[Physics] Compatibility with and/or the properties of the Standard Model (SM)

[Arend Lammertink]

On Tue, Apr 28, 2020 at 5:52 PM Ilja Schmelzer <ilja.schmelzer at gmail.com> wrote:
>
> 2020-04-28 17:53 GMT+06:30, Arend Lammertink <lamare at gmail.com>:
> > On Mon, Apr 27, 2020 at 8:01 PM Ilja Schmelzer <ilja.schmelzer at gmail.com>
> > wrote:
> >> 2020-04-27 14:49 GMT+06:30, Arend Lammertink <lamare at gmail.com>:
> >> > On Sun, Apr 26, 2020 at 6:18 PM <mikelawr at freenetname.co.uk> wrote:
> > Think what you want, but if a guy like Tesla claims to have
> > transmitted waves with a speed vastly exceeding that of light, it may
> > be a good idea to pay attention.
>
> Maybe, your choice. Tesla has received enough attention from a lot of
> freaks, if there would have been something worth in his research
> ignored by the mainstream, it would have been already found and
> demonstrated.

Are you seriously suggesting we could just as well stop researching
altogether, because if there would be "something worth" in researching
something "it would have been already found and demonstrated"?

> Last but not least, even freaks have today technical
> possibilities much better than Tesla at his time.

Yep, count me in. I have two VNA's these days, which are essential for
researching Tesla technology.

>
> > The prediction of "spooky
> > action at a distance", requiring not only a force propagating at an
> > infinite speed but requiring an infinite magnitude as well, is one of
> > those predictions that's obviously incorrect.
>
> The tests of the Bell inequalities are quite accurate now, and require
> quantum causal influences having a speed of at least 10^4 c or so. If
> you want to join the Bell freaks community too, your choice.

I've taken a look at Aspect's experiment, back in 2013:

http://www.tuks.nl/wiki/index.php/Main/QuestioningQuantumMechanics

What I said then was:

"First of all, it says that about 5 * 10^7 photon pairs are emitted
per second by the source. That's a lot. Then it says that single rates
are over 10^4/sec and that dark rates are about 10^2/s and that the
accidental rate is about 10/s. Finally, actual rates are in the order
of 0-40/s.

Let's say for the sake of the argument that the "actual rate" is about
100/s. That means that 100 - (100/5e7 * 100) = 99,9998% of the
supposedly generated pairs are somehow not labeled as "actual". I
don't know, but it seems to me that if you throw away that much of
your data points because they don't fit with the desired results that
you are doing something wrong."

What they studied and measured handled about the question of whether
or not some kind of “correlation of pairs of photons emitted in a
radiative cascade of calcium” could be found and the answer was: yes.

Now one has two fundamental possibilities to explain this:

1) fundamental randomness as a cause for random emission of photons,
be it in pairs or not;

2) resonance.

Obviously, option 2 will have to be ruled out by means of spectral
analysis, or something to that effect, if the Quantum Magicians want
to have a point. Note that in this case over 99,9998% of the
measurements are thrown away because they don't fit with the desired
result.

Fortunately, the question of whether or not photon emission has to
with a fundamental random process or has to do with resonance is quite
easy to answer. All one needs to do is consider the 21 cm hydrogen
line:

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

I mean, how on Earth one can possibly maintain that a single atom with
a Bohr radius of about 5.3×10^−11 m is able to emit a photon with a
wavelength of no less than 21 cm because of the transition of a single
electron between the two hyperfine levels of the atom at a random
moment is beyond me.

Obviously, the whole fundamental randomness idea has to go and should
be replaced by resonance. I happen to agree with Einstein that the old
one does not roll dice.


>
> >> Fine, but Paul Stowe is also no authority.  As far as I know, he has
> >> failed yet to give a theory which is able to recover the predictions
> >> of SM and GR.
>
> > Well, he can explain the anomalous magnetic dipole moment of the
> > electron as well:
> > https://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment
>
> So he can compute some correction to the standard QED computation
> which is more accurate than QED?
> Getting not a_{e} = 0.001 159 652 181 643(764) but something closer to
> a_{e} = 0.001 159 652 180 73(28)?  That would be impressive, but I doubt.

Well, I'm sure he's willing to explain it, if he reads this. I've put
him in the cc. You can also take a look at his paper, it's in there as
well.

