[Physics] Do longitudinal FTL "Tesla" waves exist and, if yes, how should they be modelled?

[Arend Lammertink]

Just realized that in Maxwell E is defined as the gradient of the scalar
potential Phi.

According to vector identities, the curl of the gradient of any
twice-differentiable scalar field Φ is always the zero vector, ∇×(∇Φ)=0.

And therefore curl E = 0 by definition!

QED.









On Thu, May 7, 2020, 11:49 AM Arend Lammertink <lamare at gmail.com> wrote:

> On Wed, May 6, 2020 at 8:18 AM Ilja Schmelzer <ilja.schmelzer at gmail.com>
> wrote:
> >
> > 2020-05-06 4:35 GMT+06:30, Arend Lammertink <lamare at gmail.com>:
> > > On Tue, May 5, 2020 at 12:23 AM Ilja Schmelzer <
> ilja.schmelzer at gmail.com>
> > >> No, the mainstream hopes a lot to unify them, but has failed up to
> now.
> > >
> > > The alternative view is that there is only one fundamental interaction
> > > of Nature, namely the electromagnetic domain. From that perspective,
> > > it is hopeless to try and fix things before fixing the electromagnetic
> > > domain model aka Maxwell's equations.
> >
> > Given the SM, it seems quite strange to think that the EM field is
> > somehow fundamental.
>
> Given the original idea that the aether behaves like a fluid, it seems
> quite strange it has not been described as such.
>
> When one starts out by taking that idea as fundamental and one
> considers that therefore the fundamental model should be a fluid
> dynamics model describing the dynamics of the aether, one is able to
> scrutinize Maxwell's equations and it becomes visible that the major
> obstacle between a fluid-dynamics based aether model and Maxwell's is
> the inclusion of Faraday's law within Maxwell's model.  From that
> perspective, it seems logical that this discrepancy can be resolved
> and thus that we can come to a single model which completely describes
> the dynamics of the aether, wherein only the four fields as defined by
> LaPlace / Helmholtz (E,B,A and Phi) are fundamental. While these would
> not be 100% equal to the EM fields as defined by Maxwell, they must by
> necessity match for the full 100% with observations as predicted by
> Maxwell, except there where there are anomalies, most notably the ones
> whereby faster than light signals have been observed. So, if it can be
> accomplished to re-arrange the equations that describe the EM fields
> such that the current predictions are retained, we would come to a
> field model that would be fundamental and would cover the whole
> electromagnetic domain which would therefore be considered as
> fundamental.
>
> >
> > >> I think this is hopeless.
> > >
> > > From my perspective, it is inevitable.
> > >
> > > Once one realizes how close Maxwell's equations actually are to a
> > > fluid dynamics model describing motion in a fluid-like medium called
> > > aether and one compares Maxwell's model to LaPlace / Helmholtz math,
> > > it is obvious that the term dB/dt is where Maxwell's equations
> > > differentiate with the fundamental theorem of vector calculus.
> > >
> > > I don't think there can be any disagreement about this fact.
> >
> > There obviously is.  As explained, you cannot get rid of the dB/dt
> > term without destroying the whole theory, and it follows simply that
> > there is no closeness.
>
> That wasn't the point. The point was that it's a fact one model
> contains the dB/dt term and the other does not.
>
> But you have a point, one can indeed disagree about the closeness of
> the two models, and it is rather interesting to note that different
> perspectives lead to different conclusions:
>
> 1) From the perspective that the aether fundamentally behaves like a
> fluid and should be described as such, one comes to the conlusion that
> Maxwell was pretty close, but deviated from this fundamental idea and
> therefore this disrepancy should be fixed.
>
> 2) From the perspective that the predictions from Maxwell's equations
> match extremely well with observations, obviously the aether does not
> really behave like a fluid. All one needs to do is consider Faraday's
> law to see that in the case where the fields are changing, there is a
> relationship that must hold, otherwise you destroy Maxwell's model and
> therefore you would fail to reproduce it's predictions.
>
> Obviously, only one of these two lines of thought can be objectively
> true. Either the aether really behaves like a fluid, or it doesn't and
> eventually the score must be settled by experiment.
>
> I think that the amount of available data around the detection of
> anomalous faster than light signals clearly favors my perspective, but
> conclusive evidence must still be obtained in order to settle the
> score once and for all.
>
> >
> > > And I also don't think there can be any disagreement about what it is
> > > that is being described by the equation curl E = -dB/dt: Faraday's
> > > law.
> > >
> > > So, the disagreement comes down to the following questions:
> > >
> > > Is Faraday's law a relation that holds on a fundamental level?
> >
> > No, this is not the question.  The first question is if curl E = 0 is
> > viable at all given Faraday's experiment.
>
> Ok, let's put the question the other way around:
>
> Is it absolutely necessary to have curl E = -dB/dt in order to be able
> to explain Faraday's experiment?
>
> If not, is Faradays law a law that should be included at the
> fundamental level in the model?
>
> And that is indeed the question if curl E = 0 is viable at all.
>
> I think it is viable, because when we fundamentally describe the
> dynamics of the aether with fluid dynamics vector theory, we by
> definition include all phenomena that can be described within the FD
> domain within our model. Only the scale factor and speeds are
> different, but theoritcal considerations, such as about vortex
> behavior, can all be applied.
>
> And because we can explain Faradays experiment with vortex physics, it
> seems clear that curl E = 0 is viable indeed.
