Representing Electrons: A Biographical Approach to Theoretical Entities by Theodore Arabatzis

introduction

Chapter 4 takes us from George Stoney’s 1891 depiction to H. A. Lorentz’s theory of electrons. The experimental discovery of the electron is usually credited to J. J. Thomson, but Arabatzis shows that Pieter Zeeman’s work (“the Zeeman effect”) deserves priority. Chapter 5 brings the biography of the electron into the quantum era, focusing on Niels Bohr’s famous three‐part paper of 1913. Chapter 6 continues the story with Arnold Sommerfeld’s efforts to generalize Bohr’s theory in his work on atomic structure and spectral lines. Before ending the story in 1925 (Ch. 7) with Sam Goudsmit and George Uhlenbeck’s “discovery” of electron spin, as a way of making sense of these rules, Arabatzis interposes an extremely interesting chapter on the differences between the physicists’ representation of the atom as a miniature solar system and the chemical atom of G. N. Lewis and Irving Langmuir, with its strangely stationary electrons.

During this period modern mathematical physics was coming into being, as physical scientists were directly investigating many things far smaller and larger than the intelligible, everyday world of classical physics that was more or less subject to direct observation. The classical view of physical reality was looking increasingly fictional. On the other hand, as Arabatzis recounts, new and improved methods of detection were coming into use (spectrographic analysis, compound microscopes, cathode rays, X‐rays, etc.). Dudley Shapere, whom Arabatzis cites in other connections, rejects the identification of observation with human perception and practically equates it with experimental detectability, pointing out that physicists today speak of observing the interior of the sun on the basis of solar neutrino detection (“The Concept of Observation in Science and Philosophy,” Philosophy of Science, 1982, 49:485–525).

notes

82p

Spectral lines wer attributed to the vibrations of ions, and thereby the features of the former were linked with the properties and behavior of the latter, in three ways, First, the frequenciies of spectral lines corresponded to the frequencies of vibration of the ions. Second, the polarization of spectral lines was linked with the direction and mode of vibrations of the ions. Third, the magnitude of the magnetic splitting of spectral lines was coordinated with their charge-to-mass ratio, assuming that the ions were subject to an elastic force, the Lorentz force, and Newton's second law of motion.

84p

To summarize here, Zeeman's experimental discovery occupies a prominent place in the early life of the electron qua theoretical entity for three reasons. First, it provided direct empirical support for Lorentz's postulation of the ion-electron. As Zeeman remarked, it "furnishes, as it occurs to me, direct experimental evidence for the existence of electrified ponderable particles (electrons) in a flame. ... Second, it led to an approximately correct value of a central property of the electron, namely, its charge-to-mass ratio. ... Third, Zeeman's results in conjunction with Lorentz's analysis of optical dispersion led to an estimate of the mass of the electron.

103p

The acceptance of Thomson's proposal was, however, gradual. Whereas his success in deflecting cathod rays by means of an electric field established that they wer charged particles, his suggestion that they were universal, subatomic constituents of matter was not accepted till, at least, 1899. In 1897 he had not shown that those entities were present in other phenomena besides the discharge of electricity through gases. Furthermore, he did not measure separately the charge and mass of the cirpuscle, and thus, the smallness of m was not sufficiently established. By 1899 these difficulties had been alleviated. In 1898 he devised a method for measuring the charge of ions in gases that had been ionized by x-rays. The results of his measurements agreed with those for the charge carried by electrolytic ions. In 1899 he published measurements of the charge-to-mass ratio of the particles produced in the photoelectric effect as well as by thermionic emission. That raio agreed with the corresponding ratio of cathod ray particles. Furthermore, he measured the charge of those particles by the new method that he had come up with, and he found that it coincided with the charge carried by hydrogen ions. This result along with the large charge-to-mass ratio implied the smallness of m. Finally, the reception of Thomson's proposal was facilitated by the theoretical and experimental developments that we examined in the previous sections - namely, the construction of Lorentz's and Larmor's theories and the discovery of the Zeeman effect.

109p

The elctron was not the product of a sudden discovery. Rather, its representation emerged from several problem situations in the study of chemical phenomen (such as electrolysis), in the context of electromagnetic theory, and in the study of the discharge of electricity in gases. By 1900 those diverse situations had fund a single solution in the representation of the electron as a subatomic, charged particle. Several historical actors provided the theoretical reasons and the experimental evidence that persuaded the physics community of the electron's reality. However, none of those people discovered it. The most that we can say is that one of those, say Thomson, contributed significantly to the acceptance of electrons as real entities.

