Myron Evans elementary errors
One of the most trivial Evans’ errors is his statement that the group O(2) is isomorphic to U(1). In his recent complains (dated August 10, 2006) to the Editors of Physica Scripta Evans writes:
"I still await the elementary politeness of a reply from you concerning the Bruhn papers. In the meantime these are some rebuttal papers and proofs. They rebut Bruhn’s comments using standard Cartan geometry. I am able to rebut eveyrthing he has ever written in all detail, and have already done so. He is not using correct mathematics or standard Cartan geometry. Some of his errors are so trivial as to raise concern about what he is really doing."
Evans includes his rebuttals, one of them concerns the issue of O(3) being isomorphic to U(1). Let us examine this issue in details, not because it is important (it is rather trivial and not essential), but because it throws some light on Evans (miss)understanding of mathematics.
Evans quotes Ryder’s monograph "Quantum Field Theory" as an authority, and he copies from Ryder the erroneous statement that the two groups are isomorphic. Of course Ryder is wrong. And Evans repeats Ryder’s error. First of all Ryder defines, though not very precisely, the group O(n) as the group of orthogonal matrices n x n, that is matrices satisfying RTR=I. From this it follows that det(R)2 = 1, and so det(R) = 1 or det(R) = -1. Rider is not using at all the symbol SO(n), that normally is being used for the connected group of orthogonal matrices of detereminant one. So, when he writes that every element of O(2) is uniquely determined by a rotation angle - he is wrong. The matrix
(1 0)
(0 -1)
is orthogonal, and yet it is not a rotation matrix. It belongs to O(2), but it does not belong to SO(2). The group U(1) is isomorphic to SO(2), but not to O(2). Evidently Evans does not understand these mathematical "subtleties", so instead of fixing Ryder’s error, he proudly repeats it and call his error a "rebuttal". It should be noted that Ryder’s monograph is not a textbook on group theory, and Ryder is not a mathematician. Ryder’s book is on QFT, and it is assumed that the readers will be smart enough to fix the small mathemathical inacurracies by themselves. In fact, it is a good exercise in critical reading!
Evans ends his letter to the Editors of Physica Scripta with:
"Questions must now be asked about the editorship of Physica Scripta itself, and its refereeing procedures. Concern about this has already been voiced in the US Supreme Court, which ruled that academic refereeing procedures are biased."
And he is partly, but only partly right. The trivial errors in Ryder’s book should have been corrected, and they were not. Yet there are different procedures for publishing monographs, and for publishing research papers in scientific journals. While it is rather usual to find errors in voluminuous monographs, it is not permissible to publish trivial errors in scientific journals that follow the peer review procedures.
We may ask: why is Evans not correcting his trivial errors? Why is he so stubbornly repeating them? Some light on this subject can be found in an opinion of one of Myron’s close ex-collaborators (L. B. C.) who wrote:
"Myron […] became increasingly hostile to any criticism of anything that he thinks is real. In effect what he thinks is serious theoretical physics has become more a matter of his own delusions. He became very hostile to anybody who deigns to point out problems with anything he claims, and his reactions are very similar to what is seen with people afflicted with delusional mental states."