>
> It seems you have trouble accepting the idea that the magnetic field
> really is a vortex. So, let's consider another experiment. Place a
> magnet under water with some baking soda and use it as an electrode
> for electrolysis and see what happens:
>
> https://www.youtube.com/watch?v=SXifaqdbLhs
>
> Again, don't mind the narrator, perhaps best to turn of the sound and
> just watch what happens.
>
> Can one analyse this with Maxwell? Sure.
> Does it come up with the right predictions? Sure, no doubt about that,
> either.
>
> Again, on the scale of such an experiment, there is absolutely no way
> to detect any trace of wave effects, so the current theory works out
> perfectly.
>
> End of discussion, you probably say.
>
> But the fact of the matter is, the idea that magnetic field really
> describes rotatinal motions of the aether sticks it's head out of the
> mud everywhere. The curl operator is all over the place in the theory
> descibing the magnetic field.
>
> So, is it really that far fetched to suggest magnetism is all about
> fluid dynamics vortex physics when we start out at the radical idea
> that the aether behaves like a fluid and should therefore be described
> as such?
>
> To me, that conclusion is inevitable, given the fundamental idea we
> started out with.
>
> > In my ether theory, it is not a law on the fundamental level (where we
> > have a discrete version of all the equations). Before caring about the
> > fundamental level, one has to accept that there should be some limit
> > where Faraday's law holds. This rules out curl E = 0.
>
> Faraday's law holds because (~irrotational) vortices imply a pressure
> gradient in practice (aka E field) because an incompressible medium
> does not exist in practice.  So, Faraday's law is the result of fluid
> dynamics vortex physics and does NOT describe something that belongs
> in a model describing the dynamics of the medium itself.
>
> So, it is fluid dynamics that on the one hand rules out curl E =/= 0
> and on the other hand is perfectly capable of explaining the
> experiment.
>
> So, stick to the radical idea that the aether behaves like a fluid and
> should therefore be described as such, and vortex physics are not only
> inevitable, they are needed in order to come to a deeper understanding
> whereby cause and effect are actually understood, rather than just
> phenomenologically described.
>
> Again, there is no argument that Faraday's law doesn't hold within the
> scale limit of a typical low frequency experiment nor within the
> two-wire distributed parallel LC network paradigm our electronics and
> radio equipment is based on.
>
> The only area I see where one could find experimental evidence it does
> not hold at the fundamental level but is the result of vortex physics
> is when you experiment with longitudinal waves within Tesla's single
> wire distributed series LC network paradigm. And because the scale
> factor kicks in when working with waves, this area is actually rather
> limited.
>
> > > Is it absolutely correct that in the case of varying fields (waves)
> > > these two fields *must* always be perpendicular to one another, no
> > > matter what?
> >
> > They must not.
>
> So, why would it be warranted to theoretically force them to be
> perpendicular in the dynamic case by writing:
>
> curl E = -dB/dt ??
>
> This is what forces the theoretical model to only predict "transverse"
> waves and rules out Tesla's longitudinal wave, which he has observed
> in practice when experimenting with his magnifying transmitter. Sure,
> there's a lot of mysticism around that out there as well, but the fact
> of the matter is that he measured a propagation speed of 471240 km/s:
>
>
> https://teslauniverse.com/nikola-tesla/patents/us-patent-787412-art-transmitting-electrical-energy-through-natural-mediums
>
> This is within .1% of the theoretical propagation speed of (pi/2) times c:
>
> >>> print 100*(471240/((pi/2)*299792.458))
> 100.069462565
>
> Remember Wheastone's 463491 km/s, who came within 2%?
>
> >>> print 100*(463491/((pi/2)*299792.458))
> 98.4239353061
>
> So, why this factor (pi/2)?
>
> Well, if one considers the magnetic field to describe rotations and
> considers the longitudinal wave to be a wave without magnetic
> component and therefore inporporating translational movements of the
> aether rather than rotational movements, the following comes to mind:
>
> For an EM magnetic wave, the medium moves in circles and therefore has
> to cover a distance of pi*r, while for a longitudinal wave the medium
> only has to cover a distance of 2*r. Divide the two and one obtains a
> theoretical speed factor of pi/2.
>
>
> So, here you have two data points that prove that Faraday's law does
> not always hold and therefore it has to be described somewhere else in
> the model. So, the dB/dt term *has* to be moved from the fundamental
> medium model to where it belongs: the two wave equations that are
> needed in order to describe the "near" and "far" fields, one
> non-radiating surface wave equation and one equation describing a wave
> that is capable of propagating trough a fluid-like medium that has a
> magnetic component and therefore must incorporate vortices in one way
> or the other.
>
>
> > > The experimental verification of the existence of a FTL wave within
> > > the electromagnetic domain would prove that Faraday's law is not a law
> > > that applies at the fundamental level. It would prove that equating
> > > curl E to -dB/dt at a fundamental level in the model is incorrect. It
> > > would prove that the elemental math as defined by LaPlace / Helmholtz
> > > also applies within the electromagnetic domain.
> >
> > First, math always applies everywhere.  Then, what you apply here is
> > not math, but a particular idea about an ether theory which is not
> > viable because curl E = 0 is not viable.
>
> It is viable, because Faraday's law is the result of vortex physics
> and does not belong in the model at a place that should only describe
> the dynamics of the medium itself.
>
> >
> > > Is it really far fetched to suggest that the way Maxwell deviated from
> > > fundamental, elemental math was, in actual fact, a gigantic blunder?
> >
> > Yes. To suggest that the Maxwell equation deviated from math is simply
> > complete nonsense, I have tried to show you a variant which makes at
> > least sense, namely that the Maxwell equations are in conflict with
> > your extremely simple ether model.
