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

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 cau ...

best known for his works on the

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

and

seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes (or generally, quakes) and the generation and propagation of elastic ...

Biography

Gustav Ferdinand Joseph Wenzel Herglotz was born in

Volary Volary (; ) is a town in Prachatice District 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 t ...

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

Doctor of Law A Doctor of Laws (LL.D.) is a doctoral degree in legal studies. The abbreviation LL.D. stands for ''Legum Doctor'', with the double “L” in the abbreviation referring to the early practice in the University of Cambridge to teach both canon law ...

) and his wife Maria née Wachtel. The family were

Sudeten Germans German Bohemians ( ; ), later known as Sudeten Germans ( ; ), were ethnic Germans living in the Czech lands of the Bohemian Crown, which later became an integral part of Czechoslovakia. Before 1945, over three million German Bohemians constitute ...

. He studied mathematics and astronomy at the

University of Vienna The University of Vienna (, ) is a public university, public research university in Vienna, Austria. Founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest ...

in 1899, and attended lectures by

Ludwig Boltzmann Ludwig Eduard Boltzmann ( ; ; 20 February 1844 – 5 September 1906) was an Austrian mathematician and Theoretical physics, theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical ex ...

. 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 physics, theoretical physicist who made major contributions to statistical mechanics and its relation to quantum physics, quantum mechanics, including the theory ...

, 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 transforma ...

. In 1900 he went to the

LMU Munich The Ludwig Maximilian University of Munich (simply University of Munich, LMU or LMU Munich; ) is a public university, public research university in Munich, Bavaria, Germany. Originally established as the University of Ingolstadt in 1472 by Duke ...

and achieved his

Doctorate A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...

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 (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

, where he

habilitated Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excellen ...

under

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

. 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 qualifi ...

for

Astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

and

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

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 (), 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 December 1409 by Frederick I, Electo ...

. From 1925 (until becoming

Emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...

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 (), in the field of what is today known as numerical analysi ...

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

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

Work

Herglotz worked in the fields of

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

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 in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...

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

hydrodynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in ...

refraction In physics, refraction is the redirection of a wave as it passes from one transmission medium, 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 commo ...

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 mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, Lithuanian-German, o ...

(during a conversation reported by

Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld (; 5 December 1868 – 26 April 1951) was a German Theoretical physics, theoretical physicist who pioneered developments in Atomic physics, atomic and Quantum mechanics, quantum physics, and also educated and ...

) 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 earthquakealso called a quake, tremor, or tembloris the shaking of the Earth's surface resulting from a sudden release of energy in the lithosphere that creates seismic waves. Earthquakes can range in intensity, from those so weak they ...

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 mechanical wave of acoustic energy that travels through the Earth or another planetary body. It can result from an earthquake (or generally, a quake), volcanic eruption, magma movement, a large landslide and a large ma ...

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) wh ...

stated by Herglotz (1909) and independently by

Fritz Noether Fritz Alexander Ernst Noether (7 October 1884 – 11 September 1941) was a Jewish German mathematician who emigrated from Nazi Germany to the Soviet Union. He was later executed by the NKVD. His father was the mathematician Max Noethe ...

(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) w ...

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

Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant vel ...

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 geometr ...

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 indep ...

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 de ...

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 d ...

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

integral In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental oper ...

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 σ-algebra that satisfies Measure (mathematics), measure properties such as ''countable additivity''. The difference between a probability measure an ...

''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 ...

. 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 theoretical physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for their discovery and theoretical explanation of the Zeeman effect. He derive ...

(1916), he showed as to how the contracted

Riemann tensor Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first ...

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 formed ...

can be geometrically interpreted.
In English:

Selected works

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

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 Mathematicians from Austria-Hungary Sudeten German people

Biography

Work

Selected works

See also

References

External links