In fact, voltage fluctuations in electrically short, unterminated transmission lines propagate much faster than at the speed of light in a vacuum. I investigated this effect last year experimentally, after I had discovered it by pure coincidence. Electrically short means that all wavelengths of the signal spectrum are significantly longer than the cable itself. Under these circumstances there are no reflections and no electromagnetic wave is built up, which propagates slower in copper than light in a vacuum.

Preprint Electronic data transmission at three times the speed of lig...

At first I believed in a measurement or interpretation error until I noticed that one can simulate the effect already with SPICE. This made me realize that it is an effect of classical physics. Afterwards I studied the effect theoretically. It became clear that the effect is already contained in the transmission line theory and that there are even possibilities to exploit the effect technologically to transmit signals with much lower latency than would be possible with light in optical fibers.

This article describes the theory of the effect:

Preprint General analytic solution of the telegrapher's equations and...

Steffen Kühn Thanks for the links. You may also want to take a look at the work of Glenn Elmore , this paper in particular:

Article Introduction to the Propagating Wave on a Single Conductor

He has shown that an EM mode exists that is guidable along a completely unshielded conductor, which propagates at c (and not at 95% c or so) and that this mode has a characteristic impedance of 377 Ohms.

This is not Tesla's longitudinal mode, but it's interesting nonetheless.

The first key question always is: Are the wires propperly sepparated?- Always some meters distance - , what also includes sepparate ground for signal generation and measurement!

At least pi/2 sounds interesting and points to a certain electron property!

Jürg Wyttenbach Yep, that's the key question that needs to be sorted out. I've taken care to ground the scope at only one place and did not use a grounded wall socket. The signal generation consists of a capacitor that is switched with a relay and is completely floating and both terminals of the capacitor face the same load, so no signals can be injected into ground, other than via capacitive coupling.

A separation of 10-20 cm is not much, but the impedance works out to over 1.5 kOhm while termination with about 377 Ohms worked to get rid of reflections, which gives an indication it's not too bad, but it's not enough to convince critics. Ideal situation would be to obtain reflections from the end of the wires back to the feedpoint, so the wires can be spread out in open space. Have thought about that and was thinking about splitting the capacitor in two, so I can ground the terminal between the two in the middle. Without grounding something somewhere, the scope does not seem to be happy. Then I can play with capacitive termination to ground, which could also consist of a rod into earth ground at a distance if the wires are spread out, but first I'd want to see what happens with both ends of both wires in the shed, which is a bit more comfortable to experiment as being in open space.

The pi/2 factor does not seem to be related to a property of the electron. These kinds of transient phenomena occur before electrons actually start moving, as I explained in my answer here:

https://www.researchgate.net/post/What_explains_the_high_propagation_velocity_for_surface_charge_during_net_charging_a_metal_object

If one considers that the presence of a magnetic field implies rotation, while in a longitudinal dielectric wave, the medium vibrates in a translational manner, you get the difference of needing to cover a distance along half a circle, pi*r, verses needing to cover of distance along a straight line, 2*r. Division of these two results in pi/2.

One can also find this factor in transmission line theory. In my paper, I referred to the work of David William Knight :

Technical Report The self-resonance and self-capacitance of solenoid coils: a...

In chapter "1.3 Single-conductor transmission-line", you find a tangent function, which goes to infinity at pi/2 radians.

You see that characteristic tangent function when you play with a vna and some wire, in this case enamelled wire. I've attached three screenshots of measurements with a vna. With a bare wire of about 30cm length, you see the reactance drop pretty suddenly from +500 Ohms to -250. When one uses capacitive coupling, this effect gets considerably stronger. And with a helical, wound from the same kind of wire (0.9 mm dia), 20 turns, inner diameter 7.5 mm, length about 48 mm, measured inductance about 1.5 uH, you see the tangent function becomes quite profound.

So, there clearly are resonances which are normally not recognized as such, which are characterized by a high absolute reactance and these are the resonances where one can find the longitudinal mode, but this is a mode that has no current and so far I have not found a way to exite it.

Classically the phase speed can be any speed > c! The problem is the classic definition of information = discrimination of energy that now is provably wrong thank to advances in quantum computing.

So I do see no problem with information propagation with any speed > c as this is done in quantum entangle lines since quite a long time. Key is to find a reliable phase encoding/recovering mechanism.

My interest comes from SO(4) physics where the electron perturbative mass (is 2D orthogonal to the relativistic mass) is able to form out long range spin current structures, that exactly act the way you see it. This mep as we call it can go into resonance with any electron on the path and form a phase conductor if the overall perturbation is not disturbing the organization.

Such phase (spin-) currents are entirely different from real electron displacement currents.

Jürg Wyttenbach I highly doubt the so-called advances in quantum computing will ever lead to an actually working "real" quantum computer, because the whole idea of quantum computing is based upon quantum entanglement, which is totally impossible for the simple reason that in order to obtain an instantaneous reaction at a distance, one not only needs a force that propagates at an infinite speed, it also needs to have an infinite magnitude. I, for one, refuse to subscribe to such a view. I know of the existence of the B-wave, but that's not a "real" quantum computer. That is based on the principle of wave mechanics, which is entirely possible.

