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

[Arend Lammertink]

@Paul Stowe : Finally figured out what's wrong with your units of
measurement for the Ampere and the magnetic domain. See below, it
actually explains quite a lot.


On Tue, May 5, 2020 at 12:23 AM Ilja Schmelzer <ilja.schmelzer at gmail.com> wrote:
>
> 2020-05-04 15:44 GMT+06:30, Arend Lammertink <lamare at gmail.com>:
> > On Sun, May 3, 2020 at 1:18 PM Ilja Schmelzer <ilja.schmelzer at gmail.com>
> > Currently, those fundamental ideas are (partly) based on the idea that
> > there are four fundamental interactions of Nature, which need to be
> > described by four independent fields.
>
> 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.

>
> > And from that perspective, the experiments by LaPoint
> > show that it is at the very least conceivable that the strong and weak
> > nuclear forces can be described within the electromagnetic domain.
>
> 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.

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?

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?


>
> > Once you have accepted this at least as a possibility, being a
> > theoretician, you can begin the process of evaluating theoretically
> > whether or not this possibility is viable and perhaps even probable.
>
> No. There is a very long way from having a dream of unifying all
> forces to actually doing this. In fact, in my approach there is also a
> partial unification, there are essentially only weak and strong forces
> in the SM model, and the EM field becomes a sort of combination of
> some parts of both.
>
> There is certainly nothing provable, and to construct a viable variant
> is a very hard job.

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.

And yes, a very hard job would remain constructing a viable variant
based upon the corrected Maxwell equations, but there would be no
other choice but to revise everything.

>
> > In other words: as long as one outright rejects the possibility, one
> > cannot begin the process of reasoning about whether or not this
> > possibility makes sense. It is the opening up of the mind for the
> > possibility rather than having to repeat a certain experiment to see
> > for yourself is the most important step a theoretican can make.
>
> Sorry, once some theoretician has found a way which has some chance of
> success, he no longer needs opening his mind to whatever alternatives.

That would almost be a contradiction in terminus. Unless he is
absolutely certain of success, he cannot rule out that some
alternative actually offers a better chance of success and therefore
he must keep an open mind for such a possibility.

> Such "opening mind" exercises may be useful for those who want to work
> in fundamental physics but have no idea how to start.

What I've been trying to tell you all this time is this: start with a
simple fluid-dynamics based aether model as your fundamental model and
compare that with Maxwell's.

What does stand out?

What does that tell you?

> I have already
> developed a model in a quite successful way, and my mind has to remain
> open for ways to improve that model, but for nothing else.

The mind must also remain open to a fundamentally different idea, such
as the radical idea that fundamental math such as the fundamental
theorem of vector calculus actually matters and means something and
that it has far reaching consequences when you deviate from this math
in your model.

Is it really far fetched to suggest that the way Maxwell deviated from
fundamental, elemental math was, in actual fact, a gigantic blunder?

>
> > You appear to be missing the point that all a theoretican needs in
> > order to verify the correctness of the fundamental ideas behind his
> > theory is the availability of a sufficient amount of data to guide
> > one's thinking.
>
> 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

> - it started with
> an ether interpretation of an alternative theory of gravity, Logunov's
> "relativistic theory of gravity", and it appeared that as an ether
> theory it works much better. This ether idea, together with the SM
> itself, appeared to be sufficient as a guide toward my ether model of
> the SM. But, of course, all the large amount of data which has lead,
> finally, to the SM, is what implicitly guided me.

Bear in mind that the development of the SM was guided by the idea
that there was "gauge freedom" in Maxwell's equations.

What if Maxwell indeed made a blunder and this whole "gauge freedom"
idea was in fact just an illusion?

>
> > In fact, it happened many times in the past that
> > theoretical ideas were described within a model years before they
> > could be experimentally verified.
>
> Yes, that's what has to be expected. My SM model is also not exactly
> the SM. It is, roughly, as close to the SM as possible (and necessary
> to be viable).

