Equivalent Transformations of Maxwell's Equations

In many cases, the problems solved in electrodynamics boil down to separation of variables and running on the supercomputer “fitted” finite differences, but, I am afraid that the “rigidity” of Maxwell's equations simply “ rips off ” the accuracy of the calculations so much that they cannot even be used for estimation. The following are elementary transformations of Maxwell's equations and, as a result, a scheme simplifying calculations / field description, but unfortunately, not volume.

(The topic is purely technical, it relates only to the processing of electrodynamics calculations, there are many formulas.)

Next, only CGS units are used , for translation into SI you can take the Material from Wikipedia “Maxwell's equations”

Filling this article, I came across the first unexpectedness (for seed ...) of the microscopic system of equations to

be reduced to the “continuity equation”

“The first part of the Myrlyzon ballet”

“The second part of the Myrlyzon ballet” The MÚNERA - GUZMÁN - Ansatz

[en] André Waser On the Notation of MAXWELL's Field Equations

“The Third Part of Myrlyzon Ballet”

Here the defect is almost invisible , but ... Find?

In a system with a Lorentz gauge or such, they all come from the gradient, and for j = q v there is not even a chance to build a consistent system (well, who will build the speed from a curl?). Hi QED!

“Before Apotheosis”


Lorentz Force:
Poynting Vector:
For the sake of expressing power functions through a single field, all this was conceived. Electrodynamics - TFKP in its purest form, see the 1958 textbook “Lavrentiev M.A., Shabat B.V. Methods of the theory of functions of a complex variable ”chapter III chapter“ Flat field and complex potential ”, the question is where to make the waist the logarithm.

Let's start with a simple question: “where does this field exist?”
- the Newtonian field is built on a “light cone” passing through the sensor (to construct a “current” it is necessary to coordinate several, ideally, surfaces (the sensor is in focus of the parabola?), Which is the most difficult operation), there is no time, photons and "short range" on it.
- Fields (not fields) on the light cone do not intersect, elementary particles retain the sum of charges, from the beginning of time to the end (yes you need to know what happened and what will happen, but bad infinity). The motion of the waves can be approximated by Newton polynomials.
Elementary particles?
- The logarithmic feature of the corresponding logarithm of a field approximated by a polynomial, if a proton is considered moving into the future, then all positive particles go there, negative ones go back, and neutral particles interfere with partons. [en] thanks to Luckmore for linking to
- Consisting of works (RR k ), R k - the coordinate of the particle relative to the sensor, on the cone. Then we crush space into space-time: (t - (RRk ) / c) + - (t + (RR k ) / c) i - for the positive, and (t + (RR k ) / c) + - (t - (RR k ) / c) i - for the negative. Feynman, once, mentioned that the electrons are similar to each other because they are essentially the same electron. How, and thanks to Feynman for returning the backward wave to electrodynamics.

a small quote from here
from review
... Maxwell's theory, as said, transfers the center of attention from the charges and potentials of conductors to the space between them. What value does the charge retain? ... For a number of Maxwell's followers, a charge often ceases to exist, as a physical fact, turning into a mathematical symbol, a measure of the flow that permeates the surface surrounding the charge. In particular, Poiting goes far along this path. According to his views, the surface of the conductor in general is such a surface beyond which the electromagnetic field ends. No movement of electricity during electric current occurs; the only significant phenomenon with current is that the magnetic energy present in the “current” field flows into the conductor in the direction normal to its surface, and when it enters the conductor, turns into a new look - into the well-known Joule heat ... The constant repetition of the same "portions" of electricity in simple multiple relations should have prompted the idea of ​​the atomic structure of electricity. But no - for decades this fact has been interpreted as the property of matter being charged with a certain amount of electricity, and not the property of electricity itself to appear in these constant quantities ...

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