The curl vector is expressed as C = Curl P, where P is the vector-potential. In the theorem of the Vector Analysis any vector is expressed by P = gradient f + Curl U. If P is called curl-free, it is not the Curl U =0?

Thanks Dmitri. I had a lot of difficulty accepting that a magnetic vector potential could be curl free and propagate with zero electric and magnetic components some form of detectable energy through shields and barriers. So I read the patents and claims, counter claims, and final resolutions plus conclusions for study of patent law.

The patents were upheld because the claimants provided a working model and the underlying principles had bee published and peer reviewed several times by different people, although obscure and unfamiliar to the non specialist. So I accepted the claims and explanations, but found them lacking in description for type of energy being transmitted.

It seems like there should be a more robust process for introducing concepts that depart from conventional wisdom. The choice of gravity wave or fifth force is not satisfactory with the available information. Either choice carries large consequences. I wonder if there is some other explanation, a third choice.

Are there curl free scalar signals? This is an interesting question! I think the answer is “yes” for the following reasons.

1.      Theodor Kaluza demonstrated that the electro-magnetic vector potential may be derived from a five dimensional (5D) version of General Relativity. This suggests that the EM field is a special kind of metrical field induced by modulating a fifth dimension, which is the scale of 4D spacetime.

2.      I have found, and published, papers clearly demonstrating that all astronomical observations may be explained if the 4D spacetime expands in scale.

3.      Such a scale expansion might by us inhabitants take the form of a very rapidly oscillating metrical scale of the 4D line-element of GR.

4.      I have further shown that this oscillation allows the derivation of Quantum Mechanics (QM) from GR.

Since an oscillating scale may induce both positive and negative energy, this suggests that scalar oscillation of the metrical scale of spacetime may be “the fabric of all material existence”. It might be what we all are “made of”.

Gravity waves don't exist. In order to explain how gravity works it's necessary to take into account abandoned by mainstream science so-called ether that should be understood as pre-matter. There is no space-time, not to mention that relativity is a false theory. There is only 3-D space in which objects can move. Time cannot be considered as a dimension, because travel in any direction "needs" time. Vectors are in maths. Science explains phenomena with objects.   

http://rationalsciencemethod.blogspot.co.uk/2012/12/the-rational-scientific-method.html

JM - " scalar oscillation of the metrical scale of spacetime may be “the fabric of all material existence"

Planck units predict a very high frequency and extremely short wave length as the fundamental properties of space and time. It points to a high but finite energy in space contained as cycles of oscillator microstates sometimes called virtual potentials, and related to the four fundamental forces. At least in principle your approach seems to be in agreement.

I feel that there is much remaining to be discovered about the microstates, but not many researchers are interested in it.

AL --- a careful reading of Einstein in English and German shows he deliberately avoided denouncing the concept of Ether, except in the versions of Ether that required a preferred flow direction in space. The pre-matter you mention is often referred to as virtual potential. Some people denounce it, but Einstein did not. He wrote several paragraphs to allow concepts of something substantial in space to support the conclusion of curvature, but reject the claims of preferred flow direction.

Jerry, I respect Einstein's good knowledge, but reject at the same time his absurdities which remain the same in any language. 

BTW regarding LIGO https://www.change.org/p/prof-karsten-danzmann-beantworten-sie-bitte-3-fragen-%C3%BCber-das-ligo-experiment?tk=9rUkqwnb3d6xDX8Z3Azl3l0GOr4m3roUuInDc5FJLVk&utm_medium=email&utm_source=signature_receipt&utm_campaign=new_signature

Look at http://vixra.org/abs/1605.0101 

This paper helps you to compare fundamentally different fields.

http://vixra.org/abs/1603.0021

But does it have anything to do with physics/nature/reality? I have my own comprehension of space, where everything is explained by objects. Science explains phenomena by means of objects, thus mathematics is not reality.

http://vixra.org/abs/1603.0231

Andrzej,

The foundation of physical reality cannot be accessed by observation. Thus the only way is to try to investigate this foundation by mathematical test models. When the foundation extends into higher levels it may reach conditions in which features become observable. Also in that case it will be impossible to prove that the selected mathematical test model is a proper reflection of physical reality. Thus the question "But does it have anything to do with physics/nature/reality?" is in fact an impertinent question. It cannot be answered.

