I.4. Fully erroneous ideas regarding Maxwell’s equations

   This section has to start from discussion on serious error related to so called “advanced” solution of Maxwell’s equations. This solution appeared in the textbook [L.4] by Ingarden and Jamiolkowski. This textbook is often quoted as a primary source reference; thus, it is unquestionably copied in other textbooks and on the Internet.
   In this textbook on Page 87 (issue from 1980), the following is written
(translated from Polish):
“It can be proven (see e.g. [13]) that in contained space Ω⊂Ε³, the following functions give the particular solution to the equation (13.45):
    u_ret(t,x)=...
    u_adv(t,x)=...”
A little further, the following explanation can be found
“The function u_ret(t,x) is so called retarded solution. On the other hand, the value of the solution u_adv(t,x) at the “t” time is not determined by the value of the function f() for times before present, but it is determined by values which this function takes in times after present. The function u_adv(t,x) is called advanced solution.
The referenced book [13] in source publications index on page 281 - [13] Marcinkowska,
Wstęp do teorii równań różniczkowych cząstkowych, PWN, Warszawa 1972 .
However, there is no information regarding advanced solutions in this referenced book.

    Prof. Andrzej Jamiolkowski who is the co-author of the textbook [L4] in response to the question where the advanced solution is derived in Marcinkowska’s book or as a matter of fact in any other textbook, gave an enigmatic answer that ‘such solution exists but it is not known”.
However, this solution cannot be found in the referenced textbook by prof. Marcinkowska or in any other accurate textbook since such solution does not exist!

   The other frequently made mistake relates to the presentation of so called integral form of Maxwell’s equations. It has to be emphasized that there is no mention of such form in any of Maxwell’s works. Integral form is not mentioned in works of Heaviside’s nor Gibbs’, neither in Feynman’s textbook. It cannot be mentioned since Stokes’ theorem regarding integral of the curl of a vector function over an enclosed surface is valid for a function determined by only coordinates of the shape. Thus, the vector function cannot be function of time. This limits the validity of integrals only to electrostatics and magnetostatics’ applications. Maxwell’s equations obviously cover electrostatics and magnetostatics, but so called “integral form” is not adequate to present these equations! Therefore, in discussion forums some attentive readers quite often inquire how to derive differential from integral form and this question remains without correct answer!

I.6. References

The references listed in here are not really needed for understanding problems described in this book, but these are items most often referenced in similar publications.
In this book, they were helpful in presenting erroneous solutions.
The Polish titles are not translated, so these items can be correctly identified.

    [L1] The Feynman Lectures on Physics
    [L2] Marcinkowska,„Wstęp do teorii równań różniczkowych cząstkowych ”,
             PWN, Warszawa 1972
    [L3] Krzyżański, „Równania różniczkowe cząstkowe rzędu drugiego”,
             Biblioteka Matematyczna, Tom 15, PWN, W-wa, 1951
    [L4] Ingarden, Jamiołkowski, „Elektrodynamika klasyczna”, PWN, W-wa, 1980