**Remarks to Albert Einstein’s**

Electrodynamics of Moving Bodies

*by Mathias Hüfner*

Electrodynamics of Moving Bodies

Masses are innumerable quantities, whereas forces are caused by electrical charges. This fact is often forgotten, although physics distinguishes between grams and newtons. Gravity and inertia are consequently directed forces and correspond to the mass of the charges. Gravitation is caused by charges bound in the atom, while ionization releases charges and induces electromagnetic forces between them.

It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena.

…so Albert Einstein began his momentous essay in 1905.

What a manipulative claim! Which statistic is this statement based on and why should a dynamic be symmetrical at all? With all due respect, Einstein obviously did not understand electrodynamics, neither that of James Clerk Maxwell, based on vortex theory, nor that of Wilhelm Weber’s discrete theory. No, he is not referring to any of these papers here, which is quite unusual in science, or did he knowingly try to mislead his readers?

However, Friedrich Zöllner was already thinking about a four-dimensional world 30 years earlier^{1}, which he saw in connection with a mirror symmetry of three-dimensional bodies and, in the course of the Enlightenment in the 19th century, earned him the reputation that he suffered from a mental illness. Perhaps the sentence in the letter to Ehrenfest dated February 4, 1917, “*I have again done something wrong in the theory of gravity, which puts me a little in danger of being interned in a madhouse”*, is an allusion to the behavior of the public on Zöllner’s idea of four-dimensional space. However, Albert Einstein in the 20th century, the age of modernism and the Counter-Reformation to the Enlightenment of the 19th century, triggered by an internal church dispute over the encyclical Pope Pius X, was celebrated for ideas on physics that harmonized with faith. Now one has to give Einstein credit for the fact that in physicist circles in his day one still thought in closed systems and found thermodynamics with its asymmetry to be extremely disturbing. But thermodynamics is electrodynamics in the microwave range. Every household these days has a microwave. I am amazed that this connection has not yet reached the academic world.

I also asked myself why Einstein’s work from 1905, whose request is so absurd, left such a deep and lasting impression on people that it continues to have an impact today. Was it the mysticism that followed from the Lorentz transformation or was it a religious belief in miracles in a god-gifted genius that was subsequently built up by the media according to the commandment from the encyclical Pascendi Dominici gregis §58 of 1907? In any case, Einstein viewed electrodynamics statically through the lens of the projective Lorentz transformation. The result is distortion since angles and lengths are not retained during this transformation. We have the same effect when we map a cube into a plane. When looking at a perspective image, nobody gets the idea that distant objects are objectively smaller only because of their distance. It is clear to everyone that if he changes his point of view towards the horizon and looks back, then the situation is reversed. But supposedly not even physicists want to see through the twin paradox as a result of time dilation. At least with a science fiction film “The Planet of the Apes” in 1968, it provided explosive entertainment in which its makers could relentlessly hold up the mirror to US society.

**The helix of dynamics **

Every dynamic has its cause in a potential difference. It creates a force through which charges are accelerated. Charges are usually carried by protons and electrons, the quantities of which are innumerable. Therefore, charge carriers bound in pairs can be recorded as weighable masses.

In general, we consider weighable masses to be electrically neutral. But that’s not true. The Earth’s potential is negative and the change in field strength is around 140V/m near the ground. This tension results from gravity. It is the force that our Earth develops with its gravitational acceleration onto another bound charge. In the case of bound charges, the forces of attraction always predominate, since the charge carriers always form dipoles. We describe these dynamics with mechanics, neglecting the charges. Free charge carriers behave differently and there we use electrodynamics. There we differentiate between the electrodynamics of the electrons in a solid, where we can neglect the weighable masses, and the electroplating or the dynamics of a plasma, where we have to consider the weighable masses.

