VOIGT, WOLDEMAR

(b. Leipzig, Saxony, 2 September 1850;

d. Göttingen, Germany, 13 December 1919), physics. For the original article on Voigt see DSB, vol. 14.

Voigt’s major contributions to physics were in the study of crystals, in which he elaborated the use of symmetry consideration, cultivated phenomenological theories and applied complicated mathematics in analysis of experiments and phenomena. His interests, approaches, and achievements made him a prominent member of Franz Neumann’s school. Voigt was a full-fledged theoretician when theoretical physics was formed as a subdiscipline in Germany, but still devoted time for laboratory study. By age and character he was a member of the last generation of classical physicists. His research was almost untouched by the relativity revolution and the early quantum mechanics, despite his precedence in formulating what was later called Lorentz transformation (see the original DSB article). By contrast, changes within classical physics during Voigt’s career, especially in electrodynamics, are well reflected in his works. The present article complements the original DSB article by discussing these issues in light of subsequent scholarship.

Role of Symmetry Considerations. In his first major research, Voigt supported the so-called multi-constants elastic theory through painstaking precise measurements on rock-salt. In a series of experiments during 1887–1889 on crystals of different systems he practically ended the controversy over the number of elastic constants by refuting the rari constants alternative, which follows from Navier-Poisson molecular theory. Voigt preferred a continuum phenomenological theory, aimed at describing the phenomena and their relations as found empirically on a minimal number of laws, without explaining their origin. Such an elastic theory and approach, which refrained from assumptions about a hidden mechanism, were especially suitable for the application of what he later called the “Neumann Principle,” according to which the physical properties of crystals must possess at least the symmetry of their form. Voigt extended Neumann’s and Kirchhoff’s previous employment of such considerations to all crystal systems, applying symmetry considerations more rigorously and completely.

Symmetry was a guiding principle in Voigt’s formulation of a general phenomenological theory of pyroelectricity and piezoelectricity in 1890. That the latter effect of mechanical strain on electric polarization is more complicated than that of stress on strain in elasticity, required from Voigt a more refined use of symmetry conditions. On that and the linearity of the effect, he developed a theory for all crystals that accounted for all observations, including those that were not explained by former (molecular) theories. It continued to be the ground for theory of the field in the early twenty-first century. In many subsequent experimental and theoretical works Voigt made himself the world’s expert on piezoelectricity.

Voigt’s successful use of symmetry probably stimulated Pierre Curie, the co-discoverer of the piezoelectric effect, in his study and formulation of a more general rule of symmetry in physics, which also relate two abstract magnitudes such as electricity and magnetism. Curie’s formulation might have contributed to Voigt’s introduction of the term tensor (originally in 1897 lectures) as a pedagogical means to display the relation between symmetry and physical properties. Thereby, he relied on the mathematical tradition in elasticity since Cauchy, and the employment of tensor-like formulas in the physics of crystals.

Theoretical and Experimental Methodology. In his theory of the Zeeman effect (the splitting of spectral lines by magnetic field), Voigt’s demonstrated the power of his phenomenological approach. Assuming two sets of coupled linear differential equations such as those of a damped harmonic oscillator, Voigt accounted (by experimentally determining coefficients) for the complicated phenomena, including the asymmetric splitting of the line to more than triplets, which Lorentz’s electron theory failed to explain. However, Voigt himself regretted the lack of physical visualizability [Anschaulichkeit] in the theory. Following Voigt’s method, his student Walther Ritz “raised Rydberg constant to a universal one, and identified the quantity whose derivation became the show piece of Bohr’s atomic theory” (Heilbron, 1994, p. 181).

Voigt usually preferred phenomenological theory, but his choice depended on the specific scientific problem and on his particular goal. So although he showed the inadequacy of the molecular explanations of piezoelectricity and elasticity and advanced phenomenological theories in these fields, he suggested in each case more complicated molecular theories that yielded the equations of the phenomenological accounts. Voigt claimed that, as in these cases, often explanatory theories are based on phenomenological descriptions. At the beginning of the twentieth century Voigt regarded the existence of atoms and electrons as proved, yet he considered phenomenological theories as indispensable because one cannot account for the observations only by these entities. This methodological position was connected to his work on crystal physics, where the limits of molecular assumptions were evident. Like his contemporaries, Voigt acknowledged the freedom of theoretical physicists in choosing their approach and assumptions, and the fertility of such mixed approaches.