It's not just about being able to produce the right numbers, you know,
it's about finding a deeper understanding of Nature, such that one is
able to understand what is really going on. And then the right numbers
come out naturally, as if by magic.


>
> >> Sounds like a theory which exist in verbal description only.  Such
> >> theories are worthless, nobody will even take a look at them.
> >
> > In a good theory, math is used to expresses the fundamental ideas one
> > has such that these ideas form the basis for a quantifiable theory.
> > These fundamental ideas should be the master over the math and not the
> > other way around.
>
> So use it for this purpose.
>

Yep, that's he idea.

> > http://www.tuks.nl/wiki/index.php/Main/EinsteinMaxwellsInfluenceOnTheDevelopmentOfTheConceptionOfPhysicalReality#PartialDifferential
> >
> > "In a particular area of theoretical physics the continuous
> > field appeared side by side with the material point as the
> > representative of physical reality. This dualism has to this day not
> > disappeared, disturbing as it must be to any systematic mind."
>
> Temperature is understood as defined by the average energy of the
> atoms. But for large distances one can approximate it by a continuous
> function T(x,y,z,t). So, thermodynamics is, for large distances, also
> a field theory. Any problem? No. It should be clarified what is the
> more fundamental notion, that's all.

Yep, see the section "Temperature and Thermal Physics" in Stowe's paper:

https://vixra.org/abs/1310.0237

"Therefore temperature becomes a measure of the excitation of (or
acceleration on) a charge q".

"T = qa = qυE = qυ(v×B)"

So, according to Stowe, we obtain a unit of measurement in [C m/s] =
[kg/s * m/s] = [kg-m/s^2]

The point being: it's perfectly possible to re-align the temperature
"field" with the basic hypothesis of the existence of a real, physical
aether which behaves like a fluid.

There really _can_ be only one.


>
> I think that this "dualism" has already disappeared. In QFT, the most
> fundamental notion is the field. The particles are only quantum
> effects, similar to phonons in quantum condensed matter theory.

These are abstract notions, because built upon an abstract field.

Because there is a difference between the "near" and "far" fields
around an antenna,

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

while Maxwell only yields one wave function, we have a problem
understanding what the Nature of the far field actually is and how it
differs from the near field.

The near field remains close to the antenna and a non-radiating EM
wave has been shown to be guidable along an unshielded wire, either
coated by a thin layer of dielectric (the well known Goubau-line) or
just plain uninsulated metal, recently discovered by Elmore:

http://www.corridor.biz/FullArticle.pdf

Also not worth the effort, because "if there would have been something
worth in his research ignored by the mainstream, it would have been
already found and demonstrated"?

Either way, since a fluid cannot support a real transverse wave, while
these can occur on the boundary between two media with a different
density, the explanation is simple and straightforward:

1) The near field is an actual transverse wave, non-radiating into
space itself, given Elmore/Goubau;

2) The far field, which has been found to be quantized, *must* be some
kind of rotational phenomenon, since it has a magnetic field and
therefore is rotational in nature.

So, again, there's your quanta:

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

Particles are not "only quantum" effects. They are geometrical dynamic
structures, which can in principle be fully described by fluid
dynamics models, because they just *have* to propagate trough the
medium.


> In my
> ether model of the SM, at the foundation is some discrete lattice
> structure, so that the continuous fields are only large distance
> approximations, nothing fundamental. That's simply the next step.

All right, now we're touch upon something interesting, which is the
idea of the vortex sponge, also described by Maxwell and further
studied by Stowe. The section "The Constants of Nature" in his paper
reads a/o the following:

"We demonstrate below that all of the major constants of nature can be
derived from the vortex momenta quanta (P) and interaction length (L).

[...]

We can derive P and L as
 P = sqrt( h q_0 )/2  = 5.1546 E−27
 L = sqrt( h / q_0) = 6.427 E−08
"

These are the numbers Paul has derived for his "vortex sponge" which
is defined on top of the lower-level medium model I'm focussing on.

What if this "sponge" which Paul described more or less as a fluid
consisting of elemental vortex rings (if I understand it correctly),
actually has "some discrete lattice structure" as in your model?

Wouldn't that be a possible line of thinking to connect your model to ours?


