# Oskar Klein

**Oskar Benjamin Klein** was born in Stockholm the 15th of September 1894. He is the greatest