My answer:But it should be kept in mind that a key point of quantum mechanics is not just a probabilistic interpretation, but the loss of an underlying objective reality

'Loss of reality' is a mental disease. Pascual Jordan deduced from it racism and the superiority of the Fuhrer. His comrade Heisenberg travelled as Hitler's envoyThe referee does not relish my point of view:

He preferred to comment anonymously. This is bad though there are referees much worse than this one. Most had turned down even my formal achievements. You can still read what the referee criticized, viz. in the preprint. The final version is published in Z.Naturforsch.If this result could indeed be deduced from deterministic chaos, it would not only be spectacular, but shake the very foundations of our current understanding of nature.

*Report on Ms A 9222, “Diffraction of Electromagnetic Waves”, by U. Brosa
*

*
In this manuscript the author develops a quite original and interesting approach to diffraction,
based on a reduction of Maxwell’s equations to decoupled amplitude equations. The required
restriction to “supporting vector fields” of the form (5) may be somewhat inconvenient
when dealing with boundaries of arbitrary shape, but is fully sufficient for a flat screen with
apertures, as considered here. Because the boundary conditions to be imposed on the
two relevant amplitudes become particularly simple for the case of a metal with infinite
conductivity (eqs. (34) and (35)), one is led directly to the transparent representation (56),
(57). The evaluation of the integral by means of the stationary phase approximation, in a
form dubbed “principle of utter exhaust” by the author, is quite ingenious, finally leading
to the elegant formula (104). I do not oversee the mathematical literature on asymptotic
expansions - there exists much more than what has been cited by the author - sufficiently
well to judge to what extent this principle is new, but in any case the calculations appear to
be correct. Applications then are given to diffraction by a straight edge, by a slit, and by a
circular aperture. In my opinion, the discussion of the improved solutions (120), (121) given
in chapter 11 is particularly striking, as far as physics are concerned. I have not followed the
details of the connection to Sommerfeld’s solution, but already the very procedure by which
the present solutions are obtained appears remarkable, and justifies publication of the main
part of the manuscript, even considering its length.*

Because of the "whimsical" paragraphs, see below, I was prepared that any referee would attempt to find errors in my article where there are no errors at all, and to deny its novelties by equating formulas which are not comparable at all. Thank you, Referee, for not doing this.

*Regarding that main part, I only have the following minor remarks. When extracting the
inhomogeneity _e(r) from Maxwell’s equations by means of an ansatz E(r, t) = E0(r) +
E1(r, t), such that E0(r) = -rc(r), one obtains a contribution _E0(r) from the static field
to the current in eq. (8). I assume that this piece has been incorporated into je(r, t) right
from the beginning, but if so this should be pointed out explicitly.*

A very substantial critique. For years I had the idea that static charges remain static by their very name even in conducting materials. The truth, however, is that there is either static charge or conductivity. The dilemma is now correctly solved, see pages 10 through 12.

*In the paragraph following
eq. (29) it might be more useful to refer to eq. (26), instead of eq. (21). There appears to
be a sign error in the second of the eqs. (33), and three lines below this equation the second
expression @x@za should be replaced by @y@za.*

Corrected. Thank you. Solitary authors grow blind when they sit over their writings for months. I spent maybe fifty hours to eliminate mistakes in the second half of the article.

*I will not dwell on certain phrasings which might be hidden jokes (such as the statement that
primary waves “travel through outer space”, see first line on p. 3), or reflect the author’s
personal style (for instance, when referring to himself as “your author”, who “does not want
to burden the honorable readers with trivial items”, see paragraph following eq. (104)). But
I strongly do object to the initial part of the introduction, and to parts of the conclusion,
regarding both style and claims made. I feel that the potential impact of the present work
could be much heavier if these parts were left out entirely, or strongly modified, and I would
like to expand on that, even though this hardly concerns the author’s main achievements,
and the following remarks may carry my own personal bias.
In times where efficient communication in science is increasingly impeded by the sheer
amount of items that are being communicated, it is mandatory that authors who wish to be
percieved focus their message to the essentials. If our author were serious about not bothering
his readers with trivialities, he would have left out the first two paragraphs altogether,*

They are left out now.