Either way, I just found out that Steffen Kühn has not only already verified experimentally that superluminous information transmission over a distance is possible, he has also done the math:

Preprint General analytic solution of the telegrapher's equations and...

"The conclusion of this article is that the fundamentals of electrical engineering, which have worked perfectly well for more than a hundred years, allow signals to be transmitted over any distance at signal speeds that are significantly higher than the speed of light in a vacuum. The fact that this contradicts the special theory of relativity is irrelevant for electrical engineering and a question that must be answered by physics."

Preprint Electronic data transmission at three times the speed of lig...

In addition to that, he has also found the exact same bug in Maxwell's equations as I did:

Preprint Proof of the inconsistency of the full set of Maxwell's equa...

Things are definitely getting more interesting by the day, especially when one realizes that while I have also mathematically proven this bug to be incorrect, I've also found the solution, which is very simple and comes down to writing out and labeling the terms in the vector Laplace operator, thus essentially applying the fundamental theorem of vector calculus, and work things out:

Preprint Revision of Maxwell's Equations

This leads to a model that is both known to be invariant to the Galilean transform, so there goes the Lorentz transform and with it relativity, it also defines the potential fields uniquely, so there goes "gauge freedom" as well and with it quantum field theory. And the best thing is that this is just elemental math, which is irrefutable and therefore there really is no argument against our theory either.

One short answer : The phase velocity can always be larger than c.

In fact much larger see:

https://www.nature.com/articles/s41467-019-08735-8

Jürg Wyttenbach Yep, but you seem to miss the point in the article you refer to:

"Here we demonstrate precise and versatile control over the group velocity of a propagation-invariant optical wave packet in free space through sculpting its spatio-temporal spectrum."

This is significant and interesting, because with radio techniques the information is modulated onto a carrier wave and therefore the information propagates with the group velocity rather than the phase velocity:

https://en.wikipedia.org/wiki/Group_velocity

"The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space."

Steffen Kühn also found a superluminal group velocity, which is why his find actually allows the superluminal transmission of information over a distance:

Preprint General analytic solution of the telegrapher's equations and...

p 4:

"As can be seen, the group velocities in the low-frequency range are also far greater than the speed of light in a vacuum, as long as the cable is not too long and no termination is carried out."

This is als what is being said in this article:

Article The speed of information in a 'fast-light' optical medium

"Recent experiments on optical pulse propagation in so-called ‘fast- light’ media—which are characterized by a wave group velocity ug exceeding the vacuum speed of light c or taking on negative values—have led to renewed debate about the definition of the information velocity ui. One view is that ui = ug (ref. 4), which would violate causality, while another is that ui = c in all situations, which would preserve causality."

How they come to the fantastic idea that causality is violated when it is found in practice that a wave propagates a bit faster than expected is beyond me.

Group and phase velocity are tightly related as the group velocity should be the "average" sum of the phase velocities of the wave collective.

The quantum cryptography people did show at least 7*c for real information propagation over a 70km optical line in Switzerland. There is no need for any discussion as current physics anyway is more than bogus.

Information is not coupled to energy!! Thus GR does not apply! Thus also GR is not fundamental!

Also classically (at least military folks know this..) the near and far field are not the same as the true electron charge is toroidal what locally looks different than in the far field. Thus all fields have toroidal components that lead to interesting effects regarding the vector potential. (like 0 energy interactions!..= phase actions)

Key is to find a stable (non inferring) mechanism to code/decode the 2Dx2D (2D orthogonal!) orthogonal coupled phase/energy pack! This is not possible with a one 1D (voltage based) manipulation. The only media I know that is able to symmetrically (SO(4) bonded) accept photons is dense Hydrogen = nuclear spin condensate. Thus such an amplifier circuit must consist of spin bound matter.

We could show the same for cold fusion or dense matter interaction that never can been seen in a CERN like setup! due to the missing symmetry in the experiment.

Jürg Wyttenbach You say many things I like, especially that the electron charge is found to be toroidal, which matches what I've been saying for a long time, which is that the toroidal ring model should be taken very seriously as a physical model of subatomic particles. From what I read here, there is no objection to that idea:

https://en.wikipedia.org/wiki/Toroidal_ring_model

However, in order to get everything straight, we must start at a solid base, which means we need to revise Maxwell's equations, which can be shown to violate the fundamental theorem of vector calculus and are therefore, in fact, incorrect.

This bug can be easily fixed by working out a single vector equation for the general case of any given vector field F, simply by writing out the terms in this equation and define a vector field for each of the terms:

-:-

The terms in the definition for the vector Laplacian can be negated and equaled to zero to obtain the vector Laplace equation:

-∇²𝐅= -∇(∇·𝐅) + ∇×(∇×𝐅) = 0,

and then the terms in this identity can be written out to define a vector field for each of these terms:

𝐀= ∇×𝐅

Φ = ∇⋅𝐅

𝐁= ∇×𝐀= ∇×(∇×𝐅)

𝗘= −∇Φ = −∇(∇⋅𝐅)

And, since the curl of the gradient of any twice-differentiable scalar field Φ is always the zero vector(∇×(∇Φ)=0), and the divergence of the curl of any vector field A is always zero as well(∇⋅(∇×A)=0),we can establish that E is curl-free and B is divergence-free, and we can write:

∇×𝗘= 0

∇⋅𝐁= 0

As can be seen from this, the vector Laplacian establishes a Helmholtz decomposition of the vector field 𝐅into an irrotational or curl free component 𝗘and a divergenceless component 𝐁, along with associated potential fields Φ and 𝐀, all from a single equation c.q. operator.

