1 Introduction

Welcome to my homepage. I gradually write here about a modernized, significantly easier, but largely equivalent form of classical electrodynamics and their consequences for physics.

1.1 What is it about?

Weber-Maxwell electrodynamics is equivalent to Maxwell's electrodynamics (i.e. the standard theory of electrical engineering) in the non-relativistic regime. It is suitable for all electrical engineering tasks, covering a wide range of applications including electrical machines, radar and high-frequency technology. In addition, Weber-Maxwell electrodynamics opens up new approaches to quantum physics and other branches of modern physics, such as optics and atomic physics. Weber-Maxwell electrodynamics is particularly well suited for the computer simulation of complex technical tasks due to its simple and fast computability and, as it is based on point charges, for the simulation of plasmas. The latter is particularly important for fusion research. And last but not least, Weber-Maxwell electrodynamics is very well suited for teaching and education.

Compared to the standard representation of classical electrodynamics by means of Maxwell's equations, Weber-Maxwell electrodynamics is considerably more compact and easier to use, since the mathematical basis is not provided by a set of differential equations, but only consists of a kind of generalized Coulomb law, which also applies explicitly to arbitrarily accelerated point charges [1]. The animation 1.1.1 shows a simple example that would be very difficult to compute with conventional methods.

: Figure 1.1.1: The field of an initially resting point charge that is accelerated to 50 percent of the speed of light within 1.5 nanoseconds.

Figure 1.1.1 shows the field of a point charge that is initially at rest and then accelerates to 50 percent of the speed of light for a short period of time. At the beginning, the field corresponds to the Coulomb force. During the acceleration phase, however, an electromagnetic wave front is created and one can see how the field lines are bent in this range. After 1.5 nanoseconds, the acceleration phase is finished and the point charge continues to move uniformly at a very high speed. The generated field now appears to be flattened in the direction of motion, but the field lines are now again pointing directly towards the field-generating point charge.

The figure 1.1.1 illustrates the capabilities of the Weber-Maxwell formula, since it was not necessary to solve any differential equations to create the animation. All electrodynamic effects are ultimately represented by a single analytic formula. Since the Weber-Maxwell formula complies with the principle actio = reactio even in the presence of electromagnetic waves, the laws of conservation of momentum and conservation of energy are always directly fulfilled for particle systems of any size [2]. This makes obvious that classical electrodynamics is a branch of Newtonian mechanics.

1.2 Origins of Weber-Maxwell electrodynamics

Around 2012, I had the idea that perhaps the electromagnetic force only seems to propagate at the speed of light for all receivers because, for some reason, receivers are unable to perceive that part of the field that is faster than the speed of light. Whether something is faster or slower than the speed of light depends, of course, on the relative speed of the receiver to the transmitter. If the receiver is moving towards the transmitter, a different part of the field is too fast than if it is moving away from the transmitter or is moving sideways. The consequence of this is that each receiver, regardless of its relative speed to the transmitter, gets the perception that the field does not propagate faster than the speed of light.

Those who have studied the basics of special relativity will probably recognize that this idea complies with Einstein's two postulates. This is interesting because, unlike special relativity, this hypothesis does not require a Lorentz transformation. This means that it is not compatible with the special theory of relativity although it provides the same predictions for almost all test experiments of special relativity that have been performed in the past.

Since the special theory of relativity was developed in 1905 and has had a huge impact on scientific developments in physics and electrical engineering, it was hardly possible to build on existing foundations. At least that seemed to be the case initially, as it later turned out coincidentally that the idea was compatible with a much older theory of electrodynamics known as Weber electrodynamics. Weber electrodynamics was developed around 1850 and is based on the work of Carl Friedrich Gauss and Wilhelm Weber. Carl Friedrich Gauss is very well known still today. Unfortunately, this does not apply to Wilhelm Weber, although one of the SI units was named after him and his extensive scientific work is outstanding and was far ahead of its time [3] [4] [5] [6].

From a modern perspective, Weber electrodynamics seems quite archaic. It actually only consists of a single formula that can be used to calculate the force that a stationary or uniformly moving point charge exerts on another stationary or uniformly moving point charge. Interestingly, the formula does not require the definition of a magnetic field. Regardless of this, it can nevertheless be used to calculate the magnetic forces between two arbitrarily shaped wires with a direct current or a low-frequency alternating current. In addition, the Weber force fulfills Newton's third law, i.e. the principle actio = reactio applies. This means that in an isolated system made up of any number of point charges, the total energy and the total momentum always remains conserved. This is not so obvious for standard electrodynamics based on Maxwell's equations, which repeatedly leads to discussions.

However, Weber electrodynamics has also clear disadvantages, because it is not possible to represent electromagnetic waves in a vacuum with the Weber force. This was also the reason why Weber electrodynamics increasingly fell into oblivion after about 1870, because around 1890 electromagnetic free-space waves were what ChatGPT is nowadays, namely a hype that rendered everything else seemingly irrelevant. The fact that Weber electrodynamics works better for electrostatics and magnetostatics than the conglomerate of Maxwell's equations and the Lorentz force was therefore no longer of interest.

The fact that my idea, which separates Einstein's postulates from the Lorentz transformation, leads to the Weber force for uniformly moving point charges and thus also explains magnetism, encouraged me to continue my work and to perform systematic experiments. It also helped me to find some shortcuts, as there is a small scientific community working on Weber electrodynamics (e.g. [7] [8] [9] [10] [11] [12] [13] [14] [15]). The last few years have therefore been very productive.

The current state of development is already well advanced. An important result of the research is Weber-Maxwell electrodynamics, which is equivalent to non-relativistic Maxwell electrodynamics, but is clearly superior in terms of simplicity, clarity and usability. The practical application of Weber-Maxwell electrodynamics to solve a wide variety of problems is demonstrated by the EM solver OpenWME.

However, there is still a lot to do, as Weber-Maxwell electrodynamics is very new and thus offers a lot of potential for optimization and the discovery of new technologies. I hope that some young scientists or PhD students will become interested in this new and exciting research area.