>
> > It should be possible to refactor the SM such that it is based on the
> > notion of the existence of a real, physical medium rather than the
> > notion of the existence of a number of abstract fields, for which
> > there is no explanation of how these are supposed to propagate trough
> > the medium.
>
> In my approach all the fields are properties of the medium itself, and
> propagate as waves of the medium through the medium. Having an ether
> and additionally all the SM fields or particles or whatever makes not
> much sense IMHO.

Well, if you can find relationships between the different fields you
have defined, by starting at the notion that they *have* to propagate
trough the single medium, it is likely you find relationships that are
unexpected.

It's a bit like the story of blind people touching an elephant and
explaining what they feel. The one touching the tail has a completely
different experience from the one touching the tusk.

So, the idea is that with having multiple fields that seem to be
unrelated, one only looks at a small part of the elephant but misses
what an elephant is actually about.


>
> > The equations are probably OK to a large degree. It's mainly their
> > units of measurements which should be adapted to the new model, which
> > only has three fundamental dimensions:
> >
> > 1) length [m]
> > 2) mass [kg]
> > 3) time [s].
> >
> > All other quantities can be expressed in these three, which is a
> > significant simplification.
>
> This is some unjustified hope. The ether may have a quite complex
> structure, and have a lot of different material constants.

IMHO, Paul has shown enough to state that this is not unjustified
hope, although I don't agree for the full 100% with his model. For
example, I don't think the units of measurement for the magnetic field
and probably current (Ampere) are correct yet:

http://www.tuks.nl/wiki/index.php/Main/StowePersonalEMail

The units of measurement for the [E] and [B] field *have* to be the
same in order for Laplace / Helmholtz to work out, so there's
obviously some debugging to do there, but all in all, he has done a
remarkable job by connecting a lot of constants and such already.

The whole discussion essentially handles about the question of how to
manage a "quite complex structure", while noting that the very word
"structure" is incompatible with what we think of as a fluid or gas.
In fact, it's the absence of structure which differentiates fluids and
gases from solid state material....

In software engineering, management of complexity is accomplished by
layering your software in a logical and consistent manner. If you
throw it all in one pile, one ends up with one big pile of spaghetti
and you don't want to be the guy who is responsible for maintaining
and extending software like that.

So, what I'm once again suggesting is that the complexity needs to go
a level higher in the model, a level above the medium model, just like
one can have structures in the shape of vortices in a fluid, which can
even form knots and such:

https://www.youtube.com/watch?v=_18avidXxqY

Also see this demonstration by Nassim Haramein, demonstrating the 3D
structures that can be formed by a rotating string:

https://www.youtube.com/watch?v=Yb1ToYeCVnI

All of this does suggest, IMHO, to move the complexity of structures
to a layer above the "hard core" medium model, be it a particle model
or some kind of in-between lattice structure made of elemental vortex
rings, like rows and rows of these:

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

But, in order to be able to do such a thing, you need a basic medium
model which can describe both longitudinal compression waves as well
as vortices and something in between: the transverse surface wave,
which is actually a combination of longitudinal waves and vortices:

https://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

Well, then we're back at Maxwell, who predicts only a "transverse"
wave and it's up to the reader to guess whether or not this aligns
with the "near" field or the "far" field, but one thing is certain:
it's not both at the same time.


>
> > I'm focussing on Tesla's longitudinal waves and single wire
> > transmission line technology. That's the nut I want to crack, because
> > we need it if we ever want to be able to attach our machinery to the
> > very wheelwork of Nature.
>
> I leave Tesla to freaks. My approach was much more successful than
> what I have dreamed about when I started to develop ether theory.
>
> > In other words: the SM is what you have to guide you, yes, but that
> > does not mean one has to take it completely for granted.
>
> I don't. So I disagree about the Higgs sector.  My ether model
> recovers the fermions and gauge fields, and adds some massive scalar
> fields (among them some dark matter candidates). Moreover, it adds
> longitudinal components to the gauge fields. It also adds two
> anomalous gauge fields, which are suppressed as non-renormalizable
> fields have to be.
>
> In fact, the mainstream is not happy with the Higgs sector too, all
> this talk about non-natural is about the Higgs sector.
>
> >> Don't forget, your ether model does not exist yet as a well-defined
> >> physical theory.  A simple liquid described by some velocity is way to
> >> primitive to make any nontrivial predictions.
> >
> > Yep, agree to that. Hence the argument a particle model is needed
> > which should be built on top of the medium model by using the SM as a
> > guideline.
>
> This will not work. If you use one SM field (the EM field) as the
> base, and construct the other fields differently, you have to explain
> why the same constant c appears in the equations for all of them in
> essentially the same way.