Electrodynamics of moving bodies is therefore a flow of weighable charge carriers through an open system with an entrance and an exit. To symmetrize this means to cut off the current, which is counterproductive for the dynamics. The question about dynamics must therefore be: **In what way is this potential equalization done?** Every natural flow is always a combination of two consecutive movements, a rotation and a translation in different forms. The resulting movement is the helical line that we observe everywhere in nature. We can observe this movement when we pour our coffee into our cup in the morning, or when we pull the plug out of the bathtub filled with water.

The vectorial description of a helix in Cartesian coordinates is:

- Here
*t*∈ R is the number of turns traversed by - Here,
*h*is the*height of fall*, i.e. the distance by which the screw winds downwards (in the direction of the cylinder axis;*z*-direction) in one full turn,*r*is the radius and*z*is the displacement of the screw in the axial direction. *k = h / ( θ r )*is the*fall line*of the helix: The helix becomes a straight line with an inclination*k*if the cylinder jacket with the helix is unfolded into the plane.- One calls α =
*arctan**(k)*the*thread angle*of the screw.

Dirac even spoke in this context of God, whom he considered to be a “highly brilliant mathematician.” Wolfgang Pauli once put it: “*Our friend Dirac has a religion, and its motto is: There is no God, and Dirac is his prophet*.” He became the creator of a number of physical phantoms, the existence of which in some cases has even been allegedly proven, such as the spin from the Dirac equation and the neutrino in the radioactive decay of the neutron. So, it came about that relativity theory and quantum mechanics emerged as intellectual fantasy products and were recognized as established theories.

Our analytical thinking has taken these two components of motion (rotation and translation) apart for mechanical understanding. In electrodynamics, these two components are brought together again. If you look at the projection of this movement in the x, y-plane, you get a wave movement from the screw movement. The basic theory of the wave behavior of matter was developed by Louis-Victor de Broglie in his dissertation in 1924, for which he received the 1929 Nobel Prize in Physics. But one has forgotten that the wave movement in the projection plane is actually a screw movement in space. The projection into a plane perpendicular to it provides the image of a vortex as Descartes and Newton first described it.

For further consideration, it is useful to use cylindrical coordinates (r; θ; z) instead of the Cartesian coordinates, which are better adapted to a screw movement.

One of the most astonishing puzzles is the apparently force-free movement of a body in a potential field, as we observe with space probes but also in the electron shell around the atomic nucleus.

Have you never wondered why Newton’s apple falls back to Earth but the moon stays in the sky? Well, our rockets are given an appropriate start impulse so that they can reach orbit. But where does the starting impulse come from for all the heavenly bodies that are circling around each other? That is supposed to be done by the one-dimensional gravity of a Newton?

But Newton’s equation fails as soon as we don’t have two point charges, as the rotation relationships in galaxies show. If we look at the moon from the Sun, the inertial center of the Earth’s orbit, we see how it makes a helical line around the Earth’s orbit. If we look at the Earth from the inertial center of the galaxy, we see how the Earth follows a helical line around the Sun’s path. If I look at an electron from an inertial center with respect to an atomic orbit, we also get a helical line, the projection of which gives the de Broglie wave.

When we look at a physical process, we are used to putting it in a framework, a closed system. This is how the movement of the Earth in the ecliptic is viewed. The Sun’s own movement is left out. But nature is not a closed system. In engineering, open systems with input and output data have been used for a long time. So it is not only the system itself that is considered, but also how it is embedded in its environment. Maxwell’s equations describe how an input current radiates an electromagnetic wave.

From a thermodynamic point of view, one would say that an accelerated electric current emits radiation as entropy. The fact that electrical currents are themselves organized in circuits is not taken into account. Only the interactions between electric and magnetic fields are described. The electrodynamics is therefore only incompletely described, and it needs to be supplemented how the current behaves, which is what Wilhelm Weber’s electrodynamics is concerned with.

