Skip to main content
Select Source:

Voigt, Woldemar


(b. Leipzig, Germany, 2 September 1850; d. Göttingen, Germany, 13 December 1919), physics.

Voigt graduated from the Nikolaischule at Leipzig in 1868. He then entered the University of Leipzig, but in 1870 his studies were interrupted by service in the Franco-Prussian War. He resumed his studies in 1871, this time at Königsberg. At first Voigt was undecided between a career in physics and a career in music, for the latter had always played a large role in his life: Felix Mendelssohn and Robert Schumann had been frequent visitors to his parents’ house. His musical ear was highly trained; and while in the army he would often pass the time while marching by reciting, note for note, the complete orchestration of entire symphonic pieces. He finally decided on a career in physics, on the ground that, unlike music, in physics there is a reasonable mean, not simply highs and lows.

While at Königsberg, Voigt came under the influence of Franz Neumann, his deep respect and love for whom largely determined his career, in terms of subject matter, the style of his research, and the manner in which he presented his work to the physics community. His dissertation on the elastic constants of rock salt was completed in 1874. He then returned to Leipzig, where he taught at the the Nikolaischule, but in 1875 was called back to Königsberg as extraordinary professor of physics. In 1883 Voigt was appointed ordinary professor of theoretical physics at Göttingen, with the promise that he and Eduard Reike were to have a new physical institute (which was not ready until 1905). His chief research interests centered on the understanding of crystals, but near the turn of the century he became more and more concerned with the Zeeman effect and the electron theory.

Voigt’s interest in crystals was closely related to Neumann’s work. At Königsberg, Neumann had worked in both the physics department and the department of mineralogy, so it was quite natural that he should do extensive work on the optical properties of crystals. Neumann had developed a mechanical theory of light propagation that assumed that light oscillations had a mechanical-elastic nature. The oscillations were transmitted through an ether conceived of as an elastic solid. He had not restricted his activities in physics to theoretical work, however, and had initiated a great number of experimental studies; his students spent many hours in his laboratories studying the properties of crystals.

Voigt brought this tradition of theoretical and experimental work to Göttingen. Although for many years he was hampered by lack of adequate facilities, he not only pursued theoretical studies of the properties of crystals but also undertook a host of very delicate experimental investigations in which the physical properties of many crystalline substances were measured.

According to the theories of Poisson and Cauchy, which were based on special molecular assumptions, certain relationships must exist between the constants of a crystal regardless of its classification. Voigt determined the elastic constants for a wide variety of crystals and showed that the predicted relationships were not at all satisfied. While some felt that this work vindicated those who objected to forming special hypotheses about the nature of crystals, Voigt did not accept this point of view and in many of his publications indicated the direction that must be taken in amending the molecular hypothesis.

In 1887, in a paper on the Doppler effect in which he analyzed the differential equations for oscillations in an incompressible elastic medium, Voigt established a set of transformation equations that later became known as the Lorentz transformations.

Voigt’s extensive theoretical and physical researches on the nature of crystals were summarized in Magneto- und Elektro-Optik (1908) and Kristallphysik (1910). These treatises reveal the elegance of his mathematical treatments and the great orderliness that has research had bought to the understanding of crystals. The elastic, thermal, electric, and magnetic properties of crystals were ordered in magnitudes of three types; scalar, vector, and tensor. In fact, it was Voigt who in 1898 had introduced the term “tensor” into the vocabulary of mathematical physics.

Even though Voigt devoted considerable time to his research and his students, and even though he acquired more administrative responsibility at Göttingen, he never gave up an active interest in music and musicology. He was recognized as an expert on Bach’s vocal works and in 1911 published a book on Bach’s church cantatas. Voigt often referred to the study of physics in musical terms. To him the region of science that represented the highest degree of orchestration and that possessed the utmost in rhythm and melody was crystal physics. It was altogether fitting that on 15 December 1919 his funeral bier was carried from his house to its final resting place to the strains of a Bach chorale.


I. Original Works. There is no comprehensive catalog of Voigt’s more than 200 publications. Among his most significant works are “Allgemeine Formeln für die Bestimmung der Elasticityäts constantan von Krystallen durch die Beobachtung der Biegung undd Drillung von Prismen,” in Annalen der Physik.16 (1882), 273–310, 398–415; “Volumen und Winkeländerung krystallinischen Körper bei all-oder einseitigen Druck,” ibid., 416–426; “Theorie des Lihtes für vollkommen durchschtige Media,” ibid.,19 (1883), 873–908; “Zur Theorie des Lichtes,” ibid.,20 (1883), 444–452; “Theorie der absorbirenden isotropen Medien insbesonder Theorie der optischen Eigenschaften der Metalle,” ibid.,23 (1884), 104–147; “Theorie der electromagnetischen Drehung der Polarisationseben,” ibid., 493–511; “Zur Theorie des Lichtes für absorbirende isotrope Medien,” ibid.,31 (1887), 233–242; and “Zur Erklärung der elliptischen Polarisation bei Reflexion an durchsichtigen Medien,” ibid.,32 (1887), 526–528.