Hmm, that's interesting, indeed. Well worth pondering about.

Historically, Maxwell predicted c and via the Lorentz transform it
eventually became accepted that c is a Universal constant which cannot
be changed and cannot vary across the Universe. This is not correct,
IMHO, but that's not the point here.

I recently found quite a number of additional papers around
superluminal anomalies, which I just oploaded here:

http://www.tuks.nl/pdf/Reference_Material/Fast_Light/

One of the most interesting ones I didn't know about before is the
"near-field anomaly in microwave propagation":

http://www.tuks.nl/pdf/Reference_Material/Fast_Light/Two%20possible%20interpretations%20of%20the%20near-field%20anomaly%20in%20microwave%20propagation.pdf

The introduction:

"Microwave and optical experiments have been demonstrated to be a
powerful tool for observing anomalies in wave propagation. The
observation of superluminal behavior, has been of particular interest
both in tunneling processes of evanescent waves and in propagation in
air with non evanescent (complex, X-shaped, Zenneck-type) waves [1–7].
A detailed analysis of the arrival time of the front-edge in microwave
propagation has recently been reported demonstrating the possibility
of observing superluminal effects: that is, the first beginning of the
pulse may result in advance with respect to the propagation at the
light velocity in vacuum [8,9]. We should note that, even if
non-evanescent like- complex or X-shaped waves can survive over
distances much greater than evanescent ones (typically, up to
distances of the order of one meter for centimeter wavelengths), the
results observed are essentially confined to -or, better, originated
in- the near-field region (see [10] where even a path-integral
approach to the problem was considered)."

Note the "originated in- the near-field region", the regio I'm
claiming you have an actual transverse wave, consisting of a
combination of vortices and FTL longitudinal waves.

Also see my answer in the thread "Do longitudinal FTL "Tesla" waves
exist and, if yes, how should they be modelled?"


>
> In my ether model, this follows from the start, given that I can prove
> the Einstein equivalence principle.

This is one of the things the late Ron Hatch argued against. Don't
remember the details, but I remember him explaining there is a
difference between a gravitational field and just acceleration:

https://www.youtube.com/watch?v=VOQweA_J4S4

His argument is based on his experience with the GPS system and had to
do with how a signal transmitted from a satellite would be influenced
by gravity. Bear in mind that Ron Hatch was THE expert on GPS and held
more than 30 patents on GPS, IIRC.

I've collected as much of his papers I could find here:

http://www.tuks.nl/pdf/Reference_Material/Ronald_Hatch/

In this one, he makes this argument:

http://www.tuks.nl/pdf/Reference_Material/Ronald_Hatch/Hatch-Clock_Behavior_and_theSearch_for_an_Underlying_Mechanism_for_Relativistic_Phenomena_2002.pdf

"In an interesting study, Mansouri and Sexl [1] show that in most
respects a Lorentz absolute ether theory with length contraction and
clock slowing is equivalent to SRT. After reaching this conclusion,
they conclude that SRT is preferable because it preserves the
equivalence of all inertial frames. However, there are at least two
reasons for seriously questioning this choice. First, the choice of
absolute equivalence of all inertial frames requires the
non-simultaneity of time while ether theories treat time as it is
intuitively understood (i.e. clock rates change but a universal now
still exists). But the major reason for choosing an ether theory over
SRT is the choice of science over magic. Fundamentally, SRT is a magic
theory. The speed of light is magically constant in all inertial
frames—no mechanism is given. Having chosen this magic proposition,
SRT then derives length contraction and clock (time) slowing as
consequences. By contrast, the Modified Lorentz Ether Theory (MLET)
models material particles as standing waves. Thus, it automatically
predicts a length contraction with motion through the absolute frame
due to the lower two-way speed of light relative to the moving
particle. Clock slowing also follows because of the effectively lower
two- way speed of light relative to the particle. With length
contraction and clock slowing, all that is needed to get an apparent
equivalence of all inertial frames is to bias the clocks such that the
one-way speed of light appears to be isotropic in the moving frames.
But most means of synchronizing clocks automatically supply the
appropriate bias.