**The two-dimensional generalized model of gravity by Wilhelm Weber space**.

Wilhelm Weber’s electrodynamics describes the forces that prevail between the weighable charge carriers from the point of view of a discrete structure of matter.^{2} If electrical forces and gravitational forces are measured with the same measuring principle, namely with the Cavendish torsion balance, there is only one difference in the amount of these forces, but not in their origin. As early as 1836, Fabrizio Mossotti described gravity as a *residual force of electrical force*.^{3} The difference between negative and positive electricity was recognized early on and that this can be traced back to the polar atomic structure of matter. The forces are the expression of the effort to balance the charge.

Forces are generated by accelerated weighable masses that are opposed to inertial forces. Weighable means that a solid body is held in the Earth’s force field by a force that is proportional to the mass of its protons and neutrons.^{4} Since a reference block is used for weighing, the weighable mass only relates to the number of *bound* positive charge carriers. Negative electricity is considered to be imponderable since it weighs only the 1836th part compared to positive electricity.

The second factor in the force equation is acceleration. It’s a change in speed. If we don’t have a change in speed, there is no acceleration. But this also means that a movement with constant speed is force-free. But powerless does not mean that there is no momentum which is the product of mass and speed.

If we now consider Newton’s law of gravitation, we have learned that:

Now the empirically derived law of gravitation has a huge blemish. It has a singularity at r = 0, which would mean that if you imagine the mass to be concentrated in one point, the potential would grow beyond all limits, which would be equivalent to a hypothetical black hole. There is no such thing in nature. You cannot concentrate all mass in one point, so we have to take mathematical precautions so that masses do not crash into each other at the speed of light. First of all, we have to put Newton’s law in cylindrical coordinates. Then we move the large mass M according to its inertia to the origin (z = 0; r = 0) and m circles around M. According to Einstein we call this an inertial system. Then an attractive force directed towards the center is negative in this frame and a repulsive force is positive. So we have to write Newton’s law like this:

It should be noted that Newton’s law is an idealization of the true relationships. Because *M* and *m* are very small in their radius compared to *r* (*r _{S}: *0.46% distance from the Earth to the Sun), they can be understood as point masses. However, slight deviations have already been observed for Mercury and Venus. There the ratio of the solar radius to the distance of Mercury is already 1.2%. That is why Wilhelm Weber made a correction and added a limiter:

This is to prevent the two point charges from generating a force that grows beyond measure when approached at will. Finally, he added a term, the 2nd derivative of the radius with respect to time, i.e. a radial acceleration *b _{r}.*

The radial acceleration determines the eccentricity of the ellipse and is responsible for the rotation of the perihelion. After all, the small body is supposed to rotate around the large body, and the smaller the distance, the faster the rotation.

In the next step, we have to deal with the electrical effects of the masses on one another. Weighable masses usually also carry *free* positive or negative charges, caused by the lack of free electrons or the excess number of free electrons. These free charges change the balance of forces. The Sun is electrically positively charged, while the Earth has a negative overall charge. While the mass density is the ratio of weighable mass to volume, the charge density is the ratio of charge to surface. Of course, this has no meaning with two point charges, but it does have a meaning in a particle flow.

Friedrich Zöllner was the first to think about the relationship between attraction and repulsion of ponderable masses, and he formulated two sentences in the second half of the 19th century:

- 1. All weighable masses are only compounds of the same positive and negative electricity.
- 2. The attraction of equal amounts of unequal electricity is greater than the repulsion of the same amounts of electricity of the same kind.

In these two assumptions, Wilhelm Weber saw the basis for the fact that the law of gravitation of all weighable bodies results as a consequence of the basic electrical law and he emphasized the importance of confirming this assumption for the whole of physics.^{5} However, he could not determine any measurable difference between attractive and repulsive force.

