Gustav Herglotz (2 February 1881 – 22 March 1953) was a

German Bohemian German Bohemians (german: Deutschböhmen und Deutschmährer, i.e. German Bohemians and German Moravians), later known as Sudeten Germans, were ethnic Germans living in the Czech lands of the Bohemian Crown, which later became an integral part o ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...

best known for his works on the

theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...

and

seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...

Biography

Gustav Ferdinand Joseph Wenzel Herglotz was born in

Volary Volary (; german: Wallern) is a town in the South Bohemian Region of the Czech Republic. It has about 3,700 inhabitants. It is located in the Bohemian Forest, close to the border with Germany. An area in the northern part of the town with timber-f ...

num. 28 to a public notary Gustav Herglotz (also a

Doctor of Law A Doctor of Law is a degree in law. The application of the term varies from country to country and includes degrees such as the Doctor of Juridical Science (J.S.D. or S.J.D), Juris Doctor (J.D.), Doctor of Philosophy (Ph.D.), and Legum Doctor (LL ...

) and his wife Maria née Wachtel. The family were

Sudeten Germans German Bohemians (german: Deutschböhmen und Deutschmährer, i.e. German Bohemians and German Moravians), later known as Sudeten Germans, were ethnic Germans living in the Czech lands of the Bohemian Crown, which later became an integral part ...

. He studied mathematics and astronomy at the

University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histor ...

in 1899, and attended lectures by

Ludwig Boltzmann Ludwig Eduard Boltzmann (; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics, and the statistical explanation of the second law of thermodyn ...

. In this time of study, he had a friendship with his colleagues

Paul Ehrenfest Paul Ehrenfest (18 January 1880 – 25 September 1933) was an Austrian theoretical physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition an ...

, Hans Hahn and

Heinrich Tietze Heinrich Franz Friedrich Tietze (August 31, 1880 – February 17, 1964) was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers. He also developed the Tietze transformat ...

. In 1900 he went to the

LMU Munich The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operatio ...

and achieved his

Doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''l ...

in 1902 under

Hugo von Seeliger Hugo von Seeliger (23 September 1849 – 2 December 1924), also known as Hugo Hans Ritter von Seeliger, was a German astronomer, often considered the most important astronomer of his day. Biography He was born in Biala, completed high school in ...

. Afterwards, he went to the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

, where he

habilitated Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

under

Felix Klein Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group ...

. In 1904 he became

Privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...

for

Astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

and

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

there, and in 1907

Professor extraordinarius Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', ...

. In 1908 he became Professor extraordinarius in Vienna, and in 1909 at the

University of Leipzig Leipzig University (german: Universität Leipzig), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 Decemb ...

. From 1925 (until becoming

Emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

in 1947) he again was in Göttingen as the successor of

Carl Runge Carl David Tolmé Runge (; 30 August 1856 – 3 January 1927) was a German mathematician, physicist, and spectroscopist. He was co-developer and co-eponym of the Runge–Kutta method (German pronunciation: ), in the field of what is today known a ...

on the chair of applied mathematics. One of his students was

Emil Artin Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing lar ...

Work

Herglotz worked in the fields of

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

, theory of

electrons The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

hydrodynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...

refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...

theory. *In 1904, Herglotz defined relations for the electrodynamic potential which are also valid in

even before that theory was fully developed.

Hermann Minkowski Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen. He created and developed the geometry of numbers and used geometrical methods to solve problems in number t ...

(during a conversation reported by

Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretica ...

) pointed out that the four-dimensional symmetry of electrodynamics is latently contained and mathematically applied in Herglotz' paper. *In 1907, he became interested in the theory of

earthquake An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, from ...

s, and together with

Emil Wiechert Emil Johann Wiechert (26 December 1861 – 19 March 1928) was a German physicist and geophysicist who made many contributions to both fields, including presenting the first verifiable model of a layered structure of the Earth and being among the ...

, he developed the Wiechert–Herglotz method for the determination of the velocity distribution of Earth's interior from the known propagation times of

seismic wave A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. S ...

s (an inverse problem). There, Herglotz solved a special integral equation of Abelian type. *The

Herglotz–Noether theorem Born rigidity is a concept in special relativity. It is one answer to the question of what, in special relativity, corresponds to the rigid body of non-relativistic classical mechanics. The concept was introduced by Max Born (1909),Born (1909b) who ...

stated by Herglotz (1909) and independently by

Fritz Noether Fritz Alexander Ernst Noether (7 October 1884 – 10 September 1941) was a Jewish German mathematician who emigrated from Nazi Germany to the Soviet Union. He was later executed by the NKVD. Biography Fritz Noether's father Max Noether ...

