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Localizability and space in quantum physics. (English) Zbl 0653.53049
Lecture Notes in Physics, 308. Berlin etc.: Springer-Verlag. 81 p. DM 34.00 (1988).
The well-known technical question of nonlocalizability of massless particles in quantum theory has been augmented in this little monograph with historical and critical remarks and turned into a conclusion that the Minkowski space is inadequate for physics. Not only that, we have to give up in addition, the author claims, the complementary principle, the wave-particle duality and the quantization procedure. When problems regarding the foundations of physics (or any other science) are unsettled or unsatisfactory, as is certainly the case for the relativistic quantum theory, there is a tendency (or a fallacy) to take certain concepts as absolutely granted and to believe in it so strongly that everything else, held true by others or proved by tradition, has to be changed into one’s premises. Clearly there are difficulties in our understanding of the complete and consistent combination of relativity and quantum theory and the formulation of particle interactions. One would therefore agree with part of the author’s historical remarks, reviews and observations; they have been said before.
However, I think few will go along with his sweeping generalizations and conclusions. The core concept in this monograph is the “photon”. And what the author takes as granted is the existence of photons as particles, mathematically as the massless irreducible representations of the Poincaré group à la Wigner. He seems to contradict himself when he criticizes quantizations but holding on the quantized concept of photon, and when he says that he assumes the foundations of quantum theory as established and that he will not enter into the interpretation of quantum theory. He gives the Compton effect as the decisive step to believe in the concept of photon as particle. But already Schrödinger derived the Compton effect on the basis of wave theory. Also the author does not seem to be aware that a rather widely developed form of quantum electrodynamics exists which does not use the concept of photon as particle but treats it as a radiation from accelerated charges as in classical electrodynamics. The electromagnetic field need not be quantized. There are many other technical remarks in this book to be critically answered which we cannot do here for lack of space. It is unfortunate that this provocative book is full of errors, both grammatically and idiomatically. I should not have mentioned this if there were only few.
Reviewer: A.O.Barut

53B50 Applications of local differential geometry to the sciences
83A05 Special relativity
81P05 General and philosophical questions in quantum theory
81T20 Quantum field theory on curved space or space-time backgrounds
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81-03 History of quantum theory