Yes, in order to build a viable model, one has to retain the
predictions made by competing models in one way or the other. So, if
one wants a chance of success, one is pretty much limited to
refactoring / rearranging the existing model, but one can't just throw
it away and start from scratch.

>
> > All a theoretican really needs are the fundamental ideas and in fact
> > these do not require any data at all.
> >
> > It's just very nice if one is able to experimentally verify the most
> > easilly verifiable prediction that differentiates one's model from
> > competing models, namely the prediction of the existence of a FTL
> > longitudinal wave.
>
> In the case of the SM, I had no chance for this. And as long as the
> mainstream ignores me completely, they will not use the alternatives
> my model will provide for the Higgs sector. You may, of course, hope
> for your FTL longitiudinal wave, but you will predictably fail.

We'll see what happens. This time I'm going to stay as close to
Wheatstone as possible and work with two wires of the same length
rather than just one and I'm going to use a mercury wetted relay for
the switching. Gonna take some time, though.

>
> >> Fake it a harsh word. It requires bad intentions. The most probably
> >> problem is honest failure. Many things can go wrong in experiments.
> >> You have cheap devices, no team which does a lot of cross-checks,
> >> thus, expect a lot of unrecognized systematic errors.
> >
> > When you consider what it really is what you are looking at with this
> > particular example, someone performing an experiment, there cannot be
> > any failure, unless bad intentions played a role.
>
> 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.

Would I obtain the same result if I would perform the experiment in
exactly the same way?

Is his result, which happens to be within 2% of what I say is the
correct result, really due to a failure on his side, or is the result
I've obtained this far due to my failure in not recreating the
necessary circumstances needed to be able to show the effect?

So far, I've identified several errors on my side which could explain
my failure to recreate and measure the effect accurately with modern
equipment. This is the only way I have to find out whether or not his
experiment was actually a failure and essentially an error of over
50%, or that it was actually remarkably accurate.

I would love to be able to start by recreating his experiment exactly
and working my way up from there in improving the accuracy of the
measurement using modern tools like a simple motor to drive the thing
rather than by hand, but that is simply beyond my capabilities because
I'd have to let others do the building and I can't afford the bill for
that.

>
> > Sure, many things can go wrong with experiments and one has to be
> > careful, but this particular experiment was not quantitative, it just
> > showed some interesting effects, including the forming of ordered
> > pattern formations by steel balls under the influence of a magnetic
> > field in a particular configuration.
> >
> > Did the steel balls fail to adhere to the laws of Nature?  Highly unlikely.
> >
> > So, what reason could there be to assume that it is impossible that
> > electromagnetic forces could possibly account for the maintenance of
> > order and stability within an atom nucleus?
>
> 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.

>
> > The point is: my experiments are guided by theoretical insights and
> > considerations and are aimed at performing the most simple experiments
> > that could verify the most easily verifiable distuingishment between
> > our "theory" and the main stream theory: the existence of a FTL
> > longitudinal wave which is one and the same phenomena as we know as
> > the "electric field".
>
> 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

Sure, there's more to it than that, but this is the fundamental
equation that defines the relationships between the E,B,A and phi
fields  that I consider to be untouchabe, because it is elemental
math.

It is clear that this relationship can be worked out using established
FD math and it is also clear that the characteristics of the aether
allow it to be described this way. All that in essence stands in
between this approach and Maxwell's is Faraday's law.

So, come to an agreement that Faraday's law has indeed been introduced
into the model at a place where it does not belong and we are looking
at a revolutionary different foundation for theoretical physics,
namely the idea that the aether actually behaves like a fluid and
should therefore be described as such.

>
> > 1) The longitudinal wave has a fundamentally different character than
> > the familiar transverse wave. Without understanding the basic physics
> > behind this, it's next to impossible to create this kind of wave.
>
> According to EM theory (Maxwell) it is simply impossible as to create
> them as to measure them.

Yep.

> You have not yet another theory.  Except the
> one where dB/dt is simply removed, which is as dead as possible. And
> that "theory" will not give any waves at all.

