[Physics] Mathematical proof Maxwell's equations are incorrect?

[Arend Lammertink]

On Sat, Apr 25, 2020 at 5:55 AM Ilja Schmelzer <ilja.schmelzer at gmail.com> wrote:
>
> 2020-04-24 22:34 GMT+06:30, Arend Lammertink <lamare at gmail.com>:
> > Ok, let's start with two possibilities of describing the fields within
> > an aether paradigm:
> >
> > 1) a basic fluid dynamics model for the aether (start with an ideal
> > Newtonian fluid) and on top of that a particle model;
> >
> > 2) Maxwell's model, with a/o a vector potential field that has not
> > been uniquely defined.
>
> I don't see a reason why to bother about age-old variants of ether
> theories constructed at a time when people have not known the standard
> model of particle physics.

Let's first quote Einstein, which quotes you can also find in the
article I wrote a couple of years ago when I first started this:

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

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

"I fully agree with you about the significance and educational value
of methodology as well as history and philosophy of science. So many
people today — and even professional scientists — seem to me like
someone who has seen thousands of trees but has never seen a forest. A
knowledge of the historic and philosophical background gives that kind
of independencefrom prejudices of his generation from which most
scientists are suffering. This independence created by philosophical
insight is — in my opinion — the mark of distinction between a mere
artisan or specialist and a real seeker after truth." Letter to Robert
A. Thorton, Physics Professor at University of Puerto Rico (7 December
1944) [EA-674, Einstein Archive, Hebrew University, Jerusalem].

The situation we find ourselves in is exactly the situation Einstein
warned about:

"Concepts that have proven useful in ordering things easily achieve
such authority over us that we forget their earthly origins and accept
them as unalterable givens."

Today, both relativity as well as the standard model are being pretty
much considered as "unalterable givens".

However, we must not  "forget their earthly origins" and realize they
are products of the human mind and therefore subject to human error.


> All the fields of that model as well as
> gravity distribute with the same characteristic speed c.  So, if c has
> its origin as a sort of speed of sound of an ether, than all the SM
> fields as well as gravity have to be ether fields. Such a model
> exists, see https://ilja-schmelzer.de/matter for the SM fields and
> https://ilja-schmelzer.de/gravity/ for gravity.

In my article linked above, you can find another quote, from Freeman Dyson:

"Maxwell's theory becomes simple and intelligible only when you give
up thinking in terms of mechanical models. Instead of thinking of
mechanical objects as primary and electromagnetic stresses as
secondary consequences, you must think of the electromagnetic field as
primary and mechanical forces as secondary. The idea that the primary
constituents of the universe are fields did not come easily to the
physicists of Maxwell's generation. Fields are an abstract concept,
far removed from the familiar world of things and forces. The field
equations of Maxwell are partial differential equations. They cannot
be expressed in simple words like Newton's law of motion, force equals
mass times acceleration. Maxwell's theory had to wait for the next
generation of physicists, Hertz and Lorentz and Einstein, to reveal
its power and clarify its concepts. The next generation grew up with
Maxwell's equations and was at home in a universe built out of fields.
The primacy of fields was as natural to Einstein as the primacy of
mechanical structures had been to Maxwell."

I agree with you that "all the SM fields as well as gravity have to be
ether fields", but I disagree with the way these fields should be
integrated.

The fundamental idea is that a medium called aether exists and it
behaves like a fluid.

A logical consequence thereof is that there is one one medium and
therefore only one (set of) field(s) suffices in order to describe
it's dynamics. There can be only one!

And therefore, gravity *must* be a force that is the result of either
waves trough the aether or a steady state flow within the aether. The
latter cannot be the case, since then the aether would accumulate in
the centre of the planet and therefore gravity must be some kind of
wave.

Tom van Flandern pointed out the following:

http://www.setterfield.org/vanflandern/gravityspeed.html
"if gravity is once again taken to be a propagating force of nature in
flat spacetime with the propagation speed indicated by observational
evidence and experiments: not less than 2 x 10^10 c."

So, if gravity were a "pulling" force and be caused by some kind of
wave, it would have to propagate at a speed orders of magnitudes
faster than the speed of light and therefore it *has* to be a pushing
force, and recourse must be taken to LeSagian type models:

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

And since it cannot be a Herzian electromagnetic wave, the only other
possibility left is that it is a longitudinal "Tesla" wave, the kind
of wave not currently described by Maxwell's equations, the equations
which I've shown to be in violation of elemental math.

When I look at your page about matter, based on the idea of the
existence of some kind of lattice, I read the following:

https://ilja-schmelzer.de/matter/

"On the space of 24 Dirac fermions of the SM, which could be
considered as well as 48 Weyl fermions, it would be possible to define
U(48), with 2^48 different gauge fields, as the maximal possible gauge
group. If we would not care about the complex structure, even O(96)
with 48⋅95 gauge fields would be allowed. Instead, only 12 of them,
the group SU(3)c×SU(2)L×U(1)YSU(3)c×SU(2)L×U(1)Y, are observed, and
their action shows very strange and unexplained regularities."