> >
>
> The point is that the predictions of such a simple aether model are
> not in conflict with the predictions of Maxwell's equations, because
> Faraday's law follows naturally from the simple model by considering
> vortex physics.
>
>
> > >> I have survived nicely without own data. I had, with some luck, a
> > >> guiding idea which put me on the way to develop an ether theory. It
> > >> had already from the start the necessary equations
> > >
> > > What I'm offering is exactly such a guiding idea, namely that this
> > > equation actually means something:
> > >
> > > ∇²𝐅= ∇(∇·𝐅) - ∇×(∇×𝐅) = 0
> >
> > Feel free to speculate about the meaning of this. I think the very
> > idea is nonsensical.
> >
>
> It follows from the radical idea that the aether behaves like a fluid
> and should therefore be described as such.
>
> What this equation means is that when you use it to describe the
> dynamics of a fluid-like medium and derive potential fields by writing
> out the terms and labeling them, it's 100% guaranteed to be correct
> and there is no room for error, whatsoever.
>
> And the data from Wheatstone and Tesla prove there is definately room
> for error in Maxwell's equations, so these need to be revised such
> that they are 100% guaranteed to be correct, which means the term
> dB/dt *has* to go.
>
> > > Bear in mind that the development of the SM was guided by the idea
> > > that there was "gauge freedom" in Maxwell's equations.
> >
> > This was not an idea, this was and is a simple mathematical fact about
> > these equations.
> >
>
> The problem is that when one fundamentally considers the aether to
> behave like a fluid, that "gauge freedom" no longer exists.
>
> So, what it comes down to is that the development of the SM was guided
> by a mathematical artifact that would not have existed if Maxwell
> would not have made the mistake of including Faraday's law at the
> wrong place in the model.
>
> > > What if Maxwell indeed made a blunder and this whole "gauge freedom"
> > > idea was in fact just an illusion?
> >
> > The Maxwell equations, as equations for E and B, predict a lot of
> > things about observables, and these predictions have been tested a lot
> > of times. This agreement between the theory and observation is
> > certainly not just an illusion, it is a very strong hard fact.
>
> Yep.
>
> >
> > This fact is so hard that you are essentially forced, if you modify
> > the Maxwell equations, to show that in the region where it has been
> > well-tested they hold approximately.
>
> Yep. They hold in all situations whereby the two-wire distributed
> parallel LC transmission line principle applies, which is the case in
> virtually everything we do that involves electronics and the EM waves
> we are familiar with.
>
> The region that has been virtually un-tested, except by Tesla and a
> hand full of dissidents, is where the single-wire distributed series
> LC transmission line principle applies, which would be associated with
> longitudinal FTL waves.
>
> This separation into two regions also matches with the two halves of
> Helmholtz decomposition. It is the introduction of Faradays law at the
> wrong place in the model which theoretically forced the model into
> "transverse" mode, thereby defining the possibility of a
> "longitudinal" mode away.
>
>
> > >> No. There can be many many failures. And looking at how some guy
> > >> performes some experiment would not be the appropriate way of error
> > >> search.
> > >
> > > That is true, but the whole idea behind physics is that mother Nature
> > > does not fail to react in exactly the same way
> > > when one performs exactly the same experiment.
> > >
> > > In that sense, Wheatsone's experiment is once again very interesting.
> >
> > Feel free to be interested and to repeat it.  That's not my problem,
> > and I cannot support you here. But what I can see is that your curl E
> > = 0 idea is completely off because it destroys the Maxwell equations
> > completely, with no chance to recover it in any limit.
> >
>
> When you realize that the equation curl E = -dB/dt is the result of
> vortex physics and you look at "water" waves, "transverse" surface
> waves:
>
> https://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html
>
> you see that those "water" waves in fact also involve vortex physics
> along with longitudinal waves.
>
> So, I believe that when we take the equations describing such "water"
> waves, we have a very good chance to recover the predictions of
> Maxwell's equations over the full limit of their applicability, namely
> the "transverse" half of the Helmholtz decomposition.
>
>
> > >> Who knows?  But I doubt that such a classical mechanism can be of any
> > >> use, given that QT predicts all these things nicely.
> > >
> > > Doubt is good. It means one can't rule it out, either, and therefore
> > > the mind is still open for the possibility.
> >
> > That's a triviality, one can never rule out that some other theory is
> > right and the own theory fails.  Such is life. This does not mean that
> > there is much of an open mind - one will not spend much own time in
> > hopeless things.
>
> Things become a lot less hopeless when one realizes we have the full
> arsenal of fluid dynamics theory at our disposal, including vortex
> physics, "water" waves as well as longitudinal "sound" waves, as long
> as we stick to the radical idea that the aether behaves like a fluid
> and should therefore be described as such.
>
> >
> > >> You have not yet a theory (with evolution equations and so on) which
> > >> gives these waves.
> > >
> > > I agree I don't have a quantifyable theory, but I do have the
> > > fundamental idea that essentially defines the fundamental foundation
> > > for a quantifyable theory in one equation:
> > >
> > > ∇²𝐅= ∇(∇·𝐅) - ∇×(∇×𝐅) = 0
> >
> > This is simply nothing.
> >
>
> It defines a complete mathematically consistent potential theory
> without gauge freedom in one equation. Just write out the terms and
> label them and there it is.
>
> >
> > > Just fill in the right
> > > parameters like density and elasticity and there you have your aether
> > > model. That's it, nothing more to it than that.
> >
> > Except that you have to make the right guesses, else the theory simply
> > fails, and that's it.  Moreover, the idea that the ether is fluid may
> > be completely wrong, it may be a solid or a plasma or whatever else.
> > In my theory, it is quite solid.