In my view fluid dynamics IS a theory. 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. And from that view,
the field and potential definitions should be derived from this
equation, so it all matches perfectly with elemental math:

∇²𝐅= ∇(∇·𝐅) - ∇×(∇×𝐅) = 0

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. Until you do, one can still doubt
whether the correct factor would be (pi/2) or sqrt(3), but it's
clearly well over 1.5 and sparsely available experimental data favors
the pi/2 factor, but there can be no doubt longitudinal waves are
possible in a fluid-like medium and propagate a lot faster than their
"transverse" counterparts.

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.

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.

>
> >> > Could be. Would he also accept and perhaps even prefer an aether
> >> > theory based on fundamental ideas and a correction of Maxwell's
> >> > equations?
> >>
> >> Certainly not. Don't forget, Einstein has never rejected neither the
> >> equations of quantum theory nor the experimental predictions based on
> >> it.
> >
> > 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.

>
> > Completely understandable if you are under the impression that the E
> > and B fields can easily be measured in great detail and that
> > everything electromagnetic is settled in stone.
>
> The question is not how easy it is to test them. The question is if I
> can present you a simple experiment which is accessible to your
> equipment to see that your nabla x E = 0 theory is not tenable.
>

The question is why you believe it is not tenable and no waves would
be possible, given that you have essentially the same fields and
potentials within fluid dynamics and there's no question that several
types of waves are possible within a fluid, most notably the
"transverse" "water" surface wave and the longitudinal "sound" wave.
In fact, more types of waves are theoretically possible if one
considers the possibility that successive expanding vortex rings would
also be a type of wave, where you have distinguishable entities, the
vortex rings, which would thus form a "quantized" wave which could
explain the "far" field.

>
> > What is clear is that the term dB/dt is what differentiates Maxwell
> > from LaPlace / Helmholtz.
>
> > So, when you remove it, you must also take the next step and
> > fundamentally consider the aether to behave like a fluid and consider
> > the consequences of taking that step.
>
> 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.

>
> >> And a current through a loop is nothing you can create with a \nabla
> >> \times \mathbf {E} = 0 field. So, \nabla \times \mathbf {E} = 0 is
> >> empirically falsified if there is a changing magnetic field.
> >
> > Ok, now we come to the two million dollar questions:
> >
> > *) what IS a current?
> > *) what IS charge?
>
> 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!

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, while from my perspective it is clear that it introduces
circular logic into the model, as I've argued before:

That brings us to the Nature of charge and it’s relation to causing
electromagnetic radiation:

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

“Electromagnetic waves are emitted by electrically charged particles
undergoing acceleration.” Now let’s consider the wave-particle
duality:

 https://en.wikipedia.org/wiki/Wave–particle_duality

“Wave–particle duality is the concept in quantum mechanics that every
particle or quantum entity may be described as either a particle or a
wave. […] Wave–particle duality is an ongoing conundrum in modern
physics. Most physicists accept wave-particle duality as the best
explanation for a broad range of observed phenomena; however, it is
not without controversy.”

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

“The photon is a type of elementary particle. It is the quantum of the
electromagnetic field including electromagnetic radiation such as
light and radio waves, and the force carrier for the electromagnetic
force (even when static via virtual particles).”

Now let’s substitute this into the sentence about the nature of EM radiation:

“Electromagnetic waves are emitted by (electrically charged) quanta of
electromagnetic radiation (undergoing acceleration).”


In a nutshell: EITHER the particles cause the fields OR the fields
cause the particles, but NOT both at the same time!

> But Faraday's experiment does not go away and does not change its
> result. So that \nabla \times \mathbf {E} = 0 remains dead.
>
> > So, the question is: is it really the changing magnetic field that is
> > "inducing a voltage across the inductor"  or is that "induced" voltage
> > actually caused by the ohmic resistance of the loop wire? And what
> > role does the "parasitic" capacitance between coil windings play?
>
> No, that is not that interesting. First of all, the interesting
> question is if \nabla \times \mathbf {E} = 0 if dB/dt is nonzero. If
> the answer is no, then you can forget about your proposal to change
> the Maxwell equations.

