)<0.4 (for the star) a photon can leave the vicinity of such a mass center. In teh calculation I have necglected changes in m(r) but it should reduce a bit at the point of closest approach, and the velocity should become a bit smaller due to the gravitational field.

Photons in matter are a different case. If we imagine that matter is a compaction of vacuum flow or aether, this impacts the propagation speed of photons. Their structure is modified by dense matter. In the quantum picture, it is assumed that verly slow photons are permanently absorbed and emitted from matter (i.e. the electronic hull).

There will be local changes in m(r) and gamma. If m_0 is changed is difficult to say. I suppose yes, because the spatial structure of photons is modified by the presence of matter. As we have argued in the paper, this has to do with the photonic rest mass. There are also similar cases known for electrons in solids, which then have an “effective mass”.

Horst

Am 29.06.2020 um 18:10 schrieb Russell Davis:

]]>Horst,

It is remarkable that the golden ratio appears in the derivation of light interaction with a gravitational mass.

In equation 47 of the paper, m(r) is assumed to be constant and leads to gamma = 1 for photons. Is this considered the case for the photons traveling through the vacuum of space, but not necessarily through material matter?

For example light passing through clear water or clear glass slows appreciably (on order of 2/3 of vacuum light speed), but the color of the light remains the same (i.e. the frequency is unchanged; excluding absorption frequency shift cases as described in ECE series of papers, and similar experiments by Santilli ). In such case, h-bar * omega is unchanged; from equation 51 of the paper, does gamma, phi, or m_0 increase to compensate for the slower photon speed to keep the equation left-hand-side (energy) constant?

-Russ

P.S This is an interesting video with computer animations showing that the golden ratio is the “most irrational number” having utility for more efficient packing of flower seeds than other irrational numbers – https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A

Great are the works of the Lord; they are studied by all who delight in them (Psalm 111:2).

It is remarkable that the golden ratio appears in the derivation of light interaction with a gravitational mass.

In equation 47 of the paper, m(r) is assumed to be constant and leads to gamma = 1 for photons. Is this considered the case for the photons traveling through the vacuum of space, but not necessarily through material matter?

For example light passing through clear water or clear glass slows appreciably (on order of 2/3 of vacuum light speed), but the color of the light remains the same (i.e. the frequency is unchanged; excluding absorption frequency shift cases as described in ECE series of papers, and similar experiments by Santilli ). In such case, h-bar * omega is unchanged; from equation 51 of the paper, does gamma, phi, or m_0 increase to compensate for the slower photon speed to keep the equation left-hand-side (energy) constant?

-Russ

P.S This is an interesting video with computer animations showing that the golden ratio is the "most irrational number" having utility for more efficient packing of flower seeds than other irrational numbers – https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A

Great are the works of the Lord; they are studied by all who delight in them (Psalm 111:2).

]]>*1. Obviously there is a length contraction in xi direction, when v is in direction of +xi, but there is a length expansion in negative xi direction at the same time. This should make a big difference in observation, when, in the moving system k, a length is measured in backward direction. Is ths true?*

The major axis of the ellipsoid in k is greater than the minor axis thereof; the minor axis in turn is equal to the diameter of the sphere in K. Thus the diameter is elongated by the Lorentz Transformation.

*2. The theory of relativity would be consistent, if tau in eqs. (6) and (7) were identical. Replacing c by c*q with an adjustable factor q … assume that the factor q is identical with the inverse of n in your calculation.*

Since n > 1, 1/n < 1, in which case the parameterisation by n would be ruined. Lorentz Transformation does not permit transformation of K system-time* t* to a system-time for k.

Kind regards,

Steve

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On Mon, Nov 4, 2019 at 8:55 AM Horst Eckardt <mail> wrote:

]]>Stephen,

this is an highly interesting article, maybe revolutionary. I have a question and a comment.