>
> We have Maxwell's equations that already describe half of the
> Helmholtz decomposition correctly. Define what charge is and move
> Faraday's law somewhere else in the model and you are already damn
> close to integrate fluid dynamics with the electromagnetic domain in a
> way that makes sense.
>
> >
> > > So, what I'm actually saying is that you have all of the phenomena
> > > known in fluid dynamics, including waves, when you describe the aether
> > > as an ideal, Newtonian fluid. So, without working things out, one can
> > > come to conclusions like that a longitudinal wave will propagate a lot
> > > faster than a "transverse" wave.
> >
> > If you have a liquid, you simply have no transverse waves.
>
> But you do have "water" waves, non radiating "transverse" *surface*
> waves, which occur at the boundary between two media with a different
> density, such as the surface of an antenna. This is why I say the
> "near" field is a "real" transverse water wave.
>
> And because the "far" field cannot be a real "transverse" wave,
> because you can't have transverse waves in a fluid, there is no other
> option but to conclude that the far field must consist of vortices in
> one way or the other.
>
> This animation of the radiation of a dipole antenna suggests a "wave"
> consisting of successive counter-rotating expanding vortex rings would
> match perfectly with observations / computations:
>
>
> https://www.didaktik.physik.uni-muenchen.de/multimedia/programme_applets/e_lehre/dipolstrahlung/bilder_dipol/web_bilder_orig/dip_1s_o.gif
>
> And there you have the most basic shape of "the quanta".
>
> >
> > > So, I'm not saying "just remove the dB/dt term and that's it", I'm
> > > saying: return to a FD model wherein you describe the aether as an
> > > ideal, Newtonian fluid and that the term dB/dt is the main obstacle in
> > > our way.
> >
> > So your curl E = 0 ether theory is dead?  Fine. But, it seems, it is
> > yet alive in your mind:
>
> Yep, I rely on elemental math to be correct.
>
>
> >
> > > In other words: all that stands in between a fluid-dynamic model for
> > > the aether and classic electrodynamics is the way Maxwell described
> > > Faraday's law by the introduction of the dB/dt term at a place where
> > > it does not belong.
> >
> > But it is at a place where you can explicitly make predictions about
> > observables, and then measure these observables, as Faraday has done.
>
> Yep, so it has to remain intact within a certain limit, but one is
> allowed to move it somewhere else in the model, such as by considering
> it to be a result of vortex physics rather than a fundamental property
> of the fields describing the dynamics of the medium itself.
>
> >
> > >> > I think he would also like Occam's razor.
> > >>
> > >> Of course. But that does not mean that he would reject established
> > >> equations which make a lot of well-tested predictions.
> > >
> > > Certainly. But I doubt he would object to re-arranging such well
> > > established equations such that they fit with a model derived from a
> > > single fundamental hypothesis:
> > >
> > > The aether behaves like a fluid and should therefore be described as
> such.
> >
> > Yes, that would be fine.  But you have to rearrange them in such a way
> > that the original testable predictions remain unchanged.
>
> Yep, totally agree.
>
>
> > >> First of all, you must recognize that the remaining theory is false
> > >> and can easily be falsified.
> > >
> > > Would be interested in such a falsification, I don't see it.
> >
> > The electric field predicted for Faraday's experiment would be
> > curl-free, and, therefore, would be unable to create a current in a
> > closed loop.
> >
>
> Were it not that the very definition of current according to Ampere's
> original law does not involve the electric field at all:
>
> J = curl B.
>
> So, this is the fundamental relation between the magnetic field and
> "current".
>
> The observed electric field is the result of the fact that in practice
> one cannot have an incompressible medium and the centripedal force has
> to be balanced by a pressure gradient aka the electric field.
>
>
> > >> The default answer is "look at wikipedia". For the information how to
> > >> measure it this should be sufficient. The result will be quite
> > >> obvious. Namely \nabla \times \mathbf {E} = 0 is dead.
> > >
> > > The correct answer is: virtually noboby has a freakin' idea!
> >
> > So what? It does not matter, given that we have devices which measure E
> and B.
>
> It matters from a theoretical point of view. As long as we don't have
> a definition for what it actually is, we are forced to resort to
> phenomenological descriptions incorporating abstract fields, which
> severely limits our ability to gain a deeper understanding of the
> mechanisms that cause the fields to behave as is being observed.
>
> >
> > > Remember what you wrote earlier?
> > >
> > > "People have started with abstract fields in thermodynamics,
> > > and then, based on the atomic theory, have learned how these
> > > observable phenomenological fields depend on the properties of the
> > > atomic models.  This research program was successful in thermodynamics
> > > as well as in condensed matter theory."
> > >
> > > Maxwell started the same way, by introducing an abstract quantity
> > > called "electric charge".
> > >
> > > Only, in this case it has never been satisfactory explained what that
> > > actually is,
> >
> > But this is not necessary to test particular equations. For testing
> > how the temperature changes we need a thermometer, not a theory about
> > the fundamental nature of temperature.
> >
>
> Yep, so we must keep the predictions of these equations intact, but we
> are free to add a theory about the fundamental nature of charge, which
> is proposed to involve the mass/charge ratio of a given "charged"
> particle that results in a frequency:
>
> f = q/m
>
> We can then take this frequency and assume a charged particle emits a
> longitudinal wave at that frequency and see where it takes us from
> there.
>
>
> > > In a nutshell: EITHER the particles cause the fields OR the fields
> > > cause the particles, but NOT both at the same time!
> >
> > In a nutshell a phenomenological theory will not tell you what is
> > cause and what is effect.
>
> Exactly!