It is interesting and necessary in order to put the \nabla \times
\mathbf {E} = 0 if dB/dt is nonzero into proper perspective. Thereby
it is helpful to consider the fundamental relationship between the
magnetic field and current, which is expressed by the relationship
describing an ideal coil L:

I = Phi_B / L

Yes, this holds only for low frequencies in practice, but in essence
this describes the simplification of considering the aether to be
incompressible in the consideration of the magnetic field, which
represents the "transverse" half of the Helmholtz decomposition.

What this makes clear is that in the *ideal* case there is no
relationship whatsoever between the magnetic field and the electric
field. And this is exactly because of the Helmholtz decomposition:

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

"Helmholtz's theorem, also known as the fundamental theorem of vector
calculus, states that any sufficiently smooth, rapidly decaying vector
field in three dimensions can be resolved into the sum of an
irrotational (curl-free) vector field and a solenoidal
(divergence-free) vector field; this is known as the Helmholtz
decomposition or Helmholtz representation."

What Helmholtz really says is that in the consideration of *ideal*
effects having to do with the solenoidal (divergence-free) half of the
decomposition, the magnetic field in this case, the other half of the
decomposition, the electric field, is totally unrelated.

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!

>
> >> By simply removing the dB/dt term you kill the transverse waves too,
> >> but that's not the point, because we can restrict ourselves to the
> >> much simpler Faraday experiment to get my point.  \nabla \times
> >> \mathbf {E} = 0  is dead because a force which has a potential cannot
> >> give a current in a loop.
> >
> > The idea is that a *rotating* magnetic field, a vortex, can drag along
> > electrons trough a wire and can thus result in a current in a loop.
> > However, the fact that this does not happen with a "steady state"
> > ("static") magnetic field, as caused by a permanent magnet, must be
> > explained in another manner, otherwise we have a problem.
>
> 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.

After all, we have already seen that for an ideal coil, there is no
relationship whatsoever between the B field and related current and
the electric field. The electric field is nowhere to be found in the
coil equations, you see, and these do not only hold for the static
case. In fact, for an ideal coil it holds up to an infinite
frequenciesy, but that's in theory of course.

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:

https://en.wikipedia.org/wiki/Vortex#Irrotational_vortices
"In the absence of external forces, a vortex usually evolves fairly
quickly toward the irrotational flow pattern, where the flow velocity
u is inversely proportional to the distance r. Irrotational vortices
are also called free vortices.

[...]

However, the ideal irrotational vortex flow is not physically
realizable, since it would imply that the particle speed (and hence
the force needed to keep particles in their circular paths) would grow
without bound as one approaches the vortex axis. Indeed, in real
vortices there is always a core region surrounding the axis where the
particle velocity stops increasing and then decreases to zero as r
goes to zero."

So, just like an ideal coil is not "physically realizable", so is an
ideal irrotational vortex. In practice your fluid is compressible and
when you have a vortex, you have a pressure gradient perpendicular
with respect to the axis of the vortex, so the relationship between
the E and B fields follow from the physics.

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!



Interestingly enough, the first sentence from the quoted WP article,
gives us a handle for explaining why it is that a loop placed in the
field of a permanent magnet does not result in a current. This
actually follows from the physics of an irrotational vortex along the
original Ampère's circuital law:

J=∇×B

A permanent magnet forms an irrotational vortex and that is why we do
not obtain a current when placing a loop around a permanent magnet.
And now we also know what "current" really is: the rotation of the
magnetic field, nothing more, nothing less.

Now look at this:

https://en.wikipedia.org/wiki/Ampère%27s_circuital_law#Shortcomings_of_the_original_formulation_of_the_circuital_law
"Second, there is an issue regarding the propagation of
electromagnetic waves. For example, in free space, where

𝐉 = 0.

The [original Ampere] circuital law implies that

∇×𝐁 = 0

but to maintain consistency with the continuity equation for electric
charge, we must have

∇×𝐁 = 1/c^2  dE/dt"

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?


>
> >> Once you have not questioned the low frequency experiments, these
> >> details become irrelevant.
> >
> > There is a significant difference between questioning the experiments
> > and questioning the theory.
> >
> > I question the latter.
>
> 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.

