Vladimir Varicak
Encyclopedia
Vladimir Varićak was a Croatia
n mathematician
and theoretical physicist of Serbian
descent.
Varićak was born in the village of Švica near Otočac
. He studied physics
and mathematics
at the University of Zagreb
from 1883 to 1887. He made his PhD
in 1889 and got his habilitation
in 1895. In 1899 he became professor of mathematics in Zagreb
, where he gave lectures until his death in 1942.
From 1903 to 1908 he wrote on hyperbolic geometry
(or Lobachevsky- Bolyai
geometry). In 1910, following a 1909 publication of Sommerfeld
, he applied hyperbolic geometry to the special theory of relativity. Sommerfeld, using the imaginary form of Minkowski space
, had shown in his 1909 paper that the Einstein formula for combination of velocities is most clearly understandable as a formula for triangular addition on the surface of a sphere of imaginary radius. Varićak reinterpreted this result as showing that rapidity
combines by the triangle rule in hyperbolic space. This is a fundamental result for the hyperbolic theory which was demonstrated later by other approaches by Robb
(1911) and Borel
(1913). The 1910 papers also dealt with several applications of the hyperbolic theory to optics. In 1911 Varićak was invited to speak to the Deutsche Mathematiker-Vereinigung in Karlsruhe on his work. He continued to develop the hyperbolic reinterpretation of Einstein's theory collecting his results in 1924 in a textbook, Relativity in Three Dimensional Lobachevski Space, now available in English. In the period 1909 to 1913 Varićak had correspondence with Albert Einstein
concerning rotation and length contraction
where Varićak's interpretations differed from those of Einstein. Concerning length contraction Varićak said that in Einstein's interpretation the contraction is only an "apparent" or a "psychological" phenomenon due to the convention of clock measurements whereas in the Lorentz theory it was an objective phenomenon.
Walter (1999) re-examined Minkowski's non-Euclidean geometry
. He begins by analysis of "the tip of a four-dimensional velocity vector" and notes Minkowski's equations where "both hypersurfaces provide a basis for a well-known model of non-Euclidean space of constant negative curvature, popularized by Helmholtz." In fact it is known as the hyperboloid model
of hyperbolic geometry.
Walter goes on to say:
Varićak is also known as a high school teacher of Milutin Milanković
, and as a university instructor of Duro Kurepa.
Varićak made scholarly contributions on the life and work of Ruđer Bošković (1711–1787) These are listed in the biography of Kurepa (1965) cited below.
Of special interest for the history of relativity is that Varićak also edited and published a little known 1755 paper of Boscovich in Latin entitled On absolute motion - if it is possible to distinguish it from relative motion ("Of Space and Time"). Varićak said that the paper "contains many remarkably clear and radical ideas regarding the relativity of space, time and motion." (Quoted from Silberstein: Theory of Relativity 1912 footnote p. 38)
He was a member of the Yugoslav Academy of Sciences and Arts, the Czech Academy of Sciences, the Serbian Academy of Sciences and Arts
, the Croatian Society for Natural Science, and the Yugoslav Mathematical Society.
A complete list of Varićak's publications on all subjects is given in the following paper:
Croatia
Croatia , officially the Republic of Croatia , is a unitary democratic parliamentary republic in Europe at the crossroads of the Mitteleuropa, the Balkans, and the Mediterranean. Its capital and largest city is Zagreb. The country is divided into 20 counties and the city of Zagreb. Croatia covers ...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and theoretical physicist of Serbian
Serbs
The Serbs are a South Slavic ethnic group of the Balkans and southern Central Europe. Serbs are located mainly in Serbia, Montenegro and Bosnia and Herzegovina, and form a sizable minority in Croatia, the Republic of Macedonia and Slovenia. Likewise, Serbs are an officially recognized minority in...
descent.
Varićak was born in the village of Švica near Otočac
Otocac
Otočac is a town in Lika, Croatia. It lies in the northwestern part of Lika, in the Gacka river valley. The population of the town is 4,354 as of 2001, with a total of 10,411 people within the municipality at large, the majority of whom are Croats ....
. He studied physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the University of Zagreb
University of Zagreb
The University of Zagreb is the biggest Croatian university and the oldest continuously operating university in the area covering Central Europe south of Vienna and all of Southeastern Europe...
from 1883 to 1887. He made his PhD
PHD
PHD may refer to:*Ph.D., a doctorate of philosophy*Ph.D. , a 1980s British group*PHD finger, a protein sequence*PHD Mountain Software, an outdoor clothing and equipment company*PhD Docbook renderer, an XML renderer...
in 1889 and got his habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
in 1895. In 1899 he became professor of mathematics in Zagreb
Zagreb
Zagreb is the capital and the largest city of the Republic of Croatia. It is in the northwest of the country, along the Sava river, at the southern slopes of the Medvednica mountain. Zagreb lies at an elevation of approximately above sea level. According to the last official census, Zagreb's city...
, where he gave lectures until his death in 1942.
From 1903 to 1908 he wrote on hyperbolic geometry
Hyperbolic geometry
In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
(or Lobachevsky- Bolyai
János Bolyai
János Bolyai was a Hungarian mathematician, known for his work in non-Euclidean geometry.Bolyai was born in the Transylvanian town of Kolozsvár , then part of the Habsburg Empire , the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai.-Life:By the age of 13, he had mastered...
geometry). In 1910, following a 1909 publication of Sommerfeld
Sommerfeld
- Place name :* The German name of Lubsko, Poland* Sommerfeld, A German town now a district of Leipzig - Family name :* Arnold Sommerfeld , a German physicist who is one of the founders of the quantum mechanics...
, he applied hyperbolic geometry to the special theory of relativity. Sommerfeld, using the imaginary form of Minkowski space
Minkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...