>
> > It describes the fields we can measure, and
> > is based on the definition how they can be measured (with certain
> > measurement devices). A theory which introduces some causal
> > explanation would have to care about such things, but the Maxwell
> > equations, as equations for E and B, are a phenomenological theory
> > about those two fields E and B which can be easily measured, and does
> > not contain speculations about causal relations.
>
> Yep, so if we want to make a step forward, we are free to introduce
> causal relations such that they fit with the established
> phenomenological theory within certain limits. We just have to make
> sure the relations we introduce are correct and lead to a better
> description and deeper understanding of physical reality.
>
> >
> > That popular explanations on wiki level contain causal ways to
> > describe some aspects of these equations is quite irrelevant.
> >
> > > It is interesting and necessary in order to put the \nabla \times
> > > \mathbf {E} = 0 if dB/dt is nonzero into proper perspective.
> > > ...
> > > So, it is very important to take this point home: For an ideal coil,
> > > having zero resistance and zero parasitic capacitance, there is zero
> > > voltage and a zero electric field!
> >
> > But zero resistance is a quite uninteresting limiting case. And we
> > don't have to care about this strange limiting case with no electric
> > field, given that we would like to measure the electric field.  One
> > way to measure an electric field is, clearly, to use a wire with some
> > resistance and measure the resulting current. Your ideal wire simply
> > distorts the E field, so it is inappropriate for measuring it.
>
> Again, the fundamental separation between the fields as established
> mathematically by LaPlace / Helmholtz correspond to two idealized
> components that match with this fundamental separation:
>
> 1) The incompressible, "transverse" part around the magnetic field
> [B]. This is represented by the ideal coil. An ideal coil stores and
> extracts energy from the magnetic field [B] in the space around the
> conductor. Translated to the FD domain, this represents the
> simplification of considering the medium to be incompressible and
> rotational.
>
> 2) The compressible, "longitudinal" part around the electric field
> [E]. This is represented by the ideal capacitor. An ideal capacitors
> stores and extract energy from the electric field [E] in the space
> between two conductors. Translated to the FD domain, this represents
> the simplification of considering the medium to be compressible and
> irrotational.
>
> So, when you go to transmission line models, in essence you are using
> superposition of the two fields in a particular way by describing it
> using distributed LC networks. The two-wire version thereof is well
> known and has been applied all over the place for decades, while the
> single wire version thereof is virtually unknonwn and incompatible
> with Maxwell's equations, because of the introduction of Faraday's law
> into the model, which essentially restricts the solutions of Maxwell's
> equations to what matches with the two-wire transmission line, but
> maks the model incompatible with Tesla's single-wire transmission line
> principle.
>
> So, when you go and make a lumped circuit equivalent model of a given
> experiment, one has three elemental circuit components:
>
> 1) the capacitor (C);
> 2) the inductor (L);
> 3) the resistor (R).
>
> And when one does this, one can obtain an accurate model of a given
> system or experiment, especially when one uses distributed LCR
> networks to model wave propagation. Even the mechanical domain can be
> modelled this way and transducers can be introduced to interface
> between domains, which can be mathematically represented by
> transformers in the shape of matrices.
>
> Even Maxwell's equations in vector notation could be built up as a 3D
> distributed LCR network. The L represenst rotation, the C
> compressibility and the R resistance or losses, the exact same aspects
> as mathematically described by LaPlace / Helmholtz.
>
> And at the end of the day, your L's and C's are either in series or in
> parallel.
>
> And again, because of the introduction of Faraday's law at the wrong
> place in the model, Maxwell essentially only allows the L and C to be
> in a parallel configuration but not in a series configuration.
>
> >
> > >> No. You already have a problem, namely an experiment where dB/dt is
> > >> nonzero and, as a consequence of the Maxwell equations, \nabla \times
> > >> \mathbf {E} =/= 0.  And where all you have to do is to measure the
> > >> electric field in this situation to see that really \nabla \times
> > >> \mathbf {E} =/= 0. This is the decisive experiment between Maxwell's
> > >> theory and your "theory".
> > >
> > > What is decisive is the consideration of what it is that causes curl E
> > > =/= 0 in a practical experiment.
> > ...
> > > So, let's once again draw in the analogy of what we're actually
> > > looking at with Faraday's experiment: a magnetic vortex, which is
> > > rather interesting, since there's a very interesting detail around the
> > > theoretical irrotational vortex I hadn't noticed before:
> >
>  > No, I couldn't care less about your vortexes, whatever they are. I
> > care about the electric field. Once an ideal coil simply distorts the
> > E field too much, I would suggest not to introduce them.
>
> You are missing the point that the ideal L and the C are just another
> way of expressing the fundamental decomposition of a given 3D vector
> field into an irrotational, compressible half represented by [E] and a
> rotational, incompressible half represented by [B].
>
> The L and the C are in essence 1D representations of quite complex
> phenomena that take place in 3D. They represent 1D projections of the
> two halves of the Helmholtz decomposition and are very useful in
> practice.
>
> So, how do you model a real coil?
>
> Well, you make an LRC network to represent "parasitic" capacitance and
> resistance. And then your E-field is represented by the capacitor and
> not the inductor.
>
> >
> > > So, yes, for this particular experiment that relationship is: curl E =
> > > -dB/dt and it holds up to rather high frequencies for practical coils,
> > > BUT that in no way implies that this is a fundamental relationship
> > > that ALWAYS holds and THAT's the whole point!
> >
> > No, that's not the point.  It is quite sufficient to have a _single_
> > experiment where curl E = -dB/dt =/= 0 to show that the theory that
> > curl E = 0 is dead. And this is the point I care about here and now.