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.

>
> >> We can agree that there are other possibilities. But once we have a
> >> domain where the Maxwell equations work well, these other
> >> possibilities are already quite restricted, namely, the modified
> >> equation has to predict, within the accuracy which was tested, the
> >> predictions of Maxwell theory.
> >
> > Yep, definitately has to. And it also has to explain a number of anomalies.
>
> 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.

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.

In practice, one gets away with this for a very long time, but it is
clear that by doing so one makes it next to impossible to analyse the
single wire transmission line, as illustrated by Elmore. One cannot
calculate an impedance for this case, even though it has been found to
equal the impedance of free space (377 Ohms) and therefore Maxwell's
equations clearly break down here and need to be worked around.

>
> > So, basically the existing equations can be re-arranged in order to
> > create room for the possibility that there may be FTL longitudinal
> > waves, but the current predictions may not be broken, except in those
> > cases where we have "anomalies".
>
> 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.

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.

>
> > However, the interpretation of what is exactly going on with existing
> > experiments may change significantly in a number of cases, most
> > notably the experiments around Faraday's law.
>
> > For instance, the notion that "charge" itself is not polarized leads
> > to considerable difference in the interpretation of certain
> > experiments, but because the vast majority of experiments rely on
> > potential differentials rather than polarity, this is not necessarily
> > of great concern.
>
> 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.

Ok, we start out with the electric side, starting at the assumption
suggested by Paul that the charge to mass ratio of a charged particle
gives a characteristic frequency for that particle and the particle
emits a longitudinal wave at that frequency:

f = q/m  ( Eq. 25 https://vixra.org/pdf/1310.0237v1.pdf )

we can work out a unit of measurent for q by first rewriting to:

q = f * m

which results in [Hz] * [kg] =  [/s] * [kg]  = [kg/s], which we can
then equate to the Coulomb [C].

The electric field is defined by:

https://en.wikipedia.org/wiki/Electric_field#Definition

E = 1/(4 pi eps_o)  q / (x1 - x0)^2

Now eps_0 has a unit of measurement in [C^2 / m^2 N], which would
become: [ kg^2/s^2  / m [kg m / s^2] ] = [ kg / m^3 ]

So, for E we would obtain a unit of measurement in  [  [m^3 / kg]  *
[kg/s] / [m^2] ] = [m/s]

This way, we do obtain different units of measurements, but we don't
break anything, because all we have really done is provide an
*additional* definition for what charge is, rather than just
postulating that it exists and work with that phenomenologically.

Now if we were to define the Ampere using the standard relation to the
Coulomb, charge per second, we would get a unit of measurement in
[kg/s /s] = [kg/s^2], which seems a bit odd and which is also what
Paul has.

However, because "real" current is carried by electrons (see Elmore),
we can take a slight detour and realize that the correct definition
for real current would not be "charge per second" but "charge carriers
per second", which would yield a frequency in [Hz] or per second [/s].

And because we know in our wires the charge carriers are electrons, we
can multiply this frequency by the mass of an electron to obtain a
mass flow in [kg/s], which we can use within the FD domain, as well as
by the charge of an electron to obtain an electric current in [C/s],
which we can use within the EM domain.

Since current is defined as the rotation of the magnetic field [B], we
now obtain a unit of measurement for the magnetic field in [m/s] as
well, thus obtaining the same units of measurement as used within
fluid dynamics for both [E] and [B], while still being able to
calculate back/forth to the old units and therefore not breaking
anything.

In other words: if we start out at the assumption that charge carriers
have a characteristic frequency given by their charge/mass ratio and
we note that real current actually describes a number of charge
carriers per second, we have defined what charge and current is in a
meaningful way that also works out perfectly with respect to the units
of measurement for the fields.

So, with this exercise we have actually learned how these "observable
phenomenological" quantities relate to the properties of the medium in
a way that makes sense, without breaking anything since we can still
calculate back/forth between these new units and the old ones.