*as they carry hardly any information. Every author was brought on to the track of her or his
works by some previous preprints, lectures, etc., but is there any need to tell all this to her or
his readers? Is ref. [1] in any way essential for the present manuscript? Does it matter what
the author thinks of refs. [2,3]? Without loss of serious information, the paper might start
with the sober statement that the systematic solution of partial differential equations for
vector fields is demanding, avoiding the “Nobody”-phrase.*

I buyed it.

*The following historical overview
may be regarded as partly witty, partly whimsical, but definitely puts high demands on the
patience of the readership. While one may still tolerate the reference to the “world-reputed
symbol of parapsychology”, the translation of “Verr¨uckung eines Aethertheilchens” as
“insanity of an etheral piece” seems pointless, as this joke can be digested by
German-speaking readers only.*

It is gone.

*And the author doubtlessly is aware of the fact that
nowadays hardly any physicist attempts to solve Maxwell’s equations be extracting one
Helmholtz equation for every component of E and B - customary solution techniques
proceed along other routes. *

You're wrong. See E.Hecht, Optics, Chapter 3. According to its publishing house, this is the worldwide most often used textbook on optics. One Helmholtz equation for every component of E and B is the standard argument to justify Kirchhoff's scalar theory in electrodynamics.

The corresponding paragraph in my article is important to direct reader's attention to a decoupling of Maxwell's equations that does not depend on coordinates. The general theorem of representation holds, for example, in elliptical coordinates, toroidal coordinates and so forth.

*My recommendation to bring the introduction into a
matter-of-fact form is not meant to frustrate the wits of the author, but to comply
with the standards of scientific communication: I am certain that many readers would
simply put away the present manuscript after just a few lines - which would be a pity,
given the excellent content later on.
*

*
Moreover, in my opinion the limits of credibility are overstretched in the outlook.*

Large parts of the outlook are cancelled.

*“All monographs and textbooks pretending to teach the solution of Maxwell’s equations should
be committed to paper recycling”, ... “the general representation theorem in section 2 beats
them all”. Really? *

Really! There is no boundary-value problem solved in Jackson's textbook that can't be solved using my theorem of representation. The theorem solves many more which are too difficult for Jackson.

*I wonder whether the author has attempted to apply this representation
to problems of actual current interest in optics, such as the propagation of light through
subwavelength apertures in realistic metal sheets (of finite thickness and finite conductivity),
the excitation of plasmon-polaritons at randomly disordered surfaces, or at metallic
subwavelength gratings.*

These suggestions are welcome. The theorem should work well on subwavelength gratings, for example. Why don't you send me references to let me know precisely what you're interested in?

*The author’s lemma of the triple curl relies to a large extent on
the fact that the second derivatives of the field (5) vanish, but the ensuing restriction to
such fields seems to render applications to nontrivial geometries rather clumsy.*

Not at all clumsy. It is the best you can have if you want to disentangle linear
vector-field equations in isotropic and homogeneous materials. Strangely enough,
it is often forgotten that Maxwell's equations are linear. So one can build solutions

supporting field_1 * representative_1 +

supporting field_2 * representative_2 + ...

This allows great flexibility. Even integrals are feasible.

*The case
considered by the author is exceptionally simple, both because the geometry of the plane
screen matches the form (5), and because the limiting case of infinite _ leads to unusually
convenient boundary conditions. But as long as the present approach has not proven its
value in other, more generic cases, the readers might be well advised not to recycle, e.g.,
their copy of ref. [18]. There are several more claims which I find hard to sustain: “For the
first time, stationary phase is applied where it is really needed”. Indeed? - *

Indeed! You can forget about one-dimensional stationary phase since for one-dimensional integrals the paths can be easily rerouted to obtain saddle-point or Laplace integrals. However, the passage is gone.

*“Hundreds of physicists will find promising foundations for their future work”.
Well, one may count the true number in a couple of years.*

It happened already once. Our work on nuclear fission induced dozens of PhD theses and hundreds of articles, conference contributions and so on. Physics Reports 197, Issue 4, December 1990, Pages 167-262 However, the passage is gone.

*In any case, I do not think
that this is the kind of outlook that should be communicated here.*

It is gone.

