Bibliography

W. Heisenberg. Die physikalischen Prinzipien der Quantentheorie. VIII + 117. Verlag S. Hirzel. Leipzig. 1930. RM. 8.

W. Heisenberg. Physical Principles of Quantum Theory.

In the thirty years of its existence the theory of quanta has undergone a complex evolution. Beginning with the assertion of the discontinuity of the emission and absorption of light and of the universality of the constant \(h\), the theory for some time oscillated between moderate and extreme forms of the initial principles (discontinuous emission and continuous absorption of light; the theory of light quanta). The center of gravity of quantum phenomena was transferred now to matter, now to light, and only in Bohr’s postulates was the quantum nature of both explicitly affirmed. However, the imperfection of Bohr’s theory, with its three separate postulates—of which the last (the correspondence principle) had a qualitative character—was evident from the very beginning. In the phenomenological theories of Heisenberg and Dirac, and in the wave mechanics of de Broglie–Schrödinger, the doctrine of quanta at last acquired sufficiently harmonious, consistent forms, though possessing an abstract mathematical character. The fundamental physical and epistemological core of the theory has apparently been found only in the uncertainty principle established by Heisenberg and Bohr. In parallel with the theory of relativity, the doctrine of quanta in the interpretation of Heisenberg and Bohr may be called the theory of uncertainty.

The small book by Heisenberg under consideration is written from beginning to end from the indicated point of view; herein lies its essential difference from the numerous other books on quantum mechanics that have appeared recently. The book arose from lectures delivered by Heisenberg in Chicago in the spring of 1929 and, according to the author, “contains in general nothing new that could not be found in published articles and especially in Bohr’s well-known investigations.” This modest estimate clearly does not correspond to reality. Before us is the first attempt at a systematic exposition of the principles of quantum theory on the basis of the uncertainty relation:

\[ \Delta p \cdot \Delta q \geq h, \]

embracing both the phenomenological theories and the theory of de Broglie–Schrödinger, and above all relying on experiment. In the text, separate, extremely important,

remarks of a physical, mathematical, and theoretical-cognitive nature, giving the book a completely independent, original imprint.

The exposition is structured as follows: in the introductory part, the experimental facts of atomic physics that constitute the experimental basis of quantum theory are compared: Wilson photographs, diffraction of corpuscular rays and electromagnetic radiation, Compton’s experiment, and the experiments of Franck and Hertz. The following section contains a critique of the physical concepts of the particle; from the collateral data on various examples considered in detail, the uncertainty relation is proved. In the third section a critique of the physical image of the wave is given on the basis of the same uncertainty relation, and it is proved that the wave representation, just like the image of the particle, is suitable only within certain limits.

The fourth section is devoted to the principles of the statistical interpretation of quantum theory in connection with the question of causality and Bohr’s concept of the “complementarity of the space-time description and causality.” According to Bohr-Heisenberg, the division of the world into the observing part and the observed parts (subject and object), generally speaking, obstructs a clear formulation of the law of causality.

In the last section of the main part of the book, on the basis of the principles set forth, the most important experimental data are considered: Wilson photographs, diffraction and interference experiments, phenomena of emission, absorption, and dispersion, the Compton effect, and black radiation. Questions of a more mathematical character are placed in a special supplement to the book: “The Mathematical Apparatus of Quantum Theory,” and on the last pages a proof is given of the mathematical equivalence of quantum theory on the basis of the representations of particles and of waves.

Heisenberg’s book achieves its stated aim, “to promote the spread of the Copenhagen spirit of quantum theory,” but at the present stage, from the physical side, the theory is not yet complete. The uncertainty principle agrees with all facts and with the mathematical formalism, but from it directly, so far as we understand, it is still impossible to derive all the fundamental propositions of the theory. For the derivation of the mathematical scheme, alongside empirical facts one has to make use of the correspondence principle. It has been proved that the uncertainty principle follows from quantum theory, but the converse remains to be done. The necessity of further development of the principles of quantum theory is indicated by the fact that, to this day, in large measure it bears a nonrelativistic character. In Heisenberg’s words, “to the changes of our customary space-time world required by the theory of relativity and characterized by the constant \(h\), and to the quantum uncertainty relations, whose symbol may be the Planck constant \(h\), there must be added still other restrictions, con-

connected with the universal constants \(e\), \(m\), and \(M\) (the mass of the proton). What the character of these limitations will be is, for the moment, difficult to say.”

The exposition of the book is very compressed and highly uneven. Some passages require a thorough acquaintance with the present state of the theory in its various modifications.

C. Vavilov.