(1909), was used by Herglotz to classify all possible forms of rotational motions satisfying

Born rigidity Born rigidity is a concept in special relativity. It is one answer to the question of what, in special relativity, corresponds to the rigid body of non-relativistic classical mechanics. The concept was introduced by Max Born (1909),Born (1909b) who ...

. In the course of this work, Herglotz showed that the

Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...

s correspond to

hyperbolic motion In geometry, hyperbolic motions are isometric automorphisms of a hyperbolic space. Under composition of mappings, the hyperbolic motions form a continuous group. This group is said to characterize the hyperbolic space. Such an approach to geomet ...

s in

R_3

, by which he classified the one-parameter Lorentz transformations into loxodromic, parabolic, elliptic, and hyperbolic groups (see Möbius transformation#Lorentz transformation). *In 1911, he formulated the

Herglotz representation theorem In mathematics, a positive harmonic function on the unit disc in the complex numbers is characterized as the Poisson integral of a finite positive measure on the circle. This result, the ''Herglotz-Riesz representation theorem'', was proved indepen ...

which concerns

holomorphic function In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex derivativ ...

s ''f'' on the

unit disk In mathematics, the open unit disk (or disc) around ''P'' (where ''P'' is a given point in the plane), is the set of points whose distance from ''P'' is less than 1: :D_1(P) = \.\, The closed unit disk around ''P'' is the set of points whose di ...

''D'', with Re ''f'' ≥ 0 and ''f''(0) = 1, represented as an

integral In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...

over the boundary of ''D'' with respect to a

probability measure In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as ''countable additivity''. The difference between a probability measure and the more gener ...

''μ''. The theorem asserts that such a function exists if and only if there is a ''μ'' such that ::

\forall z \in D \ \ f (z) \ = \ \int_ \frac\ d\mu(\lambda).

: The theorem also asserts that the probability measure is unique to ''f''. *In 1911, he formulated a relativistic

theory of elasticity Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and ot ...

. In the course of that work, he obtained the vector Lorentz transformation for arbitrary velocities (see History of Lorentz transformations#Herglotz (1911)). *In 1916, he also contributed to

. Independently of previous work by

Hendrik Lorentz Hendrik Antoon Lorentz (; 18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the Lorentz t ...

(1916), he showed as to how the contracted

Riemann tensor In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. I ...

and the

curvature invariant In Riemannian geometry and pseudo-Riemannian geometry, curvature invariants are scalar quantities constructed from tensors that represent curvature. These tensors are usually the Riemann tensor, the Weyl tensor, the Ricci tensor and tensors forme ...

can be geometrically interpreted.
In English:

Selected works

* ''Gesammelte Schriften / Gustav Herglotz'', edited for d. Akad. d. Wiss. in Göttingen by

Hans Schwerdtfeger Hans Wilhelm Eduard Schwerdtfeger (9 December 1902 – 26 June 1990) was a German-Canadian-Australian mathematician who worked in Galois theory, matrix theory, theory of groups and their geometries, and complex analysis Complex analysis, ...

. XL, 652 p., Vandenhoeck & Ruprecht, Göttingen 1979, . * ''Vorlesungen über die Mechanik der Kontinua / G. Herglotz'', prepared by R. B. Guenther and H. Schwerdtfeger, Teubner-Archiv zur Mathematik; vol. 3, 251 p.: 1 Ill., graph. Darst.; 22 cm, Teubner, Leipzig 1985. * ''Über die analytische Fortsetzung des Potentials ins Innere der anziehenden Massen'', Preisschriften der Fürstlichen Jablonowskischen Gesellschaft zu Leipzig, VII, 52 pages, with 18 Fig.; Teubner, Leipzig (1914). * ''Über das quadratische Reziprozitätsgesetz in imaginären quadratischen Zahlkörpern'', Ber. über d. Verh. d. königl. sächs. Gesellsch. d. Wissensch. zu Leipzig, pp. 303–310 (1921).

References

External links

* * * *
Herglotz, Gustav (1881–1953)
at the

MathWorld ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Dig ...

Gustav Herglotz
by Joachim Ritter and Sebastian Rost {{DEFAULTSORT:Herglotz, Gustav 1881 births 1953 deaths 20th-century German mathematicians Austrian mathematicians German geophysicists Seismologists Science teachers Ludwig Maximilian University of Munich alumni German Bohemian people German people of German Bohemian descent People from Volary Austro-Hungarian mathematicians Sudeten German people

Biography

Work

Selected works

See also

References

External links