Space and time are high level concepts that cannot be treated without first introducing number systems. At the deepest level of physical reality numbers do not (yet) exist!

On the other hand, it is possible to discover structures from which number systems emerge when these structures are extended.

http://vixra.org/abs/1607.0146

Hans, I cannot agree with you.

"The foundation of physical reality cannot be accessed by observation."

Physics does not explain foundations, it explains phenomena, by means of objects, of course.

"Thus the only way is to try to investigate this foundation by mathematical test models."

First we need to have rational explanation of phenomenon, then we can use maths, but for its description.

"When the foundation extends into higher levels it may reach conditions in which features become observable."

We can observe only objects and obviously not all.

"Also in that case it will be impossible to prove that the selected mathematical test model is a proper reflection of physical reality. Thus the question "But does it have anything to do with physics/nature/reality?" is in fact an impertinent question. It cannot be answered."

Any mathematical description must be derived from observation of physical objects. First we observe phenomena, then on the basis of hypotheses rationally explain them by theories. Thus mathematics can only describe what we observe.

"Space and time are high level concepts that cannot be treated without first introducing number systems. At the deepest level of physical reality numbers do not (yet) exist!"

Space is physical reality (I explained it as per earlier referred link). Time of any physical object exists along with the object, in other words with matter. Time spontaneously does not occur. My explanation of time among other: http://vixra.org/abs/1602.0323

"On the other hand, it is possible to discover structuren from which number systems emerge when these structures are extended."

Numbers are not physics. What physics is, you can find for example, here:

https://www.youtube.com/watch?v=ASN6zN00JuQ

The reasoning behind the investigation of the foundation of physical reality is the following:

If the foundation of physical reality can be characterized by a structure, then this structure must necessarily be very simple. If a structure is complicated, then it is constituted from simpler structures. Quite certainly the structure of the foundation of physical reality is long ago discovered by scientists and is added as a part to mathematics. The extension of the structure of the foundation to a more complicated structure must be restricted such that after sufficient extension steps the result shows features and behavior that we recognize from observing reality.

The orthomodular lattice extends naturally into the set of closed subspaces of a separable Hilbert space. This is the preferred development tool for quantum physicists. The Hilbert space is a structured storage space for physical observables.

The orthomodular lattice is very simple and does not contain observables, but its extension does that job.

In 1936 the orthomodular lattice was discovered by Garret Birkhoff and John van Neumann. They called their discovery "quantum logic".

http://vixra.org/abs/1607.0146

http://vixra.org/abs/1606.0028

http://arxiv.org/abs/1101.5690

The Rational Scientific Method requires that a person presenting a theory define the Key Terms upon which their presentation depends. It is the responsibility of the theorist to do this so that all persons understand what it is THEY mean. A definition is a restriction on the utility of a word. While dictionary definitions are fine for ordinary conversations, scientific terms are precise, unambiguous, non-contradictory, non-circular, and non-synonymous. They can be used consistently throughout a presentation.

...

RSM proposes that all words resolve to either objects, or concepts. There is no third category.

...

What is object:

http://hubpages.com/education/What-is-an-Object

Another possibility is that the curl free potential represents a stress energy that imitates dynamic mass and moves at less than light speed for some finite distance, like a resonance. This can be tested and would seem to demand a substantial proof. The prevailing view is that all momentum transfer moves at light speed or is attached to a rest mass. 

It is possible to conceive of stress energy fields in space, moving at light speed that do not contribute to or subtract from a gravitational curvature, even in a transient like a gravity wave, but also are lacking detectable electric or magnetic components.. Gravity waves and their proposed opposites are said to have a fairly exact transverse and longitudinal character that momentarily adds to or subtracts from a gravity field. Other wave interference patterns are well known and taught in engineering design of radio wave directional transmitters.Then a substantial group of other stress energy patterns lacking those characters seems to be possible, although not observed in nature, but possibly created by constructions, selections, and combinations of generators. In that context the evidence is not compelling for a fifth force or a gravity wave, especially since the detectors receive an electric potential by excluding magnetic potentials with superconducting components.