>
> > The "far" field is not actually predicted by Maxwell's equations. In
> > simulator software, the "far" field is computed as a post-processing
> > step, whereby the E and B fields that have been computed within a
> > certain boundary box are taken and some kind of transformation is
> > applied in order to compute the "far" field. So, that offers some
> > guidance to get all that correct as well.
>
> The far field is actually predicted by Maxwell's equations. Given that
> this is simple enough, it is natural for similation software to
> simplify the computations too. Such software simplifications don't
> change the fact that the far field is actually predicted by Maxwell's
> equations.

I think you're right on this one. I got confused because the far field
powers are calculated as a post processing step.


> > 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.

But again the point: Yes, they can be easily tested in many details
and the observations match, PROVIDED you stay within the fundamental
concept of having CIRCULAR currents forming a closed loop, as ALL of
our electronics do.

The exception where it doesn't work is in the case where you work with
Tesla's form of energy, characterized by the single-wire transmission
line concept.


> > As long as you restrict yourself to closed loop circuits and
> > "transverse" waves, they predict the correct results and this has a
> > consequence for at what frequencies the model breaks down, but because
> > frequency and wavelength are related, there is a scale aspect as well.
> > This is easiest to illustrate along the Telegraphers' equations model.
>
> In the low frequency domain, say, in Faraday's experiment, waves play
> no role at all.

Well, the electric field emitted by an electron in the shape of a
longitudinal wave has a frequency of about 175 GHz.

> And that closed loop circuit is not necessary. Use
> kork balls to identify the direction of the force. To falsify  \nabla
> \times \mathbf {E} = 0 they will be good enough:
>
> no force     force ->          force <-
> |                \                  /
> |                 \                /
> o                  o              o
>
> Then, simply let the kork follow the direction of the force. If you
> finally arrive at the starting point, you have falsified  \nabla
> \times \mathbf {E} = 0. (Again, I don't worry about the details, you
> would need some dB/dt ~ const some time, this is not what I care
> about, these are theoretical thought experiments, and you have to care
> about the practical details.)

You have falsified nothing. All you have shown is that in practice the
medium is not incompressible and that as a result of the rotating
aether in the vortex also a pressure gradient arises which is needed
to balance the centripedal force within the vortex.

The point is: this is the result of the physics of a vortex and
therefore Faraday's law does not belong in the eqations which describe
the dynamics of the medium itself.

>
> > We see this when we look back at two historic detections of FTL
> > longitiudinal phenomena:
> >
> > 1) Wheatstone.
>
> 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.

>
> >> Faraday says if there is some  dB/dt then this gives some electric
> >> current through a loop. A current through a loop is something which
> >> cannot be created by an electric field with \nabla \times \mathbf {E}
> >> = 0.
> >
> > The idea is that a current can be created by a magnetic field and that
> > the voltage, which has been interpreted by Maxwell as being associated
> > with the electric field, is not caused by an external electric field,
> > but is the result of ohmic resistance of the wire and/or the load.
>
> There is a clear causal relation - if there is a changing magnetic
> field, there is a current, if not, not.  If you change the direction
> of the change of B, the current also changes its direction.

If the magnetic field is not changing, you have an *irrotational*
vortex aka a "static" magnetic field and that is why curl B = 0 and
therefore why there is no current.

As long as the magnetic field is changing, the vortex is no longer
irrotational and thus you get a current.

And because the medium is not incompressible, there is also an
electric field. But that is the result of vortex physics and not a
fundamental relationship between the E and B fields that should be
part of the medium model.

>
> >> > Well, if we could cooperate, things may change for the better.
> >>
> >> Yes, this would be my hope.
> >
> > Well, if there is an intention, there is a way. (Rough translation of
> > the Dutch saying: "waar een wil is, is een weg")
>
> Or in German "Wo ein Wille ist, ist auch ein Weg". :-)

Ohne Zweifel.