Voigt’s ordinary chair for theoretical physics was one of the two of this kind in Germany, whereas others positions for teaching theoretical physics were of the inferior status and often regarded as temporary stages in the way for a chair of experimental physics. “Unlike his predecessor Listing, Voigt was trained in theoretical physics and regarded it as his field, so that his appointment at Göttingen was an important step in the establishment of theoretical physics in Germany” (Jungnickel and McCormmach, 1986, p. 115). Voigt’s institute for theoretical physics also included a laboratory, in which its head was expected (as a theoretician) and was very willing to carry out experiments. These were measurements, carried out to obtain precise quantitative data of various coefficients, which contemporaries differentiated from experiments, which did not always involve quantitative information.

Precision was central in this kind of laboratory activity. Voigt devoted much energy to the exactness of his results. Like others in Neumann’s school, he preferred theoretical-mathematical elimination of errors, after recording the data. Voigt’s measurements were used for confirmation of theories (e.g. piezoelectricity), more often to determine values of constants (e.g. elastic), but also for detecting the existence of genuine effects (e.g. direct pyro-electricity, and direct electro-optics, by Friedrich Pockels his former student) and to decide between two theories (e.g. rari versus multi constants in elasticity).

Although the atomic structure of crystal was revealed only at the eve of Voigt’s career, and despite the revolutionary changes that physics underwent at the time, parts of his work continued to be relevant in fields of complex matter physics, such as elasticity and piezoelectricity. His 1910 textbook on crystal physics was reprinted in 1946 and it is still occasionally cited. That suggests the durability of his phenomenological accounts, which are independent of fundamental theories, and the continuity in the study of a few physical subfields despite the quantum revolution.

SUPPLEMENTARY BIBLIOGRAPHY

WORKS BY VOIGT

“Bestimmung der Elasticitätsconstante des Steinsalzes.” Annalen der Physik und Chemie suppl. vol. 7 (1876): 1–53, 177–214. Elaboration of his dissertation.

“Theoretische Studien über die Elasticitätverhältnisse der Krystalle.” Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 34 (1887): 1–52. Molecular theory of elasticity.

“Allgemeine Theorie der piëzo- und pyroelectrischen Erscheinungen an Krystallen.” Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 36 (1890): 1–99.

With E. Riecke. “Die Piëzoelectrischen Constanten des Quarzes und Turmalines.” Annalen der Physik und Chemie 45 (1892): 523–552.

“Ueber Arbeitshypothesen.” Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Geschäftliche Mitteilungen (1905): 98–116.

“Phänomenologische und atomistische Betrachtungsweise.” In Physik, edited by Emil Warburg. Die Kultur der Gegenwart, Tl. 3, Abt. 3,1. Berlin: Teubner, 1915.

OTHER SOURCES

Försterling, K. “Woldemar Voigt zum hundertsten Geburtstage.” Die Naturwissenschaften 38 (1951): 217–221.

Heilbron, John L. “The Virtual Oscillator as a Guide to Physics Students Lost in Plato’s Cave.” Science and Education 3 (1994): 177–188. On Voigt’s view of theories and the Zeeman effect.

Jungnickel, Christa, and Russell McCormmach. “Göttingen Institute for Theoretical Physics.” In Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, vol. 2. Chicago: University of Chicago Press, 1986. On Voigt’s role as a theoretical physicist.

Katzir, Shaul. “The Emergence of the Principle of Symmetry in Physics.” Historical Studies in the Physical and Biological Sciences 35 (2004): 35–65.

———. The Beginnings of Piezoelectricity: A Study in Mundane Physics. Dordrecht, Netherlands: Springer, 2006.

Olesko, Kathryn M. Physics as a Calling: Discipline and Practice in the Königsberg Seminar for Physics. Ithaca, NY: Cornell University Press, 1991. On Voigt’s early works with Franz Neumann and the latter school, especially pp. 288–296, 434–439.

Reich, Karin. Die Entwicklung des Tensorkalküls: von absoluten Differentialkalkül zur Relativitätstheorie. Basel, Switzerland and Boston: Birkhäuser Verlag, 1994. See pp. 111–129.

Wolff, Stefan L. “Woldemar Voigt (1850–1919) und Pieter Zeeman (1865–1943): eine wissenschaftliche Freundschaft.” In The Emergence of Modern Physics: Proceedings of a Conference Commemorating a Century of Physics, Berlin, 22–24 March 1995, edited by Dieter Hoffmann, Fabio Bevilacqua, and Roger Stuewer. Pavia, Italy: Università degli Studi di Pavia, 1996.

———. “Woldemar Voigt (1850–1919) und seine Untersuchungen der Kristalle.” In Toward a History of Mineralogy, Petrology, and Geochemistry, edited by Bernhard Fritscher and Fergus Henderson. Munich, Germany: Institut für Geschichte der Naturwissenschaften, 1998.

Shaul Katzir