Thus, SRT has it backwards. It assumes the apparent equivalence of
inertial frames is real and uses that result, together with the magic
of a universal speed of light, toderive length contraction and clock
slowing. On the other hand, the ether theories use the length
contraction and clock slowing to show that there is an apparent
equivalence of all inertial frames and an apparent common universal
speed of light.

An extension of the Lorentz Ether Theory has been made to include the
gravitational effects. Thus, the Modified Lorentz Ether Theory (MLET)
combines into one coherent theory the relativistic phenomena covered
under Einstein’s two disjoint theories. Because this theory covers the
change in measure or gauge of the fundamental parameters of mass,
length, and time as a function of speed (SRT type effects) and
gravitational potential (GRT type effects), it is also referred to as
an Ether Gauge Theory (EGT). A concise review of the theory has been
published [2] and is also available at the web site
http://www.egtphysics.net"

This website is no longer available. Will have to consult archive.org

>
> >> Or how does it follow that we have, in the SM, three generations,
> >> instead of four or two?  Can the variants of the SM with four or two
> >> generations be described by your ether model or not?  If not, fine,
> >> this would make three generations a prediction of your ether model.
> >> If yes, if your ether model does not restrict the resulting field
> >> theories at all, then it is worthless, because it does not make any
> >> nontrivial predictions.
> >
> > The point is that because our aether model does not restrict the
> > resulting field theories, those theories can be adapted / refactored
> > to incorporate the new found information.
>
> Instead, in my ether model, the three generations are predicted. You
> cannot obtain the SM with two or four generations using something
> similar to my ether model.  You would have to throw it away and start
> to invent something completely different.
>

Really can't follow that. Generations of what?

Higher order versions of the same resonant geometric structures
(vortices), higher frequencies, smaller particles, with a certain
relationship between these resonant frequencies??


> > Nope, but again, it allows one to rebase the current model from an
> > abstract field model base onto a base wherein two real physical fields
> > of force are defined, which are obtained from a fluid dynamics aether
> > model. These fields being the irrotatinonal [E] field and the
> > incompressible [B] field for which superposition holds, so can add a
> > third field [X]=[E]+[B] if one so desires.
>
> Makes no sense.


>From the definitions I've derived from the Laplace operator, you get
two fields of force:

1) the irrotational, compressible [E] field and associated scalar
potential [Phi], and

2) the rotational, incompressible [B] field and associated vector
potential field [A].

These are the Helmholz decompositon of c.q. the second order spatial
derivatives of some field [F].

Ok, so far, so good, I presume.

I was sure I read somewhere that superposition holds for these fields,
which is logical since they are fields of force and for force
superposition holds, one can add them together to obtain a field that
describes both the forces due to elasticity (compressibility) as well
as due to vorticity (rotational). Dollard said something like this
also:

http://www.tuks.nl/pdf/Eric_Dollard_Document_Collection/General%20Theory%20of%20Telluric%20Electric%20Wave%20Transmission%20and%20Reception%20-%20N6KPH_Hertz_Tesla.pdf

"In the operation of the oscillation transformer the winding is not a
simple reactance coil and magnetic field of induction. The
[irrotational, compressible] dielectric field of induction now plays
an important role, as energy now resides in the [compressible]
dielectric field in addition to energy residing in the [rotational]
magnetic field. In oscillation transformer operation the total energy
divides evenly between the [rotational] magnetic field and
[compressible] dielectric field of induction. The superposition [!] of
these two fields of induction give rise to complex electric waves. The
oscillation transformer winding, thus operates as a wave guide
structure, giving rise to electric waves through the exchange of
magnetic and dielectric energy."


In other words: both halves of the decomposition describe a
simplification of the higher order field, which may be computed (more
or less) separately, while at the same time addition of the resulting
two fields yields a field that describes the whole field.


>
> >> Complete nonsense, the SM gauge fields have well-defined physical effects.
> >
> > In any case, the effects are not expressed in terms of the real
> > physical fields of force they should work trough.
> >
> > The most direct experimental data which illustrates this is the
> > Aharonov–Bohm effect:
>
> The Aharonov-Bohm effect is nice, and shows that one would better use
> the gauge potentials as fundamental, instead of the force fields.
> Which is what I do anyway. This is done for the EM field as well as
> for the other gauge fields.