Comparison can be made to elastic vibration in a solid. It might be of mechanical origin, implying the electromagnetic force is the underlying principle, even if the fields are balanced and components are not detectable of net electric or magnetic fields. Vibration like changes in the stress energies and potentials of space are a bit harder to understand.

To me it suggests the topic of vacuum stress energy has categories that are not fully researched. It doesn't say that we will make surprising discoveries there, but does leave open the possibility that we might. There is also hope that some of the fundamental constants and parameters will emerge from a better understanding of vacuum stress dynamics.

Following the rules of conservative vector fields, the curl free magnetic vector potential should be the gradient of a scalar gravity field, and have no detectable electric or magnetic components.

I have been able to show that QM may be derived from GR if the metrical scale of 4D spacetime oscillates at the Compton frequency. This scale may treated as a fifth dimension of GR. Theodor Kaluza showed that Maxwell's equations may be derived from GR if a fifth dimension is added. His derivation use four of the five components of the added dimension. However, the fifth scalar dimension was not explained, which has been an embarrassment. 

To me this means that gradients in this metrical scale creates gravitation as well as the QM wave  functions.

JM I have been doing some writing about unification of QM and GR in the high energy range of a fast moving vehicle. Results seem to predict that additional dimensions 5 and possibly 6 are available but not always needed in the smooth second order curve of GR. But in higher energy of fast transport vehicles the additional dimensions are apparently used for folding of space into higher order curves driven by kinetic energy. So scale one seems to be 4D, scale two 5D, scale three 6D, and scale four the opening of a worm hole containing a Galilean flat space in a warped field.

Compton frequency is also recommended to me as a deciding factor in selecting scales and squeezed quantum states for systems that are not driven by high speed kinetic energy.

Jerry -

You said that...

"A magnetic field can be represented as the curl of a magnetic vector potential. When generated with no curl the related vector potential passes through barriers and is detected by a special type of super conducting junction. This curl free potential is said to have no electric or magnetic components, but still transmits detectable energy over a distance, such that information can be sent and received by modulating the generator apparatus.

Several patents have existed for a long time and survived challenges to become text book examples in the complexity of patent law."

I published a 2012 paper, "Toward a More Complete Electrodynamic Theory," by L.M. Hively (me) and G.C. Giakos. You can get a PDF copy by doing a search on the title via scholar.google.com. This revision of electrodynamics allows for a curl-free vector potential and a curl-free current. I also published a patent on antennas to create the curl-free current that in turn generates a scalar-longitudinal wave (SLW) that has B=0 and a non-zero E. The patent shows experimental evidence for the SLW.

I am very interested in the details about your claims above. Specifically, can you point me to publications/patents about the special type of superconducting junction that detects the wave with B=E=0.

Thanks - Lee Hively (Oak Ridge National Laboratory, retired)

Jerry and Lee,

I approached this from a different direction by considering the possibility that the cosmological expansion is in the metrical scale of both space and time, while the Big Bang theory only considers expansion in the spatial scale.

This simple idea leads to a cosmos model that better agrees with astronomical observation, in which the Dark Energy and Dark Matter become natural consequences of the cosmological expansion.

Each epoch becomes physically identical since the GR field equations are identical, which suggests perpetual existence. No Big Bang.

As seen by an inhabitant, who participates in this scale expansion, the word seemingly always remains the same, except for a few additional observable consequences. One being that the velocities of freely moving objects diminish over time. This is a relative phenomenon caused by the with time expanding scale.

In the four dimensions of GR this scale expansion mode may be handled by assuming that the metrical scale expands incrementally, which would make it seem like the scale is oscillating at very high frequencies. This situation may be analyzed using GR and we find that Quantum Mechanics then may be derived from GR! The deBroglie/Bohm version of QM may be derived from GR; GR’s geodesic relation becomes the “pilot wave” and the Schrödinger equation may also be derived.

This suggests that the QM wave function are waves in the metrical scale of spacetime, with this scale as an additional fifth dimension.