>
> Curl E = 0 is required, because otherwise you ruin the fundamental
> decomposition into the two fields for which superposition holds.
>
> An experiment wherein curl E = -dB/dt happens to hold does not explain
> the causality of why that is and therefore no experiment can reveal
> that causal relation for the simple reason we cannot perform
> experiments with ideal components.
>
> >
> > > This once again begs the question: what IS charge?
> > >
> > > Why is it on the one hand a property of certain "charged" particles
> > > yet at the same time a fundamental quantity that causes the fields,
> > > which makes that it becomes impossible to consider the possibility
> > > that "particles" are actually caused by the fields as well?
> >
> > Before caring about such speculative questions, one has to get the
> > equations straight.  And to reject nonsense like curl E = 0 as a
> > general equation once we have found situations where curl E = -dB/dt
> > =/= 0.
> >
>
> The two go hand in hand. Without an answer to the question of what
> charge is, we can't establish causal relationships and thus we cannot
> get the equations straight in such a way that we don't break anything.
>
>
> > >> Ok, but if there is a theory consistent (for those low frequencies)
> > >> with the experiments, and you don't question the experiments, you have
> > >> to be able to recover, in your modified theory, the successful
> > >> predictions of the old theory you have questioned.
>  > >>
> > >> But you fail. For Faraday's experiment, your \nabla \times \mathbf {E}
> > >> = 0 equation predicts no current, but Faraday has observe one.
> > >
> > > It's actually the other way around: the relationship describing how an
> > > ideal coil interacts with a magnetic flux is what predicts a current,
> > > but no voltage and no electric field.
> >
> > We don't care about ideal coils, we care about Faraday's experiment.
> >
>
> We care about establishing equations in such a way that the correct
> causal relationships are established AND existing experiments are
> predicted correctly as well.
>
> In this case, the fundamental causal relationship between the magnetic
> field and a current is given by Ampere's original law:
>
> J = curl B.
>
> So, it is clear that a relationship with the electric field is either
> caused by parasitic capacitance and/or resistance of the coil or by
> the physics of the (~irrotational) vortex that is described by the
> magnetic field [B] under the assumption that the medium is
> incompressible.
>
> So, one could say the electric field is "parasitic" in the
> consideration of the interaction between a magnetic field and a wire
> loop or coil and we cannot ignore that in practice, it's definitely
> there, but we have to maintain the fundamental separation of the
> Helmholtz decomposition that is reflected in the idealized capacitor
> and coil. Otherwise, we create more problems than we solve.
>
>
> > > The electric field is being observed, yes, but that's because in
> > > practice one cannot have an ideal coil and neither can one have an
> > > incompressible medium and therefore a pressure gradient will be
> > > observed in practice, which is what we call the electric field.
> >
> > Whatever, once we have found situations where curl E = -dB/dt =/= 0
> > the theory curl E = 0 is dead.
> >
> > What's the problem with acknowledging this?
> >
>
> The theory where curl E = 0 is required at that place within the model
> in order to maintain the fundamental decomposition given by Helmholtz
> / LaPlace.  Experimental data wherein curl E = -dB/dt follows from the
> symmetry between the fields as defined by the LaPlace operator in
> combination with an analysis of the physics involved, which implies
> vortex physics whenever one deals with magnetic fields.
>
> In the ideal case, under the assumption of incompressibility, there is
> no electric field. In the practical case, there is, because balance
> between the fields must be maintained in practice. Depending on the
> application, one can ignore the electric field, but in other cases one
> has to account for it by considering the physics involved in more
> detail.
>
>
> > >> Don't distract. If it fails to recover the result for the Faraday
> > >> experiment, it is dead, and nobody cares about what it thinks about
> > >> those hypothetical anomalies.
> > >
> > > The result for Faraday's experiment can be easily explained by
> > > starting out at the equation for an ideal coil and considering why
> > > this in practice leads to the presence of an electric field as well.
> >
> > But I'm not interested in a theory about what happens inside ideal
> > coils, that's the theory of superconductivity, but in a theory about
> > the EM field. The E field is simply trivial inside, the magnetic field
> > will be expelled by the Meissner effect,
> > http://www.supraconductivite.fr/en/index.php?p=supra-levitation-meissner
> > so that the result is a trivial theory inside, and this thing cannot
> > test dB/dt =/= 0.
> >
> > But, ok, no problem, I admit that your theory curl E = 0 is viable
> > inside a superconductor where we have E = B = 0, and, therefore, also
> > dB/dt = 0 so that the Maxwell equations hold too.
> >
> > Let's now stop to consider superconductivity and handle a usual
> > vacuum, using the forces acting on charged kork balls to measure E and
> > using wires only to create a variable B.  Or with wires which have a
> > resistance so that the resulting currect can be used to measure the E
> > field.
>
> Because superposition holds, one can always describe any given
> experiment arbitrary accurate by composing a model out of elemental
> ideal components L,C, and R in a (distributed) network, either in 1,
> 2, or 3 dimensions. The more accuracy you want, the more of theze
> ideal components you need, even an infinite number in the case of the
> distributed transmission line analysis, but the principle holds.
>
>
> >
> > > What's problematic is enforcing this result at the fundamental level
> > > in your model such that it HAS to apply exactly like this for all
> > > possible experiments which involve either a changing electric or a
> > > changing magnetic field.
> >
> > Yes. The starting point would be to accept the Maxwell equations as
> > they are, as phenomenological equations for E and B.
>
> Yep, within their limit of applicability: the "transverse" half of the
> Helmholtz decomposition.