*Finally I would like to add some remarks concerning the various allusions to quantum physics.
According to the author, Maxwell’s equations are “foundations of optics and quantum
electrodynamics” (p. 2, top). I am willing to buy optics, and I would buy classical electrodynamics,
but there is more to quantum electrodynamics than Maxwell’s equations. In the final
chapter, Kirchhoff is enthroned as “the true inventor of the probabilistic interpretation”, who
was more or less copied by Born. But it should be kept in mind that a key point of quantum
mechanics is not just a probabilistic interpretation, but the loss of an underlying objective
reality,*

'Loss of reality' is a mental disease. Pascual Jordan deduced from it racism and the superiority of the Fuhrer. His comrade Heisenberg travelled as Hitler's envoy to tell scientist abroad they should surrender because he, the Genius Heisenberg, was developing the nuclear bomb for Nazi Germany. Fortunately the Genius was too stupid to solve the diffusion equation. Next their so-called scientific work: There are about ten or twenty papers on the theme 'Known recursion relations of the confluent hypergeometric function rewritten' and maybe five on the theme 'Quaternions multiplied by i '. These comrades were opportunists and obscurants because they had to hide their low qualification. Their story is worse than Emperor's New Clothes, but must be ended since it hampers research.

*which was certainly not anticipated by Kirchhoff. *

Kirchhoff was brought up in Konigsberg, I.Kant's town, and in Berlin, G.W.F.Hegel's town. Both philosophers agreed that ideas rank higher than material beings, especially the idea of the state - the Prussian state. Kirchhoff had ingested that and thus suffered from loss of reality. You can see this in his papers. The quantum mechanics of the 'loss of reality' was not revolutionary. It was just an extremization of ideas ignited in the 19th century, similar to National Socialism.

*Moreover, the author claims to have
shown that electrodynamics does not need a probabilistic interpretation (p. 42, bottom).
Fine - but has there ever been any indication that it might need one? *

Yes. See e.g. E.Hecht, Optics, Chap.1, (Fig 1.8 in my copy). Experiments of the Tonomura type, see below, are fashionable with photons since long. The pictures were shown on conferences, but I found it hard to find a citable reference.

*Likewise, it is absolutely
correct that there is “no compatible probability formalism for the Dirac equation”,
and the reasons underlying this fact are quite well understood, but this causes no problem
at all if the Dirac equation is properly regarded as a quantum field equation, rather than as
a wave equation. Hence, is there any point in mentioning this issue? Finally, the suggestion
that “Heisenberg’s mysticism regarding quantum ‘particles’ and ‘uncertainty’ will be gone
soon” does not appear to be borne out by the content of the present paper. “Uncertainty”
implies more than merely the infamous uncertainty relation; it also covers experimentally
established facts such as entanglement, Bell’s inequality, or quantum teleportation. *

That don't impressah me much. Presently, I've got urgent duties. You must exercise a little patience.

*It is hard
to see how these should be explained on the basis of deterministic chaos, as suggested by the
author. Ref. [36], which is quoted at the end as an example for random behavior, actually
demonstrates the gradual buildup of an interference pattern from single incoming electrons,
as required by basic quantum mechanics. (I would like to point out that this important
paper has a fifth author, H. Ezawa, who should not be left out.)*

Thank you, I had overseen [wrong, correct: missed] the name. But the reference it gone with the major part of the outlook.

*If this result could indeed
be deduced from deterministic chaos, it would not only be spectacular, but shake the very
foundations of our current understanding of nature. I may be just a stupid referee, and thus I
would not bet on this option. Instead, I suggest to omit these so far unfounded speculations;
they tend to overshadow the fine work reported in earlier chapters.
*

*
In summary: As far as the mathematical treatment of diffraction is concerned, this is a
most interesting and stimulating manuscript. Even if it should not be feasible to extend
the approach advocated by the author to situations under consideration in topical research,
and the results reported in secs. 9 to 12 should remain singular achievements, they clearly
possess their own intrinsic value and deserve to be published. On the other hand, the present
version of the manuscript runs the risk of losing a major fraction of its potential impact
because of undue allegations, exaggerations, and speculations. I therefore recommend that
the manuscript be published in Zeitschrift f¨ur Naturforschung only if the author revises (at
least) both the introduction and the outlook, along the lines suggested above.*

Done. Parts of the introduction and the conclusion, the "whimsical" paragraphs, were written as a very mild satire on very sad facts, see above. I wrote it as a gift to Z.Naturforsch. to attract more readers to it, but there is no use to press a gift upon somebody who does not want it.

U.Brosa

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