, had shown in his 1909 paper that the Einstein formula for combination of velocities is most clearly understandable as a formula for triangular addition on the surface of a sphere of imaginary radius. Varićak reinterpreted this result as showing that rapidity
Rapidity
In relativity, rapidity is an alternative to speed as a framework for measuring motion. On parallel velocities rapidities are simply additive, unlike speeds at relativistic velocities. For low speeds, rapidity and speed are proportional, but for high speeds, rapidity takes a larger value. The...
combines by the triangle rule in hyperbolic space. This is a fundamental result for the hyperbolic theory which was demonstrated later by other approaches by Robb
Alfred Robb
Alfred Arthur Robb or Alfred A. Robb FRS was a British physicist.Robb studied at Queen's College in Belfast and at St John’s College in Cambridge. He then proceeded to University of Göttingen, where guided by Woldemar Voigt, he wrote his dissertation on the Zeeman effect. He also worked under J. J...
(1911) and Borel
Émile Borel
Félix Édouard Justin Émile Borel was a French mathematician and politician.Borel was born in Saint-Affrique, Aveyron. Along with René-Louis Baire and Henri Lebesgue, he was among the pioneers of measure theory and its application to probability theory. The concept of a Borel set is named in his...
(1913). The 1910 papers also dealt with several applications of the hyperbolic theory to optics. In 1911 Varićak was invited to speak to the Deutsche Mathematiker-Vereinigung in Karlsruhe on his work. He continued to develop the hyperbolic reinterpretation of Einstein's theory collecting his results in 1924 in a textbook, Relativity in Three Dimensional Lobachevski Space, now available in English. In the period 1909 to 1913 Varićak had correspondence with Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
concerning rotation and length contraction
Length contraction
In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...
where Varićak's interpretations differed from those of Einstein. Concerning length contraction Varićak said that in Einstein's interpretation the contraction is only an "apparent" or a "psychological" phenomenon due to the convention of clock measurements whereas in the Lorentz theory it was an objective phenomenon.
Walter (1999) re-examined Minkowski's non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
. He begins by analysis of "the tip of a four-dimensional velocity vector" and notes Minkowski's equations where "both hypersurfaces provide a basis for a well-known model of non-Euclidean space of constant negative curvature, popularized by Helmholtz." In fact it is known as the hyperboloid model
Hyperboloid model
In geometry, the hyperboloid model, also known as the Minkowski model or the Lorentz model , is a model of n-dimensional hyperbolic geometry in which points are represented by the points on the forward sheet S+ of a two-sheeted hyperboloid in -dimensional Minkowski space and m-planes are...
of hyperbolic geometry.
Walter goes on to say:
- More than any other mathematician, Varićak devoted himself to the development of the non-euclidean style [of relativity], unfolding Minkowski's image of velocity-vector relations in hyperbolic space, and recapitulating a variety of results in terms of hyperbolic functions. The use of hyperbolic trigonometry was shown by Varićak to entail significant notational advantages. For example, he relayed the interpretation put forth by Hergloz and Klein of the Lorentz transformation as a displacement in hyperbolic space, and indicated simple expressions for proper time and the aberration of light in terms of a hyperbolic argument.
Varićak is also known as a high school teacher of Milutin Milanković
Milutin Milankovic
Milutin Milanković was a Serbian geophysicist and civil engineer, best known for his theory of ice ages, suggesting a relationship between Earth's long-term climate changes and periodic changes in its orbit, now known as Milankovitch cycles. Milanković gave two fundamental contributions to global...
, and as a university instructor of Duro Kurepa.
Varićak made scholarly contributions on the life and work of Ruđer Bošković (1711–1787) These are listed in the biography of Kurepa (1965) cited below.
Of special interest for the history of relativity is that Varićak also edited and published a little known 1755 paper of Boscovich in Latin entitled On absolute motion - if it is possible to distinguish it from relative motion ("Of Space and Time"). Varićak said that the paper "contains many remarkably clear and radical ideas regarding the relativity of space, time and motion." (Quoted from Silberstein: Theory of Relativity 1912 footnote p. 38)
He was a member of the Yugoslav Academy of Sciences and Arts, the Czech Academy of Sciences, the Serbian Academy of Sciences and Arts
Serbian Academy of Sciences and Arts
The Serbian Academy of Sciences and Arts is the most prominent academic institution in Serbia today...
, the Croatian Society for Natural Science, and the Yugoslav Mathematical Society.
Publications
- Varićak, V. (1908) "Zur nichteuklidischen analytischen Geometrie", Proceedings of the International Congress of MathematiciansInternational Congress of MathematiciansThe International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
, Bd. II, SS. 213–26. - Wikisource translation: Application of Lobachevskian Geometry in the Theory of Relativity
- Wikisource translation: The Theory of Relativity and Lobachevskian Geometry
- Wikisource translation: The Reflection of Light at Moving Mirrors
- Wikisource translation: On Ehrenfest's Paradox
- Wikisource translation: On the Non-Euclidean Interpretation of the Theory of Relativity
- Varićak, V.(1924) Darstellung der Relativitatstheorie im drei=dimensionalen Lobatschefskijschen Raume, Zagreb (Narodni Novini); English translation (2007) Relativity in three dimensional Lobachevski Space, A.F. Kracklauer translator ISBN 1847533647, at Amazon.comAmazon.comAmazon.com, Inc. is a multinational electronic commerce company headquartered in Seattle, Washington, United States. It is the world's largest online retailer. Amazon has separate websites for the following countries: United States, Canada, United Kingdom, Germany, France, Italy, Spain, Japan, and...
.
A complete list of Varićak's publications on all subjects is given in the following paper:
External links
- http://www.unizg.hr/rektori/vvaricak.htm