Furthermore, Kaluza’s finding that Maxwell’s equations may be derived from a five-dimensional version of GR suggests that the EM waves also are waves in the scale of spacetime, for which the CURL is not zero.

Tesla discovered these scalar pulses, which were formed during high voltage discharges. It is quite possible that scalar pulses of the spacetime scale may be used for instantaneous communication.

Lee, is this what you also have found?

Johan -

My work to date shows that high-voltage discharges are not needed. A curl-free current (or equivalently) a curl-free vector potential is required to generate the SLW. 

A 2011 paper by Jiménez and Maroto [“Cosmological magnetic fields from inflation in extended electromagnetism,” Phys. Rev. D 83, 023514] proposed a quantum electrodynamic field in an expanding universe that is incompatible with the Lorenz gauge in a time-dependent geometry. The Jiménez and Maroto theory (JMT) predicts a dynamic, propagating, scalar state together with a longitudinal electric field, plus transverse-photon dynamics. The scalar field is excited gravitationally with a cosmological energy density whose value agrees with observations for inflation at the electroweak scale. The JMT is compatible with all local gravity tests and is free from classical or quantum instabilities.

Here are a few references.

In the European Patent Web Site

https://worldwide.espacenet.com/advancedSearch?locale=en_EP

Search Title - Curl Free

Search Inventor - GELINAS

There are 11 patents assigned to the Honeywell Corporation.

Repeat the search but with patent -  US5845220

There is one patent by Puthoff assigned to EarthTech.

This patent by Puthoff was disputed on technical grounds although the Gelinas patents were not disputed. Puthoff's patent was upheld after 5 years of arguments and became a text book case in patent law.

Page 1304 in the link, begins pages where technical arguments are summarized.

https://web.archive.org/web/20150925131935/http://hosted.law.wisc.edu/lawreview/issues/2006-4/rislove.pdf

Lee, I hope these references are helpful as a starting place for entry into a fairly obscure but well documented branch of science. As you can find in the references the concepts are firmly established and defended.

So it brings my question about what type of force is carrying energy a distance of inches across an apparatus, produced from electric energy, but modified in an interference pattern from which a vector potential emerges with B=0 and E=0.

It might be a modulated set of very weak gravity waves, but I'm open to the possibility that it could be some other form of vacuum stress energy. In recent work I have concluded that kinetic energy is carried in a convex curvature of space, unlike the concave curvature of gravity. There seems to be a way of choosing one or the other by testing in some of the patented apparatuses by adding an array of detectors.

Jerry -

I am familiar with the Gelinas patents, which disclose antennas for creation of a curl-free vector potential (A), and its detection by Josephsen junction devices. I was not aware of the patent by Puthoff. I note that a curl-free vector potential [curl(A)=0], implies that B=curl(A)=0, which further implies that DB=(mu)curl(J)=0, where D is the D’Alembertian (wave) operator and mu is the permeability (not necessarily vacuum), which in turn implies that curl(J)=0. This last condition is a necessary and sufficient condition for the SLW, as my 2012 paper shows.

Regarding your question about the nature of waves with B=E=0, I recommend a 2009 paper by Dale Woodside in the American Journal of Physics. Here is a link to that paper.

http://ricardoheras.com/wp-content/uploads/2016/05/Woodside.pdf

Woodside derives a revision to classical electrodynamics, assuming only Minkowski 4-space. Eqs. (53)-(54) are the equations for the revised formulation. However, Woodside does not derive the wave equation for the scalar field. For B=E=0, the equations reduce to a wave equation for the scalar field, which I discuss in my 2012 paper (referenced above). Woodside's derivation relies on his previous papers in 1999 and 2000 in the Journal of Mathematical Physics. If you are unable to get those latter two papers, please send me your e-mail, and I will forward them to you.

Best regards - Lee [lee.hively314(at)comcast.net]

Lee,

I did send you an e-mail.

The Puthoff patent was interesting because of the prolonged arguments and eventual conclusions that did dot occur with the Gelinas patents.