The situation is different with the expression in brackets in formula (2). Felix Tisserand^{6} a French astronomer had found discrepancies in the perihelion of Mercury and Venus that could explain this factor. He stated a deviation of δ = +13.65 ‘‘ per century and for Venus δ = +2.86 ‘‘. The current forecast of perihelion rotation for Mercury is δ = +42 ‘‘. It was not until 1898 that Paul Gerber succeeded in completely deriving the formula for the perihelion twist^{7}. Gerber’s equation for the rotation of the perihelion was already formally identical to the equation later set up by Einstein. Paul Marmet confirmed Gerber’s derivation without relativity theory only with the theorem of the conservation of mass and energy^{8}, which played no role in Einstein’s principle of relativity.

Currently established physics is far from recognizing electrodynamics in the cosmos. It continues to rely on symmetry in particle physics. Regardless of this, let us dwell a little longer on Weber’s thoughts.

We assume that the cosmic medium consists of atoms, molecules, and dust particles, all of which have electrically charged masses in the plasma state. For the electron, no weighable mass fraction should be taken into account whereby the charge is always different from its weighable mass, depending on whether there is a lack of imponderable electrons or an excess of them. Weighable mass is a comparative measure for the non-countability of the set of elementary particles. There are only two stable elementary particles– the proton and the electron–between which the forces that are responsible for keeping matter together can develop. Due to the atomic structure of the positive atomic nucleus and negative atomic shell, there are no neutral particles, but the atoms behave like dipoles. This means that atoms always arrange themselves in such a way that they attract each other. However, positive or negative *k* or *l* free charge carriers can dock on the surface of dust particles.

So, we can write* – m = – ε ± k ∙ q *and* M = E ± l ∙ Q .*

The force according to formula (1) now distinguishes 4 possible cases according to the charge, of which two are repulsive forces

If we only consider the factor of the charges, we have the following cases:

If we now add the forces from (4) to (7) and form the mean value, we get Eε. This shows that in the case of point charges at a large distance, the free surface charge is irrelevant for the forces between them and that contradicts the 2nd sentence of Zöllner’s assumption, just as Weber found it. Newton’s law not only finds its limit when the two mass radii become comparable with the distance between them but also when many point charges interact, like the stars in the galaxies show.

According to Kepler, the rotational speeds must be indirect with the distance from the center of rotation decrease proportionally to the square, instead, the curves remain almost constant over the entire galaxy disk after a steep increase. While Kepler’s observation was valid for two mass points, we are dealing here with very many mass points. Consequently, we cannot expect a galaxy to behave like two mass points very far apart.

Instead of assuming a halo of mysterious dark matter for this speed distribution, Klaus Gebler showed a very simple and plausible estimate. Imagine that the entire mass M is divided into two masses and the resulting spheres are again divided into two equal spheres. This division is continued until the space between the mass M and the sample mass is evenly filled with smaller and smaller balls. *M* is then distributed over a cylindrical disk with the radius *r* and the thickness *d*. Then the mass of the galaxy is the product of the volume *V* and the mean density ρM over the radius; and the volume results from V = 2πr²∙d, from which it follows *M= 2πr²∙d* ∙ *ρ _{M }*.

We can assume that during the process of the crumbling of the mass, free charges form on the surface of the spheres, which increase with the sum of the surfaces, otherwise the galaxy would not shine. Hence, the charge density *ρ _{Q }*is proportional to

*ρ*. If the test charge

_{M }*m*then sits on the surface of

_{Q}*V*, its distance from the center is also

*r*.

We put the obtained expression for *M *in

and get

*F = m **∙ b*

The radial acceleration is then proportional to the radial density distribution and the radial force is equal to zero since it cancels out with the centrifugal force. Consequently, the acceleration must also be zero, but this does not have to apply to all of its components.