The propose existence of no less than 2^48 different fields is a
violation of the fundamental idea of the existence of a physical
aether which behaves like a fluid and therefore there can be only one
field, as defined by the Laplace operator and culminating in two the
closely related vector flow velocity fields [E] and [B] with a unit of
measurement in [m/s].

So let's take a look at your model:

https://ilja-schmelzer.de/matter/laymen.php

This approach has very much in common with the old ether concept. The
most important differences are:

> Based on modern physics: The old ether theories have tried to find models for the electromagnetic field. Today we know much more about the fundamental fields: We have the so-called standard model of particle physics, which describes all known particles and fields except gravity, and general relativity as the theory of gravity. The aim of our ether theory is not to obtain the EM field, as in the old ether theories, but these modern physical theories. These theories are much more complex — they contain about 250 real field components, in comparison with four fields Aμ(x) of the EM field. But this makes the job, in some sense, easier: False models can be easily seen to be false — they will be unable to give the whole picture.

Occam demands a model with only one fundamental field definition
should be preffered.

> Quantization: Quantum theory has been developed at a time when the old ether concept was already abandoned. Thus, it was not part of the old ether idea. But quantization is a natural and important part of our ether concept: We need it to obtain the elementary particles from the waves of the ether. And, especially, we are free to use all the interesting results about quantum effects in condensed matter theory.

Yep, we need it to obtain the elementary particles from the waves of the ether.

And we need to explain what "charge" is as well. It is not hard to see
that vortex rings can be combined into complex structures, which share
attributes both associated with waves as well as particles:

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

There you have your natural quantization. It is a consequence of the
properties of vortex rings.  According to Paul Stowe, one can compute
the value for elemental charge, e, from a vortex ring topology, hence
the idea that the electron should be modelled as a single vortex ring,
while more complex particles should be modelled as a combination of a
number of vortex rings.


> Universality: The old ether was a medium for the electromagnetic field. It was assumed, that, except the ether, there are also other things in the universe, like usual matter and gravity.

Yep, and that's why the old ether model has to go. There are no other
things in the universe but the aether, so things like matter and
gravity *must* be described as the result of some kind of phenomena
that can occur in a fluid-like medium, like waves and vortices.

> Today, we describe all fields, including gravity and the fermion fields, with wave equations which have the same fundamental speed as the electromagnetric field. Of course, it would be strange to have an ether for the EM field, but to explain other fields, which have the same "speed of light" c in their equations, without an ether. The new ether is, therefore, the medium for all fields which have the same characteristic speed c in their equations — that means, for all fields we know: Gravity, the gauge fields of the standard model (which includes electromagnetism, weak and strong forces), and all fermions of the standard model — quarks, leptons (like the electron) and neutrinos. Thus, the new ether has to be (and is) universal — it describes all fields of our universe. There is nothing in our world except the ether.

There _can_ be only one.


> On the other hands, there is a long list of concepts shared with the old ether idea:

>  Absolute space: We have a classical, Euclidean space R3, with the classical (global) Euclidean symmetry group E(3), generated by translations and rotations in space.
> Absolute time: We have a classical, Newtonian concept of absolute, true time.
>Time dilation caused by the ether: The time measured by clocks is distorted by effects of the ether: Moving clocks are slower.

Agree.

>Length contraction caused by the ether: As well, ether effects lead to a contraction of moving rulers. Thus, relativistic effects are described in a way similar to the Lorentz ether.

Mostly agree, as long as it's clear that the Lorentz transform should
not be applied, no matter what. We *have* to stick to absolute space
and therefore Galilean coordinate transforms.

>Medium fills space: The space is filled with some medium — the ether. This medium has parts, and these parts have a well-defined (even if unobservable) velocity.

Agreed.

> Speed of light as the speed of sound of the medium: The speed of light in the vacuum is the characteristic speed of waves in this medium, similar to the speed of sound.

Disagree. Besides the familiar "transverse" wave, there is also a
longitudinal wave, which propagates at either pi/2 or sqrt(3) times
the speed of light.  Speed of light is not a universal constant, but
follows from the local properties of the aether. Hence no application
of the Lorentz transform.


>
> > In fluid dynamics, we have both incompressible flow as well as
> > irrotational flow:
>
> And we also have flows which are neither incompressible nor irrotational.

Those are theoretical simplifications that have their place in theory,
but not in reality. No incompressible fluids nor materials exist.

One cannot have something physical that is rotating and also has zero
curl/rotation. See:

https://en.wikipedia.org/wiki/Vortex#Irrotational_vortices

>
> The fluid dynamic model of the ether has the velocity of the ether
> defined by the gravitational field as v^i = g^{0i}/g^{00}.  It is
> neither incompressible nor irrotational.
>
> >  𝐀=∇×𝐅
> >  Φ= ∇⋅𝐅
>
> ???????