No, it actually shows the fallacy of using gauge potentials.

"An electric Aharonov–Bohm phenomenon was also predicted, in which a
charged particle is affected by regions with different electrical
potentials but zero electric field, but this has no experimental
confirmation yet."

To return to your earlier argument: if the electric version actually
existed, it would have been found by now. ^_^

And when you look at the experimental setup, it's not hard to see this
measurement is also flawed:

"Schematic of double-slit experiment in which the Aharonov–Bohm effect
can be observed: electrons pass through two slits, interfering at an
observation screen, with the interference pattern shifted when a
magnetic field B is turned on in the cylindrical solenoid."

You see, yes, in theory one can have a rotating [B] field with zero
curl, or "irrotational vortices".  In practice, though, things are a
bit different, which is easy to see in the FD domain:

https://en.wikipedia.org/wiki/Vortex#Irrotational_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. Within that region, the flow is no longer irrotational:
the vorticity becomes non-zero, with direction roughly parallel to the
vortex axis."

So, in practice, with the B field created by a coil, you get the same
thing. The aether whirls around the coil and forms a vortex and
therefore the centripedal force required to keep the aether
constituents to follow their cirular paths must also be present and
therefore a pressure variation (aka Electric field) must also be
present to keep the thing balanced. And that is why, in practice, one
cannot have a B-field with zero curl nor zero vector potential.

Both halves of the Helmholtz decomposition are tightly coupled via
mathematical relationships and there is no actual gauge freedom and
therefore gauge fields make no sense at all.


>
> >> My ether model is already much simpler than the SM, and predicts much
> >> of its properties. This is certainly increasing our understanding of
> >> the SM.  And once the SM describes what is actually going one in
> >> particle physics, it is increasing the understanding of this last
> >> thing too.
> >
> > Increasing our understanding of the SM is a good thing, certainly.
> >
> > But if you really want to understand what's actually going on, you
> > have no choice but to define your fields in such a way that you also
> > understand how these fields propagate trough a medium characterized by
> > a permittivity 𝞮 of 8.854 pF/m, a permeability 𝞵 of 4𝞹 x 10^-7 H/m
> > and a characteristic impedance of 377 𝞨.
>
> I have to take care of many many other physical constants predicted by
> the SM. No time to list them all, but no reason to focus my interest
> on those parameters related to the EM field.
>
> > But again, in order to make physical predictions, one's theory will
> > have to be based on something physical, the aether.
>
> No. The SM is not based on such a physical model, nonetheless it makes
> physical predictions.
>
> > There is just no way one can ever achieve a "Theory of Everyting" if
> > one starts out by defining abstract fields that cannot be mapped to
> > the characteristics of the medium we know to exist.
>
> Nonsense. 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.

But with Maxwell, we have a completely different story.

Instead of learning how the observable fields are closely related to
one another and learning that both fields propagate at different
speeds, the propagation speed of the transverse wave was taken as
absolute fact and got a life of it's own within relativity.


>
> >> >> > What Helmholtz says is:
> >> >> > A vector field 𝐅 exists such that:
> >> >> >  𝐅 = −∇Φ + ∇×𝐀
> >>
> >> No. He says that for every field F there exists potentials \Phi, A
> >> with this property.
> >> That give some  \Phi, A  there exists also an F with this property is
> >> a triviality, all you have to do is to compute the derivatives.  No
> >> theorem necessary.
> >
> > There is one detail to add:
> > "if additionally the vector field F vanishes as r → ∞, then F is unique."
>
> Again you confuse theorems. If Φ, A are given (and smooth), then
>
> >> >> >  𝐅 = −∇Φ + ∇×𝐀
>
> is obviously unique. Simply compute the derivatives.

So, where exactly do you think there is any room left for "gauge freedom" then?


>
> >> Which makes no sense at all.
> >
> > It's just taking the equation that's given and has been mathematically
> > proven to be correct:
> >
> > ∇²𝐅= ∇(∇·𝐅) - ∇×(∇×𝐅)
> >
> > And substitute
> >
> > ∇·𝐅  = Φ, and
> > ∇×𝐅 = 𝐀
>
> If you take these formulas as definitions for the Φ,A, fine, but the
> potentials in Maxwell theory are in no way obliged to follow this
> definition.