114p

These constraints appeared in the form of "quantum numbers" which "characterize the state of the electron in question." By 1916 three of these quantum numbers had been introduced by Bohr and Arnold Sommerfeld. In 1920 another quantum number was added and was initially interpreted as a collective property of the atom. In 1924 Pauli ascribed a fourth quantum number to the valence electron itself. One year later that number was interpreted, without Pauli's approval, as a manifestation of the internal rotation of the electron, the so-called spin.

124p

Bohr's new account of radiation portrayed the production of spectral lines as the outcome of an electron's transitions between stationary states and uncoupled for the first time the spectral frequencies from the orbital frequencies of the electron. This mechanism is widely considered "perhaps the greatest and most original of Bohr's breaks with existing tradition.

153p

The term "quantum number" was introduced bySommerfeld in 1916. See Jammer, The Conceptual development of Quantum Mechanics, p.93.

158p

As late as 1923, Sommerfled remarked that "in its present state the quantum treatment of the Zeeman effect achieves just as much as Lorentz's theory, but no more. It can account for the normal triplet, including the conditions of polarisation, but hitherto it has not been able to explain the complicated Zeeman types." The subsequent development of the electron's representation was intertwined with the physicists' attempts to construct an adequate explanation of the "anomalous" phenomena. The taming of these phenomena became possible only with the proposal of the spin concept by Sameul Goudsmit and George Uhlenbeck in 1925;

160p

Sommerfeld's relativistic calculations were in agreement with Friedrich Paschen's very precise measurements of the spectral lines due to ionized helium. To bring about the agreement in question, Sommerfeld introdced the so-called selection rules, which arbitrarily limited the allowed quantum transitions. This agreement suggested that the various orbits corresponding to a given quantum sum n+n' had "real existence. Furthermore, it constitued a "spectroscopic confirmation of the theory of theory of relativity". In particular, Paschen's measurements confirmed Einstein's relativistic representation of the electron.

173p

That underlying reality had to be such as to accoun for all the relevant observable features of spectral lines (their frequency, intensity, polarization, magnetic and electric splitting, fine structure, etc.). In other words, every observable feature had to have its counterpart in the properties and behavior of electrons inside the atom. When a quantum representation of the electon was introduced, only the frequency of spectral lines cound be accounted for. Their intensity, polarization, and so on, were left unexplained.

219p

Questions of interpretation aside, this novel property of individual electrons turned out to be essential for the explanation of the anomalous Zeeman effect, a phenomenon that had challenged the ingenuity of physicists for more than twenty-five years. After a long and ardious process, a satisfactory coordination between the observable and the unobservable realms was finally achieved thorugh the attribution of four quantum numbers to each electron.

224p

The road to spin passed through another development, the unification of the classification of the electron's states in the hydrongen atom (in general, one-electron systems) with the corresponding classification in the alkalis (many-electron systems). In the former case, three quantum numbers \((n,k,m)\) were employed, whereas in the latter four wer needed (as indicated by Pauli's work). The distinction was grounded on the fact that the hydrogen atom exhibited a normal Zeeman effect, which had been explained by Sommerfeld in 1916, whereas the alkalis displayed anomalous Zeeman patterns for which Sommerfeld's analysis was inadequate.

229p

The construction of an adequate representation of the electron, free of contraditions, was not possible in a classical context. It was only made possible with the new quantum mechanics, which reformulated the notion of spin without reference to any classical visualizable model.

230p

"The ratio of the magnetic moment of the electon to its mechanical angular momentum must be for the intrinsic rotation twice as great as for the orbital motion." Moreover, the occurrence of doublet spectral terms would be the observable manifestation of the differenct directions that R could assume in relation to the orientation of the orbit.

235p

The result of Thomas's analysis was surprising: "It seemed unbelivable that a relativistic effect could give a factor of two instead of something of order v/c... Even the cognoscenti of the relativity theory (Einstein included!) were quite surprised. It was, however, crucial for the reception of spin. For instance, it neutralized Pauli, who was one of the most vigorous opponents of the new hypothesis. As he mentioned in his Nobel Lecture, it was Thomas's calculation that persuaded him of the validity of spin.

articles

• Heilbron, John L., and Thomas S. Kuhn. ‘The Genesis of the Bohr Atom’. Historical Studies in the Physical Sciences 1 (1 January 1969): vi – 290. doi:10.2307/27757291.