Also see “Ueber das Doppler’sche Princip,” in Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1887), 44–51; “Theorie des Lichtes für bewegte Medien,” in Annalen der Physik, 35 (1888), 370–396; 524–551; “Zur Theorie des Lichtes,” ibid.,43 (1891), 410–437; “Ueber einen einfachen Apparat zur Bestimmung der thermischen Dilation fester Körper, special der Krystalle,” ibid., 831–834; “Bestimmung der Elasticitätsconstanten einiger quasiisotroper Metalle durch langsame Schwingungen von Stäben,” ibid.,48 (1893), 674–707; “Bestimmung der Constanten der thermische-Dilation und des thermische-Druckers für eingie quasi-isotrope Metalle,” ibid.,49 (1893), 697–708; “Die specifischen Wärmen cp and cn einiger quasi-isotroper Metalle,” ibid., 709–718; “Beiträge zur molecularen Theorie der Piëzoelectricität,” ibid.,51 (1894), 638–660; “Ueber Medien ohne innere Kräfte und über eine durch sie gelieferte mechanische Deutung der MAxwell-Hertz’schen Gleichungen,” ibid.52 (1894), 665–672; and “Beiträge zur geometrischen Darstellung der physickalischen Eigenschaften der Krystalle,” ibid.,63 (1897), 376–385.

Additional works are “Zur kinetischen Theirie idealer Flüssigkeiten,” in Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1897), 19–47, 261–272; “Lässt sich die Pyroelectricität der Krystalle vollständig auf Piëzoelectrische Wirkungen zuruckführen?” in Annalen der Physik,66 (1898), 1030-1060; “Doppelbrechung von im Magnetfelde befindlichen Natriumdampf in der Richtung normal zu den Kraftlinien,” in Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1898), 355–359; “Ueber das bei der sogenannten totalen Reflextion in des zweite Medium eindringende Licht,” in Annalen der Physik, 67 (1899), 185–200; “Zur Theorie der magneto-optischen Erscheinungen,” ibid., 345–365; “Ueber die Proportionalität von Emissions- und Absorptionsvermögen,” ibid., 366–387; “Weiteres zur Theorie der Zeemaneffectes,” ibid.,68 (1899), 352–364; “Neuere Untersuchungen über die optischen Wirkungen eines Magnetfeldes,” in Physikalische Zeitschrift, 1 (1899), 116–120, 128–131, 138–143; “Zur Festigkeitlehre,” in Annalen der Physik, 4 (1901), 567–591; “Beiträge zur Elektronentheorie des Lichtes,” ibid.,6 (1901), 459–505; “Elektronenhypothese und Theorie des Magnetisums,” in Nachrichten von der Königlichen Gesellshaft der Wissenschaften zu Göttingen (1901), 169–200; and “Ueber einige neuere Beobachtugen von magneto-optischen Wirkungen,” in Annalen der Physcik, 8 (1902), 872–889.

Further, see “Ueber das optische Verhalten von Kristallen der hemiëdrischen Gruppe des monokinen Systemes,” in Physikalische Zeitschrift, 7 (1906), 267–269; “Betrachtungen über die komplizierteren Formen des Zeemaneffektes,” in Annalen der Physik, 24 (1907), 193–224; “Beobachtungen über natürliche und magnetische Drehung der Polarisationsebene in Krystallen von K. Honda,” in physikalische Zeitschrift, 9 (1908), 585–590; Magneto- und Elektro-Optik (Leipzig, 1908); Kristallphysik (Leipzig-Berlin, 1910; 2nd ed., 1926); “Zur Theorie der komplizierteren Zeemaneffecte,” in Annalen der Phyesik, 36 (1911), 873–906; “Allgemeines über Emission und Absorption in zusammenhang mitder Frage der Intensitätsmessungen beim Zeeman-Effect,” in Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1911), 71–97; “Ueber Emission und Absorption schichtenweise stetig inhomogener Körper,” in Annalen der Physcik, 39 (1912), 1381-1407; “Weiteres zur Polarisation des Rowaland Gitterbn gebeugten Lichtes,” in Nachrichten von der Königlichen Geselleschaft der Wissenschaften zu Göttingen (1912), 385–417, written wtih P.Collet; “Ueber die anormalesn Zeeman-effekte der Wasserstofflinien,” in Annalen der Physick40 (1913), 368–380; “Weiteres zum Ausbau der Koppelungstheorie der Zeemanneffekte,” ibid., 41 (1913), 403–440; “Ueber die zeemaneffekte bei mehrafachen Serienlinien besonders auch beidem O-Triplet λ =3947,” ibid.,43 (1914), 1137-1164; and “Ueber sekundäre Wirkungen bei piëzoelktrischen vorgängen, insbesondere im Falle der Drillung und Biegung eines Krieszylinders” ibid.,48 (1915), 433–448.

II. Secondary Literature. See E.T.Whittaker, A History of the Theories of Aether and Electricity, 2 vols. (New York, 1960), I, 333, 415; II, 33, 160, 238–239. Obituary notices are by H.L[amb?], in Preceedings of the Royal Society, 99A (1921), XXiX-XXX; and by C. Runge in Physikalische Zeitschrift,21 (1920), 81–82; and in Nachrichten von der Königlichen Gesellschaft Zu Göttingen: Geschäftliche Mitteilungen aus dem Jahare 1920 (Göttingen, 1920), 47–52.

Stanley Goldbers

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Voigt, Woldemar." Complete Dictionary of Scientific Biography. . 18 Aug. 2017 <>.

"Voigt, Woldemar." Complete Dictionary of Scientific Biography. . (August 18, 2017).

"Voigt, Woldemar." Complete Dictionary of Scientific Biography. . Retrieved August 18, 2017 from

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.



“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.


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

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Voigt, Woldemar." Complete Dictionary of Scientific Biography. . 18 Aug. 2017 <>.

"Voigt, Woldemar." Complete Dictionary of Scientific Biography. . (August 18, 2017).

"Voigt, Woldemar." Complete Dictionary of Scientific Biography. . Retrieved August 18, 2017 from