All I did was to take the terms one finds in the Laplacian, elemental
math, wrote them  out and labeled them as follows:

-:-
The Laplacian IS the second order spatial derivative
of ANY given vector funtion 𝐅, the 3D curvature if you will, and is
given by the identity:

 ∇²𝐅= ∇(∇·𝐅) - ∇×(∇×𝐅)

The terms in this identity can be written out as follows:

 𝐀=∇×𝐅
 Φ= ∇⋅𝐅
 𝐁=∇×𝐀=∇×(∇×𝐅)
 𝗘=−∇Φ= −∇(∇⋅𝐅)

And because of vector identities, one can also write:

 ∇×𝗘= 0
 ∇⋅𝐁= 0
-:-

This math establishes a Helmholtz decompositon of any given vector field 𝐅:

https://en.wikipedia.org/wiki/Helmholtz_decomposition
"In physics and mathematics, in the area of vector calculus,
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 this comes down to is that "Potential Theory"  IS  "the
fundamental theorem of vector calculus".


>
> > Now to answer the question: it seems to me that with a little more
> > puzzling, we can work out a complete theory that fits like a glove,
> > were it not for Faraday's law. And as I argued in my reply to Daniel,
> > IMHO there are ample reasons to introduce Faraday's law somewhere else
> > in the model.
>
> In other words, you want to speculate about some ether theory, but
> have not even fully worked out formulas for this. Even if successful, the
> result would be worthless because a viable ether theory would have to
> cover the whole SM together with gravity, and not only the EM field.

This is established by modelling the gravitational force as
experienced on the surface of a planet as being caused by longitudinal
waves.

And it can be shown in the laboratory that the other two so-called
"fundamental interactions" can also be fully accounted for by EM
forces:

https://www.youtube.com/watch?v=siMFfNhn6dk
Don't mind the narrator too much, focus on what is being shown.

Again, the fundamental idea is that there is only one aether and
therefore only one field as defined by the fundamental theorem of
vector calculus.

This is not speculation, this is logical thinking.


>
> But you present this as if there is a problem with Maxwell's theory.
> There is none.
>
> > There is no argument that the application of the Lorentz transform is
> > what changes "flat spacetime" into "curved spacetime":
> >
> > https://en.wikipedia.org/wiki/Spacetime
> >
> > "Minkowski's geometric interpretation of relativity was to prove vital
> > to Einstein's development of his 1915 general theory of relativity,
> > wherein he showed how mass and energy curve flat spacetime into a
> > pseudo-Riemannian manifold."
>
> Nobody has to care about what motivated Einstein. If he would have
> guessed GR meditating about the Kamasutra GR would be fine too.


The conclusion is what really matters:  we want "flat spacetime" and
not "curved spacetime".


>
> > The point is:
> >
> > 1) The Laplacian defines some kind of derivative;
> >
> > 2) Locically, therefore, something should exist where the Laplacian
> > defines the derivative of.
> >
> > Just think of integration: finding an Integral is the reverse of
> > finding a Derivative.
>
> So you want to claim that for every function f(x,y,z) there
> exists some F(x,y,z) so that \nabla^2 F = f, and think for
> this theorem it is sufficient to say that this is a second
> order differential operator?  LOL.

No, what I'm trying to say is that the Helmholtz decomposition, the
fundamental theorem of vector calculus, says this:

https://en.wikipedia.org/wiki/Helmholtz_decomposition#Fields_with_prescribed_divergence_and_curl
"The Helmholtz theorem canalsobe described as follows. LetAbe a
solenoidal vector field and Φa scalar field on R3which are
sufficiently smooth and which vanish faster than 1/r^2 at infinity.
Then there exists a vector field F such that:

∇⋅F=Φ and ∇×F=A,

and if additionally, the vector field F vanishes as r → ∞, then F is unique."

And, as shown, the Helmholtz decomposition is pretty much one and the
same as the Laplace operator.

>
> But don't worry, it exists, see
> https://en.wikipedia.org/wiki/Poisson%27s_equation
>
> > Or to put it the other way around: if a derivative exists, it's
> > reverse should also exist.
>
> No. Once the square of a real number exists for all real numbers,
> the inverse, the square root,  should exist too?
> No, it exists only for nonnegative reals.

As I said, I now it doesn't always count.

The point is that according to Helmholtz the "reverse" of:

∇⋅F=Φ and ∇×F=A

exists.

And because in Maxwell we have ∇×E != 0, this is not the case.


>
> > Elsewhere, I made this argument:
> >
> > Gauge theory is built on the principle that you can add curl-free
> > components to the vector potential field [A] and divergence free
> > components to the scalar potential field Φ. Vector theory learns that
> > doing so results in the null vector for the resulting force.
> > Therefore, we can conclude that gauge theory yields no force and
> > therefore no physical effect at all. It should thus be rejected and
> > therefore QFT should be revised.
>
> ????????  If you add them to some potential, the resulting force
> does not change.  a + 0 = a, for arbitrary a,  not 0.

That's exactly the point:

"the resulting force does not change" and therefore there is no effect at all!

No differential force == no effect.