1. Obviously there is a length contraction in xi direction, when v is in direction of +xi, but there is a length expansion in negative xi direction at the same time. This should make a big difference in observation, when, in the moving system k, a length is measured in backward direction. Is ths true?

2. The theory of relativity would be consistent, if tau in eqs. (6) and (7) were identical. Replacing c by c*q with an adjustable factor q then gives:

and

Equating both expressions gives a quadratic equation for q with solutions:

or, when the sign of v is changed:

I assume that the factor q is identical with the inverse of n in your calculation. For q=v/c we obtain tau=0, but for q=v/(2c) I obtain a complex-valued tau.

Nevertheless there is an the interesting point. Myron Evans had shown in UFT papers 324/325 that the deflection of light by gravitation can simply be explained by a gamma factor of

gamma = 1/sqrt(1 – v^2/(2 c^2)).

This gives gamma=sqrt(2) for v –> c. Thus it is possible that a photon has a mass despite of travelling with speed of light. This result may point into the direction of you findings.

Horst

Am 03.11.2019 um 10:59 schrieb Steve Crothers:

Crothers, S.J., Special Relativity and the Lorentz Sphere, http://vixra.org/pdf/1911.0013v1.pdf

ABSTRACT. The Special Theory of Relativity demands, by Einstein’s two postulates (i) the Principle of Relativity

and (ii) the constancy of the speed of light in vacuum, that a spherical wave of light in one inertial system

transforms, via the Lorentz Transformation, into a spherical wave of light (the Lorentz sphere) in another inertial

system when the systems are in constant relative rectilinear motion. However, the Lorentz Transformation

in fact transforms a spherical wave of light into a translated ellipsoidal wave of light even though the speed of

light in vacuum is invariant. The Special Theory of Relativity is logically inconsistent and therefore invalid.

Virus-free. www.avg.com

this is an highly interesting article, maybe revolutionary. I have a question and a comment.

1. Obviously there is a length contraction in xi direction, when v is in direction of +xi, but there is a length expansion in negative xi direction at the same time. This should make a big difference in observation, when, in the moving system k, a length is measured in backward direction. Is ths true?

2. The theory of relativity would be consistent, if tau in eqs. (6) and (7) were identical. Replacing c by c*q with an adjustable factor q then gives:

and

Equating both expressions gives a quadratic equation for q with solutions:

or, when the sign of v is changed:

I assume that the factor q is identical with the inverse of n in your calculation. For q=v/c we obtain tau=0, but for q=v/(2c) I obtain a complex-valued tau.

Nevertheless there is an the interesting point. Myron Evans had shown in UFT papers 324/325 that the deflection of light by gravitation can simply be explained by a gamma factor of

gamma = 1/sqrt(1 – v^2/(2 c^2)).

This gives gamma=sqrt(2) for v –> c. Thus it is possible that a photon has a mass despite of travelling with speed of light. This result may point into the direction of you findings.

Horst

Am 03.11.2019 um 10:59 schrieb Steve Crothers:

]]>Crothers, S.J., Special Relativity and the Lorentz Sphere, http://vixra.org/pdf/1911.0013v1.pdf

ABSTRACT. The Special Theory of Relativity demands, by Einstein’s two postulates (i) the Principle of Relativity

and (ii) the constancy of the speed of light in vacuum, that a spherical wave of light in one inertial system

transforms, via the Lorentz Transformation, into a spherical wave of light (the Lorentz sphere) in another inertial

system when the systems are in constant relative rectilinear motion. However, the Lorentz Transformation

in fact transforms a spherical wave of light into a translated ellipsoidal wave of light even though the speed of

light in vacuum is invariant. The Special Theory of Relativity is logically inconsistent and therefore invalid.

Virus-free. www.avg.com

It is great to see such important progress being made!

As the theory is simplified, it becomes more accessable and compelling and will gain ever greater acceptance!

