# Mie, Gustav

# MIE, GUSTAV

(*b*. Rostock, Germany, 29 September 1868; *d*. Freiburg im Breisgau, German Federal Republic, 13 February 1957)

*physics*.

Mie, the son of a pastor, spent his childhood and went to high school in Rostock. He studied mathematics and the physical sciences at the University of Heidelberg, completing his doctorate in 1891 with a dissertation on a mathematical problem in partial differential equations. He then went to Dresden as a teacher of mathematics and physical sciences in a private school but did not stay there long. He accepted an assislantship in the Physics Institute of the Technische Hochschule in Karlsruhe. Mie’s interests had turned from mathematics to physics, and in Karlsruhe, where Heinrich Hertz had done his famous experiments on electrical oscillations, Mie reassembled Hertz’s apparatus and repeated the experiments. On completing his *Habilitation*, Mie became a *Privatdozent* at Karlsruhe in 1897.

Mie married in the spring of 1901. He was appointed extraordinary professor of experimental physics at the University of Greifswald in 1902 and was made an ordinary professor and director of its Physics Institute in 1905, He remained at Greifswald for fifteen years, a happy and scientifically productive period. From Greifswald, Mie moved to the University of Halle in 1917 as professor of experimental physics and stayed there until 1924, Mie then became the director of the Institute of Physics of the University of Freiburg im Breisgau, where he remained until his retirement in 1935.

In 1908 Mie published the rigorous electrodynamic calculation of light diffraction from spherical dielectric and conducting particles. This, together with the explanation of color effects, led to the discovery of the asymmetry in the intensity distribution and the precise determination of the optical constants of suspended particles, Called the Mie effect, it has had increasing importance in the determination of molecular clusters in solutions and the investigation of interstellar matter.

Before 1914, encouraged by Russian researches in the field, Mie solved the problem of the anomalous dispersion of water by using his quenched-spark oscillator as emitter and thermal elements connected with a spherically coated galvanometer as receiver. These experiments led to the determination of an invariant dielectric constant for water. They also brought understanding of the free rotation of polar groups in molecules and the frictional dispersion of dipole molecules in highly viscous solutions.

The other main direction of Mie’s experimental work was a series of X-ray analyses of the crystal structure of organic compounds, especially anthracene and naphthalene, which he began at Halle soon after the work of the Braggs. Mie continued these studies in collaboration with Staudinger at Freiburg, and the investigation of different polyoxymethylenes (as the model substances for cellulose) led to the verification of the molecular lattice.

Mie’s greatest personal involvement was in his effort to understand the fundamental and general principles of physical phenomena, and to state them suitably. At Greifswald, during 1912–1913, he made the first attempt to construct a complete theory of matter in the twentieth century. In an imaginative extension of Maxwell’s theory in the framework of special relaihity, the elementary particles known at that time (electrons and protons) appear in Mte’s work as offspring of a universal electromagnetic field. His goal was to overcome the traditional opposition between “field” and “matter,” thereby seeking to obtain a “unity of the physical world-view.” In particular, he wanted to explain “the existence of an indivisible electron and to relate the phenomenon of gravitation to the existence of matter.”

Three assumptions formed the basis of Mie’s theory:

1. Electric and magnetic fields exist both inside and outside the electrons.

2. The principle of special relativity is valid throughout.

3. “The hitherto known states of the ether, namely the electric field, the magnetic field, the electric charge, and the charge current are entirely sufficient to describe all phenomena in the material world.”

From these three assumptions, Mie was led to a generalization of the equations for the ether. This extension of the Maxwell-Lorentz theory was determined on the basis of the validity of the principle of conservation of energy and the existence of a localizable energy. Mie did not realize how many unnecessary assumptions were built into his derivation. His theory ran into serious difficulties, some of which stem from the fact that no one has succeeded in deriving solutions for static electrons in which the charge is “quantized.”

Mie was the first to recognize the necessity of “quantizing” the field variables of the electromagnetic field, long before Heisenberg and Pauli developed the first fundamentals of a rational quantum field theory. This insight aroused the admiration of David Hilbert, who was inspired by the “deep ideas and original concepts on which Mie had built his electrodynamics.” This theory, together with Einstein’s ideas on gravitation and relativity, led Hilbert to develop an axiomatic theory of the foundations of physics, from which he derived the field equations of gravitation (together with their auxiliary conditions as given by the Bianchi identities) and the equations of the electromagnetic field.

Although Mie did not discover the appropriate “world function” that could account for the existence, asymmetry, and stability of the proton and the electron, his investigations later inspired the work of Max Born and Leopold Infeld on “nonlinear electrodynamics,” which corresponded entirely with Mie’s program. Mie’s theory of matter would probably be regarded as his greatest contribution to physics.

The originality of Mie’s ideas lay in his treatment of electromagnetic phenomena. His *Textbook on Electricity and Magnetism*, with the subtitle *An Experimental Physics of World-Ether*, was constructed on the fundamental distinction between the “quantities of intensity” and “quantities of magnitude.” The “quantities of magnitude” are the length of a path or the duration of an event, the inertial mass of a body, and the electric charge. The “intensive” quantities are, for instance, “force” in mechanics, and the electric and magnetic field strengths *E* and *B* in the expression for Lorentz” ponderomotive force.

## BIBLIOGRAPHY

**I.** Original Works. Mie’s articles include “Grundlageneiner Theorie der Materie,” in *Annalen der Physik*, **37** (1912), 511–534; **39** (1912), 1–40; and **40** (1913), 1–66; and the autobiographical sketch “Aus meinem Leben,” in *Zeitwende*, **19** (1948), 733–743.

Among his books are *Textbook of Electricity and Magnetism* (1910; 2nd ed., 1941; 3rd ed., 1948); *Die Grundlage der Quantentheorie* (Freiburg im Breisgau, 1926); *Elektrodynamik*, **XI** , pt. 1 of the series Handbuch der Experiment talphysik, W. Wien and F. Harms, eds. (Leipzig, 1932); *Molecules, Atoms and Ether; Die Einsteitische Gravitationstheorie; Die Denkweise der Physik; Naturwissenschaft und Theologie; and Die Grundlagen der Mechanik* (1950).

**II.** Secondary Literature. Articles on Mie are H. Hönl, “Intensitäts-und Quantitätsgrössen,” in *Physi-kalische Blätter*, 24 (1968), 498–502, commemorating the centenary of Mte’s birth; and W. Kast, “Gustav Mie,” *ibid*., **13** (1957), 129–131.

Max Born’s review article on the Born-lnfeld nonlinear electrodynamics, in *Annales de l’ Institut Henri Poincaré*, **7** (1937), 155, gives an explicit discussion of the relation of this work to Mie’s. For Mie’s work on the field theory of matter see J. Mehra, “Einstein, Hilbert, and the Theory of Gravitation,” in *The Physicist’s Conception of Nature* (Dordrecht, 1973).

Jagdish Mehra

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