-:-

This way, we come to a model whereby the electromagnetic domain is seamlessly integrated with the fluid dynamics domain, yielding a model that is known to be invariant to the Galilean transform, adheres to the fundamental theorem of vector calculus and is therefore known to be mathematically consistent and free of singlarities, defines the potential fields uniquely so no more "gauge freedom" to confuse one's self with and on top of that all units of measurement are expressed in just three fundamental ones: mass, length and time:

Preprint Revision of Maxwell's Equations

I added a chapter that shows a possible solution for your equation. There is a much older (US military) paper that shows the same - I couldn't find it again so far as I had an other focus the last 2 years...

The problem is that before you dismiss classic Maxwell equations you have to adapt them for the toroidal fields with a 4D source totroidal source current.

The correction to the 2D x 2D Hydrogen coulomb field in SO(4) physics is straight forward (cyclic as needed in SO(4)) and give the 10 digit correct Hydrogen potential solution) Thus there is absolutely no doubt that the electron has an toroidal SO(4) manifestation that is conform with your equation.

Jürg Wyttenbach It seems you are missing the point that the general field definitions given above are the result of writing out the terms in the LaPlace operator for any given vector field F and are therefore fundamental and irrefutable.

That is why the following equation is clearly in violation of the elemental math shown above and therefore Maxwell's equations are shown to be, in fact, incorrect:

∇×𝗘em= -∂𝐁em/∂t

How could one possibly maintain that Maxwell's equations are correct now that they have been shown to be in violation of the fundamental theorem of vector calculus?

In addition to the above, in my paper I've also shown that there is a unique solution F=0 (within the fluid dynamics domain) by means of analysis of the units of measurement involved, so the solutions to the fields thus defined are solutions to the vector Laplace equation by definition. In neither Maxwell’s equations nor in fluid dynamics vector theory this result has been recognized, which causes the potential fields to not be uniquely defined, which also has important consequences for fluid dynamics potential theory.

The problem is that for over 120 years it has been has attempted to "correct" this bug rather than fixing it. This can simply be done by removing the parts that are in violation of the fundamental theorem of vector calculus and work things out correctly.

In neither Maxwell’s equations nor in fluid dynamics vector theory this result has been recognized, which causes the potential fields to not be uniquely defined.

That's exactly what I said. The classic field is single radial the toroidal field is two radial but then you have to use the 4D (6D) laplace operator for 3 acting dimensions in respect to the 4th for 3D,t representations.

Maxwell is wrong is just the wrong term. It's, incomplete. The error shines up at the 5th digit. The force free solutions for toroidal fields have been found more than 40 years ago. These solutions do prove an action in places where B=0 E=0 ∇×𝐀= 0, due to non canceling phase effects with no source charges/fields. Start at 6.40 in the upload that shows a possible solution and explain how scalar waves can be use for new technology.

Jürg Wyttenbach You wrote: "Maxwell is wrong is just the wrong term. It's, incomplete."

It's actually objectively true that Maxwell is wrong, since mathematically proven to be the wrong. What we have is a fundamental mathematical theorem that is irrefutable, just like:

a^2 + b^2 = c^2

and then see Maxwell write:

a^2 + b^2 = c^2 + db/dt.

So, there is no objective possibility to deny the conclusion, but that does not mean our minds are capable of accepting the obvious. Einstein said it very nicely:

"Concepts that have proven useful in ordering things easily achieve such authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they might come to be stamped as "necessities of thought," "a priori givens," etc. The path of scientific progress is often made impassable for a long time by such errors. Therefore it is by no means an idle game if we become practiced in analysing long-held commonplace concepts and showing the circumstances on which their justification and usefulness depend, and how they have grown up, individually, out of the givens of experience. Thus their excessive authority will be broken. They will be removed if they cannot be properly legitimated, corrected if their correlation with given things be far too superfluous, or replaced if a new system can be established that we prefer for whatever reason." Obituary for physicist and philosopher Ernst Mach (Nachruf auf Ernst Mach), Physikalische Zeitschrift 17 (1916), p. 101

It really takes quite some time to get used to the idea that an aether theory actually forms a simple "theory of everything" that is self-evident and able to explain the workings of the Universe, both mathematically as well as conceptually. The idea itself forces one to leave one's comfort zone and our minds do not like that at all, because you know you're going to be ridiculed and thus psyschological defense mechanisms kick in that are hard to overcome.

In equation 6.40, there's a 1/c^2, which is one of the results of the entanglement of Faraday's law with the medium model in Maxwell's equations. The reason Tesla's superluminal waves are not understood is because they have no magnetic component, which is the very reason they can propagate at a superluminal speed. There are very few souls on this planet that have a clue about how Tesla's superluminal waves actually work. Eric Dollard is one of them and it seems Steffen Kuhn is another, but other than those two, I have yet to find someone that actually understands this is a superluminal phenomenon and why this is so.

