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 and
seismology.
Biography
Gustav Ferdinand Joseph Wenzel Herglotz was born in
Volary num. 28 to a public notary Gustav Herglotz (also a
Doctor of Law) and his wife Maria née Wachtel. The family were
Sudeten Germans. He studied mathematics and astronomy at the
University of Vienna in 1899, and attended lectures by
Ludwig Boltzmann. In this time of study, he had a friendship with his colleagues
Paul Ehrenfest,
Hans Hahn and
Heinrich Tietze. 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 in 1902 under
Hugo von Seeliger. 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 i ...
, 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 for
Astronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galax ...
and
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. From 1925 (until becoming
Emeritus 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 know ...
on the chair of applied mathematics. One of his students was
Emil Artin.
Work
Herglotz worked in the fields of
seismology,
number theory,
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,
special relativity,
general relativity,
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 theory.
*In 1904, Herglotz defined relations for the
electrodynamic potential which are also valid in
special relativity even before that theory was fully developed.
Hermann Minkowski (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
earthquakes, 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 (an inverse problem). There, Herglotz solved a special integral equation of Abelian type.
*The
Herglotz–Noether theorem stated by Herglotz (1909) and independently by
Fritz Noether (1909), was used by Herglotz to classify all possible forms of rotational motions satisfying
Born rigidity. 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 motions in
, 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 functions ''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'', with Re ''f'' ≥ 0 and ''f''(0) = 1, represented as an
integral 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 ge ...
''μ''. The theorem asserts that such a function exists if and only if there is a ''μ'' such that
::
: The theorem also asserts that the probability measure is unique to ''f''.
*In 1911, he formulated a relativistic
theory of elasticity. 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
general relativity. Independently of previous work by
Hendrik Lorentz (1916), he showed as to how the contracted
Riemann tensor 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
Hans Wilhelm Eduard Schwerdtfeger (9 December 1902 – 26 June 1990) was a German-Canadian-Australian mathematician who worked in Galois theory, matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchis ...
. 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).
See also
*
Acceleration (special relativity)
Accelerations in special relativity (SR) follow, as in Newtonian Mechanics, by differentiation of velocity with respect to time. Because of the Lorentz transformation and time dilation, the concepts of time and distance become more complex, which ...
*
Möbius transformation
*
Spherical wave transformation
Spherical wave transformations leave the form of spherical waves as well as the laws of optics and electrodynamics invariant in all inertial frames. They were defined between 1908 and 1909 by Harry Bateman and Ebenezer Cunningham, with Bateman gi ...
*
Squeeze mapping
In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is ''not'' a rotation or shear mapping.
For a fixed positive real number , th ...
*
Rindler coordinates
References
External links
*
*
*
*
Herglotz, Gustav (1881–1953)at the
MathWorld
Gustav Herglotzby 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