>
> >> The way Maxwell has written the equations for the A \Phi, which is
> >> described today as the Coulomb gauge, is indeed not nice. The Lorenz
> >> gauge is much better.
> >
> > The point is that LaPlace / Helmholtz describe the proper relations
> > between the four fields E,B,A and Phi at a fundamental level, in such
> > a way that it not only removes "gauge freedom" but also has a
> > fundamental symmetry which thus does not need to be re-established
> > afterwards by the application of some kind of gauge.
>
> No. There is no such animal as such "proper relations", they may be
> proper only in the context of a particular theory. Here, your ether
> theory. But your theory is in no way relevant for the Maxwell
> equations.  They are well-defined, are about observable fields E and
> B, and are well-tested.

I still think fundamental mathematical theorems matter, especially
when they give you a hint about how to define things like "what is a
current". I actually started out thinking from the unit of measurement
of the [B] field when I wanted to understand what current is and found
that way that current should have a unit of measurement in [Hz].
That's what I needed to come to the realization that a real current is
actually a movement of charge carriers and not of charge per se.

>
> > The current units of measurement are actually quite arbitrary, because
> > of the introduction of the concept of "charge" as the fundamental
> > cause for the fields to exist.
>
> 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.

>
> > However, for the B fields things are not as clear cut, but in order
> > for LaPlace / Helmholtz to be applicable the units of measurement for
> > E and B as well as Phi and A must match.
>
> 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.

>
> >> But so what?  Such simulations are a nice way to obtain the empirical
> >> predictions. And you can test them even if you can measure in a single
> >> experiment only the E field at a single point. Once the simulation
> >> predicts something well-defined for this point, this is already an
> >> empirical test of the equations.
> >
> > Yes, there is no question the "transverse" part of the Helmholtz
> > decompositon as essentially described by Maxwell works out extremely
> > well, so there's no question the predictions derived from this part of
> > the decomposition describe reality well as long as one remains within
> > the two-wire transmission line paradigm.
> >
> > Where it breaks down is when one moves over to it's single wire
> > transmission line counterpart, as illustrated by Elmore's boundary
> > case as well as several anomalies around observation of FTL signals,
> > of which Wheatsone is one of the most interesting ones, because that
> > one can be used as a guide for additional experimentation using TDR
> > methods.
>
> This is your hypothesis. Unfortunately, the "transverse" part seems
> sufficient to test all the terms used in the Mawell equations for E
> and B.  The proposal you have made simply destroys the equations
> completely, without leaving the "transverse part" unchanged.

Not really. Conceptually, the E and B fields now propagate trough a
medium with well defined properties and dynamics, whereby the
Helmholtz decompositon forms the fundamental theorem that defines the
dynamics of the medium via the definition of potentials and velocity
fields, that can be related to the existing fields by actually
defining what charge is and then it also follows from a units of
measurement analysis what current is and what unit of measurement it
should have,

>
> >> To see that \nabla \times \mathbf {E} = 0 fails it is sufficient to
> >> find some loop so that the E field points, say, in clockwise direction
> >> along the whole loop. Then you can either repeat Faraday who has found
> >> a current created along the loop, or do several experiments measuring
> >> the E field only at one point but checking that the direction is
> >> always the same clockwise direction.
> >
> > This relation is actually incorrect. See Elmore.
>
> ???????????

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.

So, what you can see with Elmore is that when you take the basic
two-wire transmission line model and calculate the distributed
inductance and capacitance for such a line, you cannot convert this to
a single-wire transmission line model by moving the return path to
infinity. But then again, it's always tricky if you move something to
infinity, so this is not the nicest way to approach the problem,
either.


>
> > But one can hardly maintain it's satisfying to have two distinctly
> > different wave phenomena and only one wave equation, which does not
> > actually match with observations, because the far field is found to be
> > quantized and this wave equation describes a continuous wave.
>
> Please don't introduce quantum things into the discussion, we consider
> now a quite classical situation, namely Faraday's experiment.

Ok, let's leave that for later. But obviously, we need to be able to
explain that in a classical way also, otherwise we have a problem
since we're defining gauge freedom away....


> > It is
> > exactly this confusion that led to the term dB/dt to be introduced
> > into the model and it forces the E and B fields to *always* be
> > perpendicular with respect to one another.
>
> 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?