Well, I guess you don't have to, but it does lead to quite a lot of
problems, that much should be clear by now.


>
> >  𝐁=∇×𝐀=∇×(∇×𝐅)
> >  𝗘=−∇Φ= −∇(∇⋅𝐅)
> >
> > And because of vector identities, one can also write:
> >
> >  ∇×𝗘= 0
> >  ∇⋅𝐁= 0
>
> That means, if you define  Φ,A in such a way, you will get only a very
> restricted subset of the solutions of the Maxwell equations. Those
> with a static magnetic field only.

No, that's a misconception.

Just think of the fluid dynamics domain. There is no such thing as a
"static" vortex nor a "static" sound wave.

Quite to the contrary, actually, because in comparison with the 1D
equivalent, you are looking at a second order differential equation,
whereby the Laplace operator defines the spatial equivalent of the
"operator"  d^2/dx^2, the "curvature" or "Jerk". So, when 𝐅=0, one
obtains the 3D equivalent of a 1D second order derivative equation,
which has quite a lot of *harmonic* solutions, including the 3D sound
wave, the transverse surface wave as well as vortices.

Ironically enough, in 3D one cannot have a "static" sound wave, so in
actual fact the "static" electric field is not static at all!

>
> >> Fine, feel free to start this process. Up to now, you have nothing,
> >> not even a prediction which could be falsified to identify a bug.
> >
> > Even though we have not fully worked out the math (wave equations) we
> > know longitudinal waves are predicted and not only that, they are
> > predicted to propagate faster than light by a factor of either pi/2 or
> > sqrt(3). That's what longitudinal waves do, they propagate faster than
> > transverse waves trough the same medium.
>
> You would better decide which factor you predict.

Yep, must first derive wave equations in order to do that, which is
not my priority. It is known this can be done and for experiments it's
good enough to have two possibilities. For now, it seems the pi/2 one
matches best to my experiments, but I haven't gotten things under
control yet, so I'm not certain.


>
> >> There is no bug in the Maxwell equations, the bug is in your
> >> understanding them.
> >
> > Failing to predict of Tesla's longitudinal waves is a serious bug in my
> > book.
>
> Longitudinal gauge fields are part of my model too, but their speed is
> not different from c.

Well, that's a problem, IMHO.


>
> >> Some nice 2D pictures seem to match.  That's nothing.
> >
> > I think it's quite remarkable that when you throw steal balls into the
> > centre of these magnets, as is shown. the steal balls maintain order
> > within a certain geometric pattern.  Even addition of more balls does
> > not result in balls colliding. All what happens is that a new
> > geometric pattern forms, whereby the particles oscillate for a while.
>
> If you think this is remarkable, fine.  I'm not impressed. I have
> played around with magnets in my childhood, at that time I was
> impressed by such things. Whatever, it has nothing to do with weak and
> strong force or gravity.

It shows by experiment that the strong and weak forces are not
necesarily required in order to be able to explain how particles
within an atom nucleus maintain their distance and order. IMHO, that
_is_ significant.


>
> > There is a prediction, however: the existence of longitudinal
> > dieletric waves which propagate faster than light.
>
> Something which has not been observed yet. (I don't care about
> conspiracy theories that they already have been observed by some
> alternative physicists or Tesla or so.)

There is a difference between "not been observed" and "conclusively
confirmed to exist".

It seems clear that both Wheatstone and Tesla observed them and
measured their propagation speed. It's just that the evidence is not
conclusive enough to be able to claim it's absolutely certain they
exist.


>
> >> Sorry, I have a model of the medium and predicted quite a lot of
> >> properties of the SM. This is because I have started from the SM.
> >> Without starting from the theories supported by a lot of evidence you
> >> have no chance.
> >
> > When your model doesn't predict FTL longitudinal dielectric waves, you
> > are going to have a problem once conclusional evidence emerges which
> > confirms their existence. Only a matter of time. Tesla has already
> > done it and one day, someone else will too.
>
> Yes. So what? The probability for this is close to 0. Your situation
> is much worse, the particles of the SM exist, and they are all already
> supported by lot of empirical evidence.

Well, check my other posts and the probability may be a lot closer to
1 than you think now.

For now, however, I'd settle to agree on 50/50...

All the best,

Arend.