It follows:

In this simple galaxy model, the radial velocity at a location in the galaxy is proportional to the mean charge density and thus also proportional to the mass density of the galaxy, which explains the plateau in Fig. 2. From this, it can be concluded that, conversely, the charge density in the center of a galaxy decreases sharply, which directly contradicts the idea of a gravitational monster in the center of a galaxy. Because mass and charge cannot disappear, a strong current in the z-direction is to be expected as the cause of the lower mass density in the center of the galaxy, and because a magnetic field is present, with a charge separation along the z-axis. In fact, we now know that mass jets from the centers of rotation occur in practically all disk galaxies, but this has nothing to do with black holes but is simply due to the conservation of mass and energy, a fundamental law of physics that Hermann von Helmholtz already formulated in 1847. And we can derive something else from (9): The surface charges of the particles in the galaxy hold the plasma together like a solid.

If this changes, an electrical vortex field is emitted, which in turn generates a magnetic vortex field and so on. In other words, when weighable charged masses move, an electromagnetic pulse is emitted, which in turn excites weighable masses in the vicinity and so is transported, since all masses are coupled and bound charge carriers. Now it is no longer the mass density, but the charge density of free charge carriers that is decisive for further consideration.

Many charged particles moving along the z-axis result in a current *I* in the z-direction. This current is characterized by its electrical charge density, not so much by its mass, and it induces a magnetic field. We now want to examine the magnetic field around this current that emerges from the center of the galaxy.

**A force-free magnetic field according to Donald E. Scott**^{ }^{9}

A useful mathematical idealization of such a physical cosmic current is a vector field of current density ** j** which, when viewed in a cylindrical coordinate system, generates an average current vector

**everywhere, which by definition flows in the direction of the z-axis. The strength of**

*I***is assumed to be independent of the z coordinate everywhere.**

*I*The basic structure of such a cosmic magnetic field is described by the momentum equation of ideal magneto-hydrodynamics.

*μ _{0}* is the permeability of free space. The left side of this expression represents the compressive magnetic (Lorentz) force and the right side is the expansion force (pressure gradient multiplied by the permeability of the plasma). We differentiate between force-free fields with the partial derivatives and pressure-balanced fields with . We want to consider the force-free case here.

Then the following applies to the electromagnetic force which every charge experiences within such a plasma:

The first term *q· E* is the electrical force and the second term

*q (*×

**ν***is called the magnetic force.*

**B**)Here *q *is the charge and *v* is its flow velocity. The name Lorentz force is used to describe expression (11). The plasma area receives a cylindrical current flow. No initial assumptions are made about the distribution of the current density over the cross-section. A flow of charge creates its own magnetic field through which the charge flows. The point at which each charged particle *q* is located is the point of origin of two local vectors in the current: *j = q · v* (current density) and *B* (magnetic induction). The current density vector ** j** naturally generates a

*curl*vector given by Maxwell [35] at every point:

**B**The derivative term added by Maxwell in (12) is called the displacement current. It is often considered a null value, as we do here when it can be assumed that there are no time-varying electric fields in the region. The integration of the curl B vectors over a cross-section of the cylindrical flow (Stokes theorem) gives

The second term in (13) is equivalent to *I*, where* I* is the total current carried by the plasma. If the cross-section is circular with radius* r*, the last term in (13) is *2π r B*, where

**is in the azimuthal direction and not aligned with**

*B**I*and the z-axis. Thus the

**-field is generated by a cylindrical plasma with its outer boundary**

*B**r = R*, which is

Expression (12) is the point shape and (13) is the integral (macroscopic) form of this Maxwell equation. Expression (12) is valid at all times. The integral forms given in (13) and (14) imply that ** B** is a vector sum of the effects of all

**vectors on the surface**

*j**S*enclosed by

*C*.

**is not generated directly from a single**

*B***In (12) it is clear that**

*j.***, the current density at a point, only produces a single curl**

*j***vector, not a**

*B***vector. In general, there can (and often is) a non-zero**

*B***-vector at points where**

*B**j =*0.

