# Heisenberg, Werner (1901–1976)

# HEISENBERG, WERNER

*(1901–1976)*

The German physicist Werner Heisenberg was born in Würzburg; he studied physics in Munich under Arnold Sommerfeld and received his doctorate from Munich in 1923. Heisenberg became a lecturer and assistant to Max Born at Göttingen in 1924. He continued his studies at the University of Copenhagen, where he collaborated with H. A. Kramers. He succeeded Kramers in 1926 as lecturer in physics there. Heisenberg was professor of physics at Leipzig from 1927 to 1941 and professor at Berlin and director of the Kaiser Wilhelm Institute for Physics from 1941 to 1945. He was named honorary professor and director of the Max Planck Institute for Physics at Göttingen in 1946 and served as honorary professor and administrative director of the Max Planck Institute for Physics and Astrophysics in Munich from 1958 to 1970. He was awarded the Nobel Prize for physics in 1932.

Heisenberg's contributions to physics are contained in more than 120 papers covering a great variety of topics. We shall here deal with two topics only, with the invention of matrix mechanics and with Heisenberg's more recent theory of elementary particles.

## Matrix Mechanics

The older quantum theory of Niels Bohr and Sommerfeld had tried to combine classical physics with the new quantum laws and to use the predictive power of both. The resulting theory was a mixture of classical notions—some useful, others apparently redundant—of new ideas and of ad hoc adaptations. Thus, for example, transition probabilities and selection rules were calculated, or guessed at, by examining the Fourier coefficients of the motions

of the independently vibrating parts of the atom, while the motion Φ* _{i}* itself had to be denied any physical significance. In addition, the theory had failed in important respects. It clearly was but an intermediate step on the way to a satisfactory mechanics of the atom. The final theory is essentially due to the efforts and the very different philosophies of two men, Heisenberg and Erwin Schrödinger.

According to Heisenberg we must abandon all attempts to give a detailed description of the unobservable internal motions of the atom. Such motions are but the result of the continued use of classical ideas in a domain that is inaccessible to direct experimental examination. Considering that these ideas may be in need of revision it would seem to be wise to construct a theory that is expressed solely in terms of such "outer" magnitudes as frequencies and intensities of spectral lines. Speaking formally this means that we want to predict by using the X* _{i}* directly and without appeal to the Φ

*. Now Bohr's investigations had already gone a long way toward determining the required properties of the X. His idea of a rational generalization corresponds exactly to what Heisenberg had in mind. Heisenberg himself provided additional rules of calculation that were sufficient for solving some simple problems, such as the problem of the harmonic oscillator. It was not known to him at the time that the rules were those of an algebra of noncommuting matrices; this was soon recognized by Born, who, together with Pascual Jordan and Heisenberg, completed the formalism a few months after Heisenberg's first paper had appeared.*

_{i}A new atomic mechanics was at last in sight. Its meaning, however, was far from clear. Macroscopic objects whose positions and momenta could be ascertained with a higher degree of precision were represented by infinite arrays of complex numbers, none of them corresponding in a simple way to visible properties. "Can you imagine," objected H. A. Lorentz at this stage, "me to be nothing but a matrix?" It was again Heisenberg who, after the theory had been completed in a somewhat unexpected fashion by Schrödinger, made an essential contribution here by showing, in his uncertainty relations, to what extent classical notions could still be used in the interpretation of microphysical theories.

Heisenberg was to use the principle to rebuild a theory by working "from the outside in" once more in 1943, in order to eliminate certain difficulties in the quantum theory of fields. Believing these difficulties to be due to the disappearance of the ordinary space-time relations below 10^{−13} centimeters, he tried to replace field theory by a formalism that for any interaction transforms asymptotic anterior states into asymptotic posterior states without dealing with the details of the interaction. This so-called S-matrix theory was taken up by Geoffrey Chew and others for the calculation of the properties of strongly interacting particles. This led to what some physicists regarded as the beginning of a "third revolution" of twentieth-century physics, to the idea that particles are composites and that the properties of all of them can be obtained in a step by step procedure, starting with the interaction of any small subset ("bootstrap hypothesis"). Spatiotemporal relations are alien to this scheme, which therefore cannot develop a theory of measurement. Nor does there seem to be any possibility of extending it to other types of interaction.

## Elementary Particle Theory

Heisenberg, who had been the first to stress the nonexistence of a criterion for distinguishing "elementary" particles from composites, has in the meantime developed a different theory in which elementary particles are stationary states of a single physical system, "matter." The field operators refer no longer to particles but to this basic matter (which Heisenberg sometimes compares to Anaximander's *apeiron* ). The masses of the particles arise wholly from the interactions due to the nonlinearity of the basic field equation. There are no "bare particles." Other properties are supposed to follow from the symmetries of the field equation. Strange particles of spin 0 and 1/2 have been dealt with, to a certain extent, on the basis of approximation methods (this refers to 1962). There are only programs, no exact predictions, for weak interactions.

Heisenberg's philosophical speculations were always intimately connected with his physics. They were original and exciting. The same cannot be said about his more general observations on philosophical matters. However, he should not be blamed for this disparity, as it is at any rate only in close connection with reality that philosophy can be both interesting and fruitful.

** See also ** Quantum Mechanics.

## Bibliography

Heisenberg's early work and its relation to wave mechanics and to experiment is described in *Die physikalischen Prinzipien der Quantentheorie* (Leipzig: Hirzel, 1930), translated by Carl Eckart and Frank C. Hoyt as *The Physical Principles of the Quantum Theory* (Chicago: University of Chicago Press, 1930). The theory of the S-matrix is explained in "Die 'beobachtbaren Grössen' in die Theorie der Elementarteilchen," in *Zeitschrift für Physik* 120 (1943): 513–538 and 673–702. For a survey of Heisenberg's new field theory, see "Quantum Theory of Fields and Elementary Particles," in *Reviews of Modern Physics* 29 (1957): 269–278, and "Die Entwicklung der einheitlichen Feldtheorie der Elementarteilchen," in *Naturwissenschaften* 50 (1963): 3–7. *Die Physik der Atomkerne* (Brunswick, Germany: Vieweg, 1943) explains nuclear physics and Heisenberg's contributions to it. *Wandlungen in den Grundlagen der Naturwissenschaften* (Leipzig: Hirzel, 1935) is a survey of advances and discoveries from 1900 to 1930. *Physics and Philosophy* (New York: Harper, 1959), which contains the Gifford Lectures given in 1955/1956, deals with the same subject on a broader historical and philosophical basis and also discusses current objections to the Copenhagen interpretation of quantum theory.

For the atmosphere at Göttingen in the "golden twenties," see F. Hundt, "Göttingen, Kopenhagen, Leipzig im Rückblick," in *Werner Heisenberg und die Physik unserer Zeit*, edited by Fritz Bopp (Brunswick, Germany: Vieweg, 1961), pp. 1–7, and Robert Jungk, *Brighter Than a Thousand Suns* (New York: Harcourt Brace, 1958).

*Paul K. Feyerabend (1967)*

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