It pleases me to read that people are working on understanding and describing them, but in order to do so, one has to address the problems in Maxwell's equations and understand why on the one hand they work very well in practice but on the other hand they fail to predict the longitudinal wave and that is because of the entanglement of Faraday's law with the medium model.

What we have is differential equations, whereby it's totally OK to assume the fields to propagate at an infinite speed, because we are working over infinitesimally small distances. So, in order to compute the propagation speed of the forces involved, one has to derive equations that describe the actual force propagation mechanisms, which has been made impossible, because the equation:

curl E = -dB/dt,

and associated forms force the E and B fields at a 90 degree angle with respect to one another and that is why only one wave equation can be derived, which describes a "transverse" wave, not otherwise specified. While this 90 degree angle is correct for *all* known electromagnetic phenomena, there is only one exception: Tesla's longitudinal wave, aka the scalar wave.

Now because the inclusion of Faradays's law in the model has made it impossible to derive the proper wave equations to describe not only Tesla's longitudinal wave, but also the distinctly different "near" and "far" fields, there was a problem that both the Coulomb as well as the magnetic force are assumed to propagate at an infinite speed in "quasi-static" approximation, the approximation that allowed these forces to be described in the first place.

So, what to do? They can't propagate at an infinite speed, after all, so what has been done is to "fix" the actual problem by simply assuming they all propagate at the same speed, the speed of light, by the introduction of "retarded potentials" aka the Lorenz gauge:

https://en.wikipedia.org/wiki/Retarded_potential

"In electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light c, so the delay of the fields connecting cause and effect at earlier and later times is an important factor: the signal takes a finite time to propagate from a point in the charge or current distribution (the point of cause) to another point in space (where the effect is measured)."

The measurement presented above (even though preliminary), together with the 18 references around detection of superluminal signals in my paper as well as the recent work of Steffen Kühn leave little doubt that the actual propagation speed of the electric field is superluminal rather than that it propagates at c:

Preprint General analytic solution of the telegrapher's equations and...

Preprint Electronic data transmission at three times the speed of lig...

He has also pointed to the exact same problem in Maxwell's equations via a different path:

Preprint Proof of the inconsistency of the full set of Maxwell's equa...

Taking all of this together, there simply is no escape to the conclusion that Maxwell's equations are indeed wrong. One cannot get away with violating the fundamental theorem of vector calculus, which is undoubtedly called fundamental for a reason, and it seems to me that after 120+ years of attempting to correct this obvious flaw by extending the model, i.e. make it "complete" by trying to find additional equations (including multi-dimensional ones), maybe it's time to try something else, like simply fixing the actual problem.

I also in one way do not agree that they are incomplete, while in another I do.

Let me explain. In one way, they are complete but wrong, because of the entanglement of Faradays law with a model describing the dynamics of the medium. When one corrects that, as I've shown in my paper, one is essentially left with a model that describes the dynamics of the medium. All it takes to connect the units of measurement in the electrodynamic domain to the units of measurement in the fluid dynamics domain is the introduction of a single multiplication constant e, elemental charge, by redefining Ampere's law to:

J = e ω = e ∇×Hem

This way, both domains can be fully integrated and thus it can be shown that Maxwell's equations actually describe a fluid dynamics model of the medium, whereby the fundamental symmetry between the fields as defined by the LaPlace operator is broken because of the entanglement of Faraday's law with the model, which has tremendous consequences.

In other words: in one way, they are complete and fully sufficient to describe the dynamics of the medium, were it not that it's totally wrong to entangle Faraday's law with the medium model.

In another way, they are not complete. In order to describe the wave and vortex phenomena that propagate trough the medium, wave equations, etc. are required, which are not there. So, in that sense one can say they are indeed incomplete.

Let me also add my reply to Daniele Sasso in another discussion here:

You wrote: "With regard to equations of electromagnetism, it is manifest that the Ampere law isn’t able to define completely ∇×B but the Maxwell correction is necessary. Equation system that you propose is valid only for static or stationary fields."

That is a logical conclusion, were it not that in our model, the electromagnetic domain has been fully integrated with the fluid dynamics domain. Essentially, all units of measurement within our model have an alternative unit of measurement that matches those within the fluid dynamics domain. Just like the Newton can be expressed in [kg-m/s^2], the Coulomb can now also be expressed in [kg/s].

Now when we compare Maxwell's equations with the field definitions given in the previous post, which are the result of writing out the terms in the LaPlace operator and are therefore fundamental and irrefutable, this equation is clearly in violation of the fundamental theorem of vector calculus and therefore Maxwell's equations are shown to be incorrect:

∇×𝗘em= -∂𝐁em/∂t

So, yes, when you remove it, what's left is the "static" fields when considered from the electromagnetic perspective.

However, because we have fully integrated the electrodynamic domain with the fluid dynamic domain by the introduction of a multiplication by a single constant e, elemental charge, to redefine Ampere's law to:

J = eω = e∇×Hem

and the definitions for the potentials as well as the fields of force are exactly the same in both domains, it is obvious that our equations are in fact NOT limited to describing only a "static" or "steady state" situation.