Before a cosmic current system devoid of external forces or fields reaches a stationary configuration, the ** j **and

**vectors interact — all**

*B***‘s generate**

*j**curl*vectors that add up to form the local

**B****vectors. At any point in the plasma where j ≠ 0 there can be a force between this current density vector and its local magnetic**

*B***-field vector. This force is a magnetic Lorentz force given by the second term in (11). This vector cross product of the velocity vector**

*B***of a moving charge and the local vector**

*v***implies that the scalar magnitude of the resulting Lorentz force is applied to each**

*B**q*through

is given, where *φ *is the smallest angle between the vectors ** v**, the velocity and

**, with amounts**

*B**v*and

*B*. We call φ the Lorentz angle. When this angle is zero or 180 degrees, the Lorentz magnetic force

**disappears at that point. The magnetic field strength (symbol**

*v × B***) is often used to describe the macroscopic force function that creates a magnetic field**

*H*The dimension of ** H** is A / m.

*N*is the number of turns.

The scalar quantity *B* in (16) results from the integral form (13). This expression shows that *B* is the result of the total current *I*. It follows that *H* is not a point-like variable. It can be shown that the energy density *W _{B}*(Joule / m³) stored in the magnetic field of such an ion current is given by

Using (16) in (17), the total energy *Ψ* (Joule) stored in the magnetic field of a cosmic current is given by:

*A _{C}* is the cross-sectional area and the inductance of the ion current is defined by the factor in brackets. This shows that the only way to reduce all of the stored energy to zero is to turn off the current completely (set

*I*= 0). In this case, the entire cosmic current structure would cease to exist.

However, we assume that the current in unrestricted plasma can move and distribute freely in cosmic space in order to minimize the potential energy stored internally due to the tensions created by magnetic Lorentz forces everywhere in the plasma. Indeed, space plasmas are uniquely positioned to obey the* principle of minimum total potential energy*^{10}, that is, a system or body must shift to a position and/or deform its shape that minimizes all of its potential (stored) energy (a formalization of the idea that “water always flows downhill”).

The energy described in (18) cannot be reduced because it is caused by the fixed quantity *I*. However, the Lorentz energies can be eliminated as they do not depend on the value of *I*, but only on the cross products between local ** B** and

**vectors. As soon as the process of throwing off the internal magnetic force-energy reaches a steady equilibrium, this structure is called a force-free current and is defined by the relationship between the magnetic field vector**

*j***and the current density vector**

*B***at every location where a charge**

*j**q*is present in the current flow:

From (19) follows that the Lorentz forces are zero everywhere in a force-free stream since every ** j** is collinear with its corresponding

**. This arrangement is therefore also referred to as field-aligned current (FAC). From (12) and (19) it follows directly, if there is no time-varying electric field, that (19) is equivalent to:**

*B*which is identical to . This is the fundamental defining property of a force-free, field-oriented flow, which is also known as weightlessness.

Expression (12) implies that if at any point in an otherwise field-aligned stream j = 0, then condition (20) is automatically satisfied even if ** B** is not zero. The value of the magnitude and direction of

**at a given point is generally insufficient information to determine the magnitude, direction, or even existence of**

*B***at that point. This was the problem Birkeland faced in his attempts to identify the currents that were responsible for the magnetic field fluctuations he measured. However, from (12) we know the direction and size of the -vector at a given point, which corresponds to the value of**

*j**μ·*there. Field-aligned, force-free currents represent the lowest level of stored magnetic energy attainable in a cosmic current

**j**^{11}). We are now looking for an expression for the magnetic field

**(r; θ; z) in such a current / field structure.**

*B*### Quantitative model of a force-free field-oriented current

Because (20) is satisfied when the current density j has the same direction (with the exception of the sign) as B (and with no requirements on its size), it has been suggested by Lundquist^{12}) and others to set

which according to (20) is equivalent to

where α is a scalar other than zero according to (21). This leads to a simple solution, but from the outset, it is important that for any non-zero value α a non-zero value *B* at any point requires the presence of a current density *j *≠ 0 at the same point, which is generally an unjustified guess. This is especially true in view of the known tendency of plasmas to form filaments (creating areas where *j* = 0, but *B* does not). However, let us consider this special case.