My work in high speed reaches out for new science in many directions. Much of what science is offering doesn't contribute anything helpful. It's nice to find something that does. In this way I have found about 5 areas of science work that are published and helpful. Without the high speed consideration, there would be no way for me to select one theory and reject another.

Maybe the classical electrodynamics is ignoring other types of stress energy, which might be a good reason to improve on it.

Results in my study are suggesting that something important remains to be discovered about the various types of stress energy and how they interact as speed increases.

The curl free potentials are interesting as they might relate to gravity or inertia because that form of energy passes through any barrier, suggesting it is additive in linear combinations.

 Considering that [A* goes to A] in a destructive interference pattern, it seems that A should be contained in A* before the interference. Then the stress curvature expressed in A could be convex meaning inertial energy as it occurs in A*. The answer to my question could be no without creating a fifth force.

The topic of hidden inertia occurs in science. The curl free vector potential could be an example. Then I can conceive of a field effect acceleration engine that develops a change of inertia instead of a displacement of gravity.

A test is possible, to suspend the generator and detector from a low friction apparatus, and discover if they attract each other or repel. Hidden inertia would be confirmed if they repel. Gravity induction would occur if they attract. 

A confirmation of hidden inertia would require a number of revisions in proposals for field effect engines.

I noticed that Oak Ridge National Laboratory has indexed your work.

The answer seems to be a choice of a gravity wave or a kinetic energy wave, with the kinetic option apparently favored by the way the curl free vector potential is produced. In that case it seems to be named incorrectly as a potential instead of a dynamic.

There is a peer-reviewed technical literature on the creation and measurement of curl-free vector potentials:

https://pdfs.semanticscholar.org/a559/df0ca4b5a902514a5f3717fab843745c1eb5.pdf

http://ieeexplore.ieee.org/abstract/document/7112483/

https://www.cambridge.org/core/journals/journal-of-plasma-physics/article/one-dimensional-macro-scale-matter-wave-dynamics-potentially-embedded-in-the-lorentz-trajectory/2AA1BF68B8A480E3E3C32F5FBD97E0FC

http://iopscience.iop.org/issue/1402-4896/86/4

A curl-free vector potential must take the form of A(curl-free)=grad(lambda), implying that B(vector)=curl(A)=curl(grad(lambda))=0.

Here, lambda is a scalar function of space and time.

Or, more simply B=0 for a curl-free vector potential.

Then, the wave equation for B is DB=0=(mu)*curl(J), where D is the D'Lambertian as I noted above.

Curl(J)=0 has the solution: J=grad(kappa).

As before, kappa is a scalar function of space and time.

There is also a peer-reviewed technical literature on the creation and measurement of gradient-driven currents:

http://www.nature.com/articles/nature07378 (an arc discharge)

https://www.nature.com/articles/cdd2010112

ojgSu9rSIBw&scisig=AAGBfm0LpT00_lPQ6bke9l4h9W6jSHQxSQ&nossl=1&ws=1234x559 (gradient-driven ion currents across living-cell walls)

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C6&q=Electrical+neuroimaging+with+irrotational+sources&btnG= (EEG is a gradient-driven current).

Consequently, I know that curl-free vector potentials and curl-free currents exist.

I don't yet know if a curl-free vector potential is equivalent to a gravity wave.

The wave equation is a second order partial differential equation.

Homogeneous second order partial differential equation have more solutions than just waves. For example they also offer shock fronts. These phenomena only occur in odd dimensions.

Gravitation waves have more in common with spherical shock fronts than with wave packages. General solutions are formed by superpositions of the basic solutions of the homogeneous second order partial differential equations. Vortexes are not solutions of homogeneous second order partial differential equation, but they are solutions of quaternionic homogeneous first order partial differential equations.

All basic fields support vibrations of that field, which can be described by superpositions of solutions of partial differential equations. Gravitational fields are no exception. What vibrations can be perceived depends on the actuators that trigger the solutions. Without triggers the field does not vibrate. Excitations produced by one-time triggers are special. The spherical shock fronts spread over the full field, but quickly loose their amplitude. The one-dimensional shock fronts keep the shape and the amplitude of the front.

See: Article Nature's Basic Dark Quanta

and Article The Mother of All Field Equations