>
> > Which, if
> > modified, have to be modified in such a weak way that they can be
> > easily recovered in some limit. And, as a consequence, to throw away
> > ideas about ether theories which are unable to reach this, because the
> > E field would have to follow the equation curl E = 0.
>
> Well, at the fundamental "idealized" level curl E = 0 must be applied,
> but that in no way rules out the possibility of reaching curl E =
> -dB/dt in particular situations involving an idealized magnetic field
> that has to remain balanced in practice by a "parasitic" electric
> field.
>
>
> >
> > >> Up to now, you have not found a viable way to rearrange something.
> > >> \nabla \times \mathbf {E} = 0 is in conflict with Faraday's
> > >> experiment.
> > >
> > > Faraday's experiment can be fully explained using physics based on the
> > > assumption of the existence of a fluid-like aether and therefore there
> > > is no actual conflict.
> >
> > No. You have not given such a full explanation.
> >
>
> Well, I explained the principles involved.
>
> > > In actual fact, it is the introduction of the term dB/dt into a
> > > fluid-dynamic model that is conflicting with the elemental math as
> > > defined by LaPlace / Helmholtz. It is really a bad idea to write
> > > equations that are in conflict with a fundamental mathematical
> > > theorem.
> >
> > Again you fall back into complete nonsense. Nobody introduces
> > something into your fluid-dynamic model, it simply fails, because in
> > reality we have Faraday's experiment where dB/dt  =/= 0.  If your
> > fluid-dynamic model does not survive the introduction of the term
> > dB/dt, that fluid-dynamic model is simply dead. Big deal. Learn to
> > live with this, I have tried hundreds of ideas and had to throw them
> > away because they did not work.
> >
>
> As always, the devil is in the details. The experiment is a practical
> application whereby a specific combination of the idealized fields is
> required in order to come to a full analysis of what is going on.
>
> > >> Whatever, we have a force acting on small charged kork balls, not?
> > >> And we can measure this force, by putting such kork balls at some
> > >> interesting places, not?  This force field is known as E, and it is
> > >> not a good idea to redefine it.
> > >
> > > Actually, the units of measurement within the electromagnetic domain
> > > are undefined, except in relation to one another.
> > >
> > > The SI unit for electric field strength is volt per meter [V/m]
> > > The Volt is defined as [J/C] or [kg m^2 / A s^3], so the unit of
> > > measurement for E equals [kg m / A s^3].
> > >
> > > The Coulomb is defined as [A s], while the Ampere is defined as [C/s],
> > > so actually these units of measurement are only defined in relation to
> > > one another phenomenologically and therefore it might be an excellent
> > > idea to actually define what charge is and what current is and I think
> > > I finally figured out the correct way to do it.
> >
> > It does not matter at all to write down the units. What the SI defines
> > is how these things are measured.  So learn how the SI works, what it
> > defines and how, namely be defining particular measurement procedures
> > for each unit.
>
> What matters is that these units are only defined in relation to one
> another and therefore we are free to introduce a deeper causal
> relationship and see where that brings us.
>
> >
> > The SI definitions make a lot of sense, because they are based on the
> > most accurate measurement procedures for each unit. Once experimental
> > science makes an advance, creating a device which measures some unit
> > more accurate then the old standard, they change the definition and
> > base the new definition on the new device. For this purpose, they
> > measure the old standard of what is 1 unit many times with the new
> > device, and use the result to define the same 1 unit now with the new
> > measurement device.  For the usual applications nothing changes,
> > because the extreme accuracy is not necessary for them anyway, and
> > they don't have to bother. 1 A remains 1 A, the old Amperemeter works
> > as before.
> >
> > Your proposal seems unaware of those basic ideas of the SI system, so
> > I will simply ignore it.
>
> Don't you see that the proposal to define charge along the proposal
>
> f = q/m
>
> and the proposal to define current in [Hz] doesn't change anything to
> the SI units, other than resulting in a *single* constant that maps
> the old Ampere unit to a frequency unit resulting in units of
> measurement that are 100% the same as in fluid dynamics for both the
> [E] and [B] fields?
>
> After all, the value for elemental charge remains the same and the
> frequency resulting from the proposed definition is not used anywhere,
> so the only question is the value of the single constant that remains.
> My first guess would be to take elemental charge, since real current
> is carried by electrons, but the point is: all I've really done is
> show that with the definition of a *single* constant, the current SI
> units can be mapped to the units used with fluid dynamics without
> changing anything in the equations themselves.
>
> >
> > >> > Bottomline is: when you revise Maxwell's equations, everything
> changes
> > >> > within theoretical physics.
> >
> > >> No. All the experiments remain the same, with the same results. You
> > >> may somehow reinterpret something, but not that much. Revising the
> > >> Maxwell equations is certainly not a good idea, they can be easily
> > >> tested in many details.
> >
> > > I did say *theoretical* physics. In the end, everything is based on
> > > Maxwell, one way or the other. So, if you change that, a lot of people
> > > are going to have a lot of work.
> >
> > Theoretical physics has to care about predicting experimental results,
> > and interpreting experimental results too.
> >
> > And as long as you care about things which can be directly measured,
> > like E and B, to change the equations is possible only if you recover
> > the well-established well-tested equations in a limit.  In this case,
> > not that much changes: Whenever that limit is sufficient, given the
> > accuracy requirements, you can use the old equations.
>
> Actually, we have only two changes:
>
> 1) the introduction of a single constant to map the SI units to the
> units applied in the FD domain;
>
> 2) moving Faraday's law to where it belongs: the two wave equations
> needed to properly describe a non-radiating "near" field and a
> radiating "far" field that is found to be quantized.