Now we can express the left side of equation (21) in cylindrical coordinates:

and the right side of (21):

In (23) and (24) all field components are functions of the position of vector ** p**. Since there is no reason to assume a variation in the current density

**in the θ or z direction in cosmic space, (22) implies that this also applies to**

*j***. From the absence of any externally applied forces except possibly a static axial electric field to maintain I (first term in (11)) and any time-varying electric fields, it follows that all partial derivatives of B with respect to θ and z are zero and therefore, after these simplifications in (23), the following three expressions remain from (21): In the radial direction is . There is no radial component of the B-vector. This agrees with Maxwell’s div B = 0. In the azimuthal direction, we get**

*B*and in the radial direction, we have

This leads to two non-trivial coupled differential equations in the two dependent variables ** B_{z}** and

**as shown in (25) and (26). The independent variable in both is the radial distance**

*B*_{θ }*r.*The combination of (25) and (26) gives a second-order differential equation in a single dependent variable.

The dependent variable *B _{z}*

*(r)*is the axial component of the force-free stationary magnetic field. The component field

*B*

_{z}*(r)*may extend as far as the current extends. No constraint is introduced for a non-zero value of r. In all real currents in space, there is a natural limit

*r = R*for the extent of the current density

**(r).**

*j*After the differential equation (27) has now been fully specified, it is identified as identical to Bessel’s equation with scalar parameters and we get the solution:

*J _{0} (x) *is the Bessel function of the first kind and zero-order, and

*Y*is the Bessel function of the second kind has the value one at the limit

_{0}(x)*x = 0,*and the function

*Y*has at the same Limit a singularity. Since reality dictates that the magnetic field remains finite, the value of the arbitrary coefficient

_{0}(x)*C*must be set equal to zero. Thus the solution to (27) is given by:

This Bessel function of the first type and the order zero is used to generate the Bessel functions of the first type and the orders 1, 2, 3, … by simple differentiation. The recursion formula for the first-order Bessel function is:

So we get from (25) and (29)

The Bessel function model of a force-free current explicitly includes only two canonical variables: the magnetic field B(r) and the electrical current density j(r). The model requires that these two vector quantities, as already stated above, are everywhere parallel (not interacting). Since we assume that the flow is of unlimited length and circular cross-section, the model does not take into account any variation of B or j in the θ or z-direction. From (13) it then follows for the current density:

and

The relationship between current density ** j **and flow velocity

**is general:**

*v*Now only the connection between mass density and charge density is missing, and we get the current density that Einstein wanted to remove from the Maxwell equations. To that, we can say that the charge density depends on the degree of ionization of the plasma. The degree of ionization can be deduced from the radiation intensity of a galaxy. The electromagnetic wave is the dissipative entropy given off by the open system that the Maxwell equations describe. So we can conclude that the rotation speed of a galaxy is proportional to the ratio of current density and mass density, which explains the waviness of the plateau of the speed distribution along the galaxy radii in Fig. 2, caused by the spiral arms.

**Summary**

Our starting point was Newton’s equation of gravitation. We asked what the cause of the force-free movement of the celestial bodies around each other is and found out that it is the electrical current flow of the plasma that is described by Maxwell’s equations and not as Einstein postulated, the curvature of an ideal closed hypersurface that the cosmos is believed to be. The laws of electrodynamics of moving bodies without Lorentz transformation are really sufficient to describe the cosmos. A mathematical transformation is just a change in viewpoint, never a change in physics. In other words: we can make a mathematical model of nature, but if we transform the model, it has no retroactive effect on nature. And then trying to draw conclusions from the model is doubtful, especially if mathematical and physical basic laws are not observed, such as the difference between space and surface (only surfaces can be curved, spaces never) and the conservation of mass and energy.

Finally, I would like to thank Prof. Andre Koch Torres Assis from the University of Campinas in Brazil for wresting Wilhelm Weber’s electrodynamics from oblivion by having translated Weber’s complete works into English and thus brought an important German contribution to the history of physics into the light of the world public.