Otherwise, mathematics must tolerate that the exact same equations describe a "static" situation in the case the fluid at hand happens to be called "aether", while they are fully sufficient to describe the dynamics of any other given fluid or gas, which obviously do support the propagation of various wave and vortex related phenomena.

Equation system that you propose is valid only for static or stationary fields.

This J = eω is what we finally do in SO(4) physics and show that the electrostatic solution of the field defines a stable relation between mass,charge,orbit. This is way more fundamental than Maxwell as charge is shown to be a topological effect of rotating magnetic flux.

Inside an SO(4) coupled mass there is no limit for exchange of EM-mass (= classic signal). The only open question is whether the product of the winding number group measures forces a limit for the photon absorption transport emission process.

Interestingly, this should only work inside dense mass and not in vacuum! May be that's the reason people missed it!

https://www.livescience.com/physicists-entangle-15-trillion-hot-atoms.html

Jürg Wyttenbach You wrote: "This J = eω is what we finally do in SO(4) physics and show that the electrostatic solution of the field defines a stable relation between mass,charge,orbit. This is way more fundamental than Maxwell as charge is shown to be a topological effect of rotating magnetic flux."

Very interesting, because our revision is also way more fundamental than Maxwell, in fact, more fundamental than any theory out there. :)

We consider the "charge" of a given particle to be a longitudinal compression/decompression oscillation at a frequency f that is given by it's charge/mass ratio:

f = q/m.

Since we can't have negative frequencies, charge is no longer considered as having a polarity and therefore the polarization aspect currently attributed to “charge” should actually be attributed to a magnetic and not a dielectric phenomenon. This oscillation results in the emission of a superluminal longitudinal wave at that characteristic frequency and thus provides the "Coulomb force". This frequency can also be used to compute a temperature for a given particle, which works out to about 2.8 K for the electron, which suggests we may have found the cause for the observed Cosmic Microwave Background (temperature):

https://en.wikipedia.org/wiki/Cosmic_microwave_background

"With a traditional optical telescope, the space between stars and galaxies (the background) is completely dark. However, a sufficiently sensitive radio telescope shows a faint background noise, or glow, almost isotropic, that is not associated with any star, galaxy, or other object. [...] The CMB has a thermal black body spectrum at a temperature of 2.72548±0.00057 K. The spectral radiance dEν/dν peaks at 160.23 GHz, in the microwave range of frequencies, corresponding to a photon energy of about 6.626 ⋅ 10−4 eV."

Red shift at play?

Either way, the removal of Faraday's law from the fundamental medium model, the part that violates the fundamental theorem of vector calculus, leads to the conclusion that the symmetry between the fields we defined is fundamental. Therefore, the relation between the [E] and [B] fields along Faraday's law is no longer considered to be fundamental, but follows from the physics of the vortex.

So, our interpretation of the toroidal ring model as a physical model of subatomic particles leads to pretty much the same conclusion, but even more fundamental:

https://en.wikipedia.org/wiki/Toroidal_ring_model

What you have is that magnetism IS rotation of the aether, which is described by the “transverse” half of the Helmholtz decompositon by means of the vector potential A in [m2/s] and magnetic field H in [m/s], the latter thus describing an (angular) mass flow velocity.

One of the problems with Maxwell is that “charge” is something of which it has not been defined what it actually IS. Within our model, such a definition has been made and as far as I’m aware, Stowe is the only one that has ever done this, but I may be mistaken on that.

Now because we previously had no idea what “charge” is and the electric field has been considered as a field of force that exclusively works on “charges”, you get the situation that whenever an electric field is present, the presence of a certain “charge” distribution is implied and _that_ is what makes things unnecessarily complicated.

Steinmetz complained about this over a hundred years ago already. Note the word "prehistoric":

https://archive.org/details/elementarylectur00steirich page 13,14 :

"As seen, the capacity current is the exact analogy, with regard to the dielectric field, of the inductance voltage with regard to the magnetic field; the representations in the electric circuit, of the energy storage in the field. The dielectric field of the circuit thus is treated and represented in the same manner, and with the same simplicity and perspicuity, as the magnetic field, by using the same conception of lines of force.

Unfortunately, to large extent in dealing with dielectric fields the prehistoric conception of the electrostatic charge (electron) on the conductor still exists, and by its use destroys the analogy between the two components of the electric field, the magnetic and the dielectric, and makes the consideration of dielectric fields unnecessarily complicated.

There obviously is no more sense in thinking of the capacity current as current which charges the conductor with a quantity of electricity, than there is of speaking of the inductance voltage as charging the conductor with a quantity of magnetism. But while the latter conception, together with the notion of a quantity of magnetism, etc., has vanished since Faraday's representation of the magnetic field by the lines of magnetic force, the terminology of electrostatics of many textbooks still speaks of electric charges on the conductor, and the energy stored by them, without considering that the dielectric energy is not on the surface of the conductor, but in the space outside of the conductor, just as the magnetic energy."

It is this exact same complication that is being run into once again.