>
>
> > >> Sorry, no. Don't look back to Wheatstone, look first back to Faraday.
> > >> Once you don't like it with measuring the current, ok, do it with kork
> > >> balls. This measures E more directly, by measuring the force acting on
> > >> those kork balls.
> > >
> > > No need, it can be easily explained with the physics of the vortex in
> > > combination with Ampere's original circuit law:
> > >
> > > J = curl B.
> >
> > No. We have no circuit here, we have charged kork balls and an
> > electric force acting on them.
> >
>
> An electric force that is the result of vortex physics, because in
> practice balance must be maintained within a rotating magnetic vortex
> and therefore an electric field is there.
>
> > About mathematical theorems you have to care if you invent an ether
> > theory.  If they tell you that in your ether theory you cannot obtain
> > the Maxwell equations, that's bad luck for your ether theory. Not for
> > the Maxwell equations.
> >
>
> Well, a single constant, probably with a value equal to elemental
> charge e, is all that separates a FD aether theory from Maxwell.
>
> And then suddenly mathematical theorems do matter.
>
>
> > >> No, they are far from arbitrary, they have well-defined measurement
> > >> procedures as the definition.  This definition is usually based on the
> > >> actually most accurate way to measure the given thing. (That's why
> > >> these definition are sometimes changed, once a more accurate
> > >> measurement device is established.)
> > >>
> > >> Once you don't have a new measurement device for whatever which is
> > >> more accurate than all known such devices, you have no base for
> > >> proposing a change of any of the definitions of those units.
> > >
> > > The point is: one can define the concept of charge in a way that
> > > explains what it actually is without changing the results of the
> > > measurements that have been performed to establish it's value.
> >
> > Such a "concept of a charge" may be part of your ether theory. No
> > problem.  But if it appears that this concept of a charge is in
> > conflict with the Maxwell equations, that's bad luck for this concept,
> > and it has to be thrown away together with the corresponding ether
> > theory.  And you have to try something else.
>
> Yep, but in this case it results in a single constant that bridges the
> two theories, so I'm not yet ready to throw it away.
>
> >
> > You are NOT free to change equations for well-defined observables like
> > E and B which have been well-tested.  EXCEPT if you are able to show
> > that in some limit these equations will be recovered.
> >
>
> So far, we haven't changed any equation. The exercise with the
> definition of charge resulted in a mapping of EM SI units to the units
> within the FD domain by a single constant connecting the Ampere to a
> frequency in [Hz]. This single constant defines all associated units
> of measurement, since hooked into the system via a single equation:
>
> J = curl B.
>
> This way, it becomes more and more obvious the curl E = -dB/dt is
> problematic and has to go, along with equating curl B to 1/c^2 dE/dt
> rather than 0.
>
> I think we have a good chance to recover the wave equation resulting
> from these mistakes by considering the analogy of the "transverse"
> "water" surface wave and working things out. Granted, this remains to
> be seen, but it surely would make sense.
>
> > >> No. The units of measurement for E and B must match the actual most
> > >> accurate measurement procedures for E and B, and nothing else. And I
> > >> would not recommend you to propose any changes.
> > >>
> > >> If your ether theory contains some fields E', B' which you, for
> > >> whatever reasons, want to add, then you have to introduce constants E
> > >> = c_e E'. B = c_B B' with the appropriate units.  These are your
> > >> ether-theoretical constructions.  E and B remain what they are, and
> > >> the SI defitions of their units remain valid too.  They make sense.
> > >
> > > I think I've made quite a step in that direction with the definitions
> > > proposed above.
> >
> > I'm not sure. I have yet to wait for your acknowledging that curl E =
> > 0 is dead.
>
> I'm afraid you're not going to get that.
>
>
> > > Ok, that was a bit vague. He reported his E-field has a longitudinal
> > > component, while his B field is transverse. I included the relevant
> > > quote in an earlier mail. But I think my conclusion was a bit too
> > > fast, would have to check better before I can make this claim. It is
> > > clear though that Maxwell's equations break down in the analysis of
> > > his wave and workarounds are needed.
> >
> > I doubt. Don't forget that I have questioned your idea that E and B
> > fields have to be orthogonal. That's for waves, not for static fields
> > where E and B don't influence each other.
>
> I've questioned the idea that they have to be orthogonal, too.
>
> In fact, I say they don't have to be and that would be just one reason
> for removing the term dB/dt.
>
>
>
> > >> No. You can create, with static charges, quite arbitrary electric
> > >> forces (with the potential you like). Then you can put permanent
> > >> magnets into the situation. Also quite arbitrary. The result will be
> > >> static fields E and B, and they will not be perpendicular. They are
> > >> not connected at all as long as they don't change.
> > >>
> > >
> > > Ok, now let's replace the permanent magnet with an electromagnet and
> > > we start with a DC current.
> > >
> > > Same situation.
> > >
> > > Now we start changing the current, but slowly, say 1 Hz, or 0.1 Hz, or
> 0.01
> > > Hz.
> > >
> > > Now the B field is changing. What happens to the E-field?
> > >
> > > All of a sudden perpendicular?
> >
> > The original E-field defined by the localized charges does not go
> > away. The changing B field leads to some E field, which is orthogonal.
> > The resulting field is the sum of both. This will be hardly
> > orthogonal.
> >
> > And, similar to curl E =/= 0, it is sufficient to have one situation
> > where they are not orthogonal to be sure that this is not a general
> > law.
> >
>
> Exactly!
>
> And that is one of the reasons why the curl E = dB/dt has to go. In
> general, one cannot maintain that the fields are always perpendicular
> towards one another and therefore one cannot make that into a general
> law.
>
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