NOTES

^{1} F. Zöllner An Wilhelm Weber S. LXXIX in Prinzipien einer elektrodynamischen Theorie der Materie Bd.I Verlag Wilhelm Engelmann Leipzig 1876

^{2} Wilhelm Weber- *Elektrodynamische Maassbestimmung insbesondere über den Zusammenhang des elektrischen Grundgesetzes mit dem Gravitationsgesetz *in Webers Werke Vol.IV *Galvanismus und Elektrodynamik* pp.479 Springer 1894

^{3} “*L’attraction universelle elle mê peut découler comme une déduction des principes qui règlent les forces électriques.*” aus F. Zöllner – *Erklärung der universellen Gravitation aus den statischen Wirkungen der Elektrizität und die allgemeine Bedeutung des Weberschen Gesetzes* Leipzig 1882 Commisionsverlag p. XXVI

^{4} The neutron consists of a proton and a nucleus electron, so in terms of charge only one proton charge for a proton-neutron pair acts outwards into the atomic shell. The residual charge realizes the core forces. Only the hydrogen atom has a larger charge available, which is expressed in the hydrogen bridge bond. Please refer E. Kaal – *The Structured Atom Model -SAM *https://etherealmatters.org/sites/default/files/document/2018-11/SAM_Presentation_2018-08%20Tesla%20Tech.pdf

^{5} W. Weber *Elektrodynamische Maassbestimmung insbesondere über den Zusammenhang des elektrodynamischen Grundgesetzes mit dem Gravitationsgesetz *in Webers Werke Vol. IV p. 481

^{6} F. Tisserand, *Sur le mouvement des planètes autour du Soleil d’après la loi électrodynamique *de Weber*. Compt. rend. 1872. Sept. 30.*

^{7} P. Gerber – *Die räumliche und zeitliche Ausbreitung der Gravitation.*in Stargard in Pommern, 1898. http://bourabai.narod.ru/articles/gerber/gerber.htm

^{8} P. Marmet *Einsteins Relativitätstheorie kontra klassische Mechanik* Vol. V *Berechnung der Drehung des Perihels von Merkur. * https://www.newtonphysics.on.ca/einstein/relativitaet05.pdf

^{9} Donald E. Scott – *Birkeland Currents: A Force-Free Field-Aligned Model *http://www.ptep-online.com/2015/PP-41-13.PDF

^{10} H. Callen – *Thermodynamics and an Introduction to Thermostatistics,* 2nd ed. John Wiley, New York, NY, 1985.

^{11} Anthony Peratt – *Physics of the Plasma Universe*. Springer-Verlag, New York, 1992, p. 44. Republished ISBN 978-1-4614-7818-8, 2015, p. 406.

^{12} S. Lundquist – *On the stability of magneto-hydrostatic fields.* Phys. Rev*.*, 1951, Vol. 83 (2), pp.307–311. Available online: http://link.aps.org/doi/10.1103/PhysRev.83.307.

Dr. Mathias Hüfner is a German translator volunteer for The Thunderbolts Project. He studied physics from 1964 until 1970 in Leipzig Germany, specializing in analytical measurement technology for radioactive isotopes. He then worked at Carl Zeiss Jena until 1978 on the development of laser microscope spectral analysis. There he was responsible for software development for the evaluation of the spectral data. Later he did his doctorate at the Friedrich Schiller University in the field of engineering and worked there 15 years as a scientific assistant. Some years after the change in East Germany, he worked as a freelance computer science teacher the last few years before his retirement.

Since 2015, Mathias has run a German website of The Thunderbolts Project http://mugglebibliothek.de/EU and has published a book entitled Modern Astrophysics Meets Engineering: The Reformation of Physics.

**The ideas expressed in Thunderblogs do not necessarily express the views of T-Bolts Group Inc. or The Thunderbolts Project.**