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

[Arend Lammertink]

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.