From the model of a fluidic vortex ring as a physical model of subatomic particles within a fluidic aether model, things become much more easy and understandable.

There are two degrees of freedom in a vortex ring with respect to rotation. You have the big axis R and the small axis r. Rotation is possible along both axes. Now in order to sustain a vortex in a fluid, a pressure gradient is required in order to have a centripetal force in order to force the fluid to move in circles and that force is related to the electric field, but "pressure" is not one and the same thing as the scalar potential Phi.

Dimensional analysis suggests that pressure = Phi * density (epsilon) * some frequency f.

Since a vortex has a certain angular rotation frequency ω, it appears that can be worked out just fine, but that still needs to be done.

Now because the presence of “charge” is currently implied whenever you have an electric field, while in reality the effect that is caused by a “charges” is a longitudinal superluminal wave, one is tempted to conclude that “charge” is a “topological effect of rotating magnetic flux”. It is not, the electric field that is related to the rotation is simply the centripetal force that keeps the vortex balanced and no actual “distributed charge” even exists.

The relation to mass is also very simple. The fluidic vortex ring occupies a certain volume wherein aether (mass) rotates, which can thus be considered as “bound” mass. Well, that’s the mass of the particle.

Could become interesting once someone works out the math…

Let me also add my reply to Peter Jackson in another discussion here:

Dear Peter Jackson ,

The problem is that everything has been built upon a broken foundation, because Maxwell's equations are wrong. There is hardly a soul to be found on this planet who has a clue about how Tesla's longitidinal form of energy works, which incorporates a single wire transmission line in contrast to the dual wire transmission line and if we want to understand that and utilize the phenemonon, we first need to get the fundamental equations 100% correct.

I've made a lot of progress on that lately, but I've not yet covered the Lorentz force and I suspect there are still some minor mistakes, like a missing multiplication factor and things like that. So what I intend to do next is to build a simulator, which I intend to build by adapting this open source program:

https://github.com/flaport/fdtd

This is a very basic simulator that has surprisingly few lines of code. Once we have a working simulator, we can make progress on the practical side, like studying the Biefeld-Brown effect, or simulate a vortex ring to study whether or not that idea could work as a particle model.

Things like radiation mechanisms, etc. are interesting from a scientific point of view, but we don't need to understand them in great detail to make progress.

You see, I have a dream. There's this beautiful instrument that's practially in my back yard:

https://en.wikipedia.org/wiki/Dwingeloo_Radio_Observatory

What I intend to do is to perform a longitudinal moonbounce with that thing. Takes about 2.5 seconds for an EM wave to bounce back on the moon, so you have enough time to hear your own echo. I know a radio amateur who works with that telescope and regularly performs moonbouncing with EM waves there.

So, we have a dish and we have a moon to reflect waves on. All we need is a feed antenna and it would be the crown on my career if we could actually demonstrate that Tesla was right all along by getting that feed antenna working!

So, that's really why I want that simulator. :)

Since we can't have negative frequencies, charge is no longer considered as having a polarity and therefore the polarization aspect currently attributed to “charge” should actually be attributed to a magnetic and not a dielectric phenomenon. This oscillation results in the emission of a superluminal longitudinal wave at that characteristic frequency and thus provides the "Coulomb force".

Since a vortex has a certain angular rotation frequency ω, it appears that can be worked out just fine, but that still needs to be done.

To give you the correct picture: Charge is a topological effect of nested magnetic flux - exactly as you believe but necessarily a higher dimensional vortex than 3D. Because magnetic flux always is linked to speed of light. People do think the current/charge does move. In a nucleus this picture assumes total symmetry as there is no need for a moving charge - relative to mass as it is by definition the difference of the two. Either you let a current run for a magnetic moment or you have moving magnetic lines that produce a stationary charge with the topology of a current filament.

The nested nuclear (not the electron) vortex is bound by 3 different topological charge structures whereof two are visible: 1) produces the magnetic moment. 2) the coulomb potential. 3) produces the strong force coupling.

The electron node is simpler as it covers only 4 out of 16 possible rotations (of 3D/4D mass in SO(4)). The wave (mass) relation is defined by the Fibonacci numbers what is mathematically necessary for the correct rotation number needed for the SO(4) Biot-Savart coupling.

electron 1,1,2, proton (1,1 -->) ,2,3,5. here, proton, 2 is the external potential 3 the magnetic moment.

See: https://www.researchgate.net/profile/Juerg_Wyttenbach/project/Nuclear-and-particle-physics-20/attachment/5e769606cfe4a7809f8a1bb5/AS:871654171373570@1584829957876/download/The+proton+and+its+resonances+NPP2.2.pdf?context=ProjectUpdatesLog

As mentioned in the very beginning: A vortex needs always a force to keep it stable. A wave as you try to model it leads to an oscillation and a fluctuation of energy what in physics commonly is known as excited state (but still a vortex!).

Dear Jürg Wyttenbach

where do you get the certainty that the standard model of particle physic has anything to do with reality? This question is not meant cynically, I just wonder seriously what can be considered a fact and what might be subsequent errors. The problem of particle physics is that there are no direct practical applications and it is based on the electrodynamic force laws and special relativity. Both are rather fragile foundations. Where is the validation by engineering? Atomic physics, on the other hand, can be validated e.g. by the findings of chemistry. Here one has a lot of experimental data to work with.