Advances in the computer coding, gives an objective dimension to ECE theory, Myron’s assertation that doubters cannot argue with correct Cartan geometry as verified by computer, becomes ever more timely.

The aias ship sales on.

Well done Horst!

Up the revolution!

Best wishes

Kerry

On Thursday, 15 August 2019, Horst Eckardt <mail> wrote:

]]>Also for the blog.

I finished the basic calculations of paper 439. When putting all parts of Cartan geometry together, we obtain a calculation scheme starting from a potential and ending in electric and magnetic fields of a given physical problem. That is within a framework of general relativity, therefore a novel approach. This is a great progress in ECE theory. Such a complete path had not been carried out before. One reason was that we had not compiled the Cartan formulas in this way so that (at least I myself) did not see that it is possible so straightforwardly. I had looked for this method for years

Another reason is that the Gamma connections can only be computed by computer algebra, and there is the ambiguity of how to choose the appearing constants. Setting them to zero gave an astonishing success in most cases I investigated.

(There remain some problems for complicated potentials. This has to be investigated further and is not addressed in the paper).One result of the paper is that the B(3) field comes out for e-m waves in a quite natural way. It is lastly a consequence of the fact that the tetrad has to be a non-singular matrix in 4 dimensions. Myron would be delighted

There remains the problem that the Lambda spin connection is not antisymmetric. Either there is still an error in the calculations, or it has to do with the charge density. For e-m waves, which correspond to the e-m free field, all connections are antisymmetric. I will have to discuss this point with Doug Lindstrom later on.I separated the Maxima code in a way that a library for all operations of Cartan geometry needed has been built. This should also be usable for the text book. In addition, this seems to be the begin of a generally usable code which Sean MacLachlan requested a long time ago.

I think we make progress in theory now. I appended the draft version of paper 439. The conclusion is still missing. I will give a perspective for the next papers where the new code path through Cartan geometry could be modified for solving new questions. For example,

1) when the e-m fields are given, what are the connections, and what is the potential (or tetrad)?

2) how can a resonant spin connection be obtained from a given e-m field?Please give your comments to the paper.

I will be on a holiday trip until Monday.Horst

I finished the basic calculations of paper 439. When putting all parts of Cartan geometry together, we obtain a calculation scheme starting from a potential and ending in electric and magnetic fields of a given physical problem. That is within a framework of general relativity, therefore a novel approach. This is a great progress in ECE theory. Such a complete path had not been carried out before. One reason was that we had not compiled the Cartan formulas in this way so that (at least I myself) did not see that it is possible so straightforwardly. I had looked for this method for years

Another reason is that the Gamma connections can only be computed by computer algebra, and there is the ambiguity of how to choose the appearing constants. Setting them to zero gave an astonishing success in most cases I investigated.

(There remain some problems for complicated potentials. This has to be investigated further and is not addressed in the paper).

One result of the paper is that the B(3) field comes out for e-m waves in a quite natural way. It is lastly a consequence of the fact that the tetrad has to be a non-singular matrix in 4 dimensions. Myron would be delighted

There remains the problem that the Lambda spin connection is not antisymmetric. Either there is still an error in the calculations, or it has to do with the charge density. For e-m waves, which correspond to the e-m free field, all connections are antisymmetric. I will have to discuss this point with Doug Lindstrom later on.

I separated the Maxima code in a way that a library for all operations of Cartan geometry needed has been built. This should also be usable for the text book. In addition, this seems to be the begin of a generally usable code which Sean MacLachlan requested a long time ago.

I think we make progress in theory now. I appended the draft version of paper 439. The conclusion is still missing. I will give a perspective for the next papers where the new code path through Cartan geometry could be modified for solving new questions. For example,

1) when the e-m fields are given, what are the connections, and what is the potential (or tetrad)? 2) how can a resonant spin connection be obtained from a given e-m field?

Please give your comments to the paper.

I will be on a holiday trip until Monday.

Horst

paper439.pdf