Best regards

Steffen

Jürg Wyttenbach Steffen Kühn

What is interesting to note is that the generalized Telegraphers' equations actually forms a complex 1D projection of one and the same phenomena as described in 3D in my paper, since that is an application of the 3D generalizion of the 1D LaPlace equation: d^2 f / dx^2 = 0.

So, Steffen's theory:

Preprint General analytic solution of the telegrapher's equations and...

is actually complementary to our 3D theory and offers a different perspective on one and the same coin.

What you have with this complex represenation of the single wire transmission line in terms of a distributed series impedance circuit is the most simple and correct 1D represenation of the complex waves that can propagate along a conductor, but there's no reason this cannot also be used to describe wave propagation along an imaginary line trough space. In that case, there simply is no "real" current.

With this analysis, you have a "real" current as well as an imaginary "current", the displacement current, whereby the real current represents the current trough the wire, and the imaginary current represents the EM fields surrounding the wire, so it seems that taking the real part of the complex wave in 1D is one and the same thing as taking the curl of the B/H field in 3D.

So, by taking these two theories together, you have a solid base to work on, which describes the EM domain completely and accurately, whereby the seemless integration of the EM domain with the fluid dynamics domain offers all you need to apply fluidic vortex physics correctly.

In other words, we now have all that is needed to revise these two basic theories:

https://en.wikipedia.org/wiki/Toroidal_ring_model

https://en.wikipedia.org/wiki/Vortex_theory_of_the_atom

and combine them with the knowledge about higher dimensional vortices and make important progress. It may very well be that it's much more convenient to describe vortices in higher dimensions, but I think if you do that, it has to be done in such a way that the these higher dimensional vortices can be projected into 3D, which is after all the dimensionality of the real world.

In other words: it may be very helpful to have "imaginary" multidimensional "currents", just like working with complex numbers is very helpful in reducing complexity, but at the end of the day, it's only the "real" current that's, well, real.

However, particle physics is just not my pint of beer.

Steffen Kühn : where do you get the certainty that the standard model (SM) of particle physic has anything to do with reality?

This question is rhetoric only..- I hope. SM has nothing to do with any reality except that it is an engineering method used to describe accelerator experiments.

In fact SM for dense matter is now replaced by SO(4) physics. The full history can be found under https://www.researchgate.net/project/Nuclear-and-particle-physics-20. The model development is ongoing. We just did notice that the method(s) used by Arendt are very closely the same we use to define the EM mass/force (charge) - field relationship.

We just stay in front of the deepest revolution physics ever will face. Dreams like unification of all forces are, since about 2 years now, a reality. I was forced to find a new model due to the fact I work for cold fusion, what is out of the SM scope. Now we exactly know how it works. The wake up call for many folks will be brutal as almost all books need adjustments. Even such fabulous thing as neutron stars seem to be nonsense as inside an alpha particle there is no neutron structure - a recent modeling surprise.

Arend Lammertink : However, particle physics is just not my pint of beer.

The common interface we have is the true electron structure you can see in the SO(4) 10 digits exact Hydrogen model. The Hydrogen model is completely magnetic flux based but I also show the "classic" physics version that has the exact same precision. There you can see how the electron splits into (1x1) X (0.5 x 0.5) 2D-2D orthogonal waves. Classically we would call the (0.5 x 0.5) orbits hybridization. In reality this is topologically induced charge/mass as already R.Mills did show. The (0.5 x 0.5) wave part (derived from the g-factor) is classically phase bound and it's the acting mass in spin-spin coupling and also the host media of the scalar waves – not bound to the speed of light.

The simplest analogy I can give. The horizon of time is the magnetic orbit thus inside we see 4D "uniform" space (inside SO(4)!) . Only real= "mass bound" interactions can be modeled= approximated 3D,t like.

Jürg Wyttenbach I always like experiments that make something visible. You may want to watch this excellent video by David LaPoint, which I watched multiple times:

https://youtu.be/siMFfNhn6dk

What he has is just plastic bowls with holes in them, which are filled with neodymium magnets. This creates a magnetic field with a specific geometry. He shows in the laboratory that with these "field emitters" one can demonstrate in a plasma chamber that a number of astronomical observations can be replicated like this.

Another very interesting demonstration is that steel balls form geometric structures under the influence of a magnetic field with this specific geometry, which look very, very much like what one would expect an atom nucleus to look like. In addition to that, he shows that those same steel balls will form structured "orbits" which look very much like what we would expect an electron orbiting an atom nucleus to look like.

It seems to me we can just simply remove the "weak" and "strong" nuclear forces from the dictionary.

Gravity is also not a problem (see my paper for more details). The gravitational force as experienced on the surface of a planet is exactly the same thing as Tesla's longitudinal dielectric wave, which creates a pushing and not a pulling force. So it appears a whole new chapter is yet to be written in the book of "Le Sage's theory of gravitation", especially now that we found a link between the characteristic longitudinal oscillation frequency of the electron and the observed Cosmic Microwave Background:

https://en.wikipedia.org/wiki/Le_Sage%27s_theory_of_gravitation#Wave_models

Wave particle duality is also no longer a mystery. A picture says more than a 1000 words:

http://www.tuks.nl/img/dualtorus.gif

And thus I fully agree with this:

"The wake up call for many folks will be brutal as almost all books need adjustments."

All of this leads to a simple integrated “theory of everything” that is based on a single hypothesis:

The medium wherein electromagnetic phenomena propagate behaves like a fluid/gas and should therefore be described as such.

And because all fields of force must propagate through the medium, there can be only one fundamental interaction and that is the one described in my paper.

I prefer the Safire project: Way more professional and with real results:

https://safireproject.com (The guy you link is silent since 2013..)

Regarding new theory: Important is that you can calculate observable constants like the gravitation constant. Just seeing an affect that looks the same is not enough!

I give a concrete (exact) SO(4) formula for the gravitation constant and also explain how it couples to distant matter.

It would be great to have a much simpler way to show the same! I also believe that at the end we must have an ether like theory based one one single effect causing mass, coupling of mass etc..

Jürg Wyttenbach You wrote: "I also believe that at the end we must have an ether like theory based one one single effect causing mass, coupling of mass etc.."

That sure sounds a lot like our theory:

Preprint Revision of Maxwell's Equations

Essentially an aether therory, whereby the aether is descibed as a compressible fluid having a certain mass density. That's where all the mass in the Universe fundamentally resides, so the mass of a particle is essentially aether mass "bound" in a vortex (ring).

Because we have integrated the units of measurements in the EM domain fully with those in the fluid dynamics domain, you do have an aether theory based on a single effect, namely the dynamics of an ideal compressible Newtonian fluid.

Within our model, all units of measurement within the electrodynamic domain now have an alternative unit of measurement, expressed in just three fundamental ones: mass, length and time. Just like the Newton can be expressed in [kg-m/s^2], the Coulomb can now be expressed in [kg/s], while it used to be undefined and was a phenomenological quantity.

In order to accomplish this, a few minor BUT important changes had to be made to the electrodynamic domain, namely the redefinition of Ampere's law to:

J = e ω = e∇×Hem,

with e the value for elemental charge, and the redefinition of the vector potential to:

H= ∇×𝐀,

thus using H rather than B.

Besides that, we have a definition for what charge IS, which is what leads to the unit of measurement for the Coulomb.

And that's about it. The rest is an exercise in working things out.

Don't let me wait for the work out...

I would like to see your calculated gravitation constant! May be I will try to integrate your solution as it looks like fitting naturally.

Jürg Wyttenbach "May be I will try to integrate your solution as it looks like fitting naturally."

That would be marvelous. I expect that if you were to do that, you will find that Maxwell's bug caused a lot of problems that are hard to overcome, while with our revision these problems have been solved at a fundamental level. Not only can the medium be considered as the fundamental cause for the forces, the math we used to describe it's dynamics is also fundamental, since in essence nothing but working out the fundamental theorem of vector calculus.

In other words: our revision is the ONLY correct way to describe the dynamics of the medium itself and thus I believe this equation will be the new E=mc2 that characterizes the biggest scientific breakthrough in decades if not centuries:

-∇2𝐅 = -∇(∇·𝐅) + ∇×(∇×𝐅) = 0.

So, one can fully expect that the multi-dimensional complexity you had to introduce in order to straighten things out will be found to reduce naturally to a simple 3D model that way.

Bear in mind that my paper has not been peer reviewed and there are probably some minor mistakes in there. For instance, the definition for Ampere's law may need a 1/2*pi, because ω usually denotes an angular frequency. Also, the Lorentz force will need to be redefined to:

F = q (E + v x H),

otherwise the units of measurement do not fit.

And I haven't yet thought about the transformation of the actual values between the two domains and how that works out. They certainly don't all translate 1:1, because of the introduction of a muliplication factor in Ampere's law.

So, while I'm certain the field definitions are 100% correct, the defining connection between the two domains (Ampere's law) and the working out of the details, which I've only added a couple of weeks ago, needs further scrutiny and it is likely that part is not 100% correct yet. Especially my definition for the Tesla does not feel right and probably misses some multiplication factor(s).

Also do read Paul Stowe's work:

https://vixra.org/abs/1310.0237

This has also not been peer reviewed and it is not always clear how he derived everything, but there are remarkable results in there, like an explanation for the anomalous magnetic moment of the electron and the expression of various constants in just the three fundamental units of mass, length and time.

Stowe's work is a bit like a rough diamond that needs polishing, but it's amazing what he has been able to do in connecting a lot of dots in unexpected ways. Do note that he introduced the idea of a "vortex sponge" on top of the medium model itself, and it is not always clear what part of the model is referred to where in the paper. That idea seems to be necessary in order to work out "The Constants of Nature", so may very well be an important part of the puzzle that needs to be considered as well in relation to your work, which suggests it's not as simple as just having a fluid-like medium.

In other words: the idea of the existence of a "vortex sponge" may very well turn out to be true and required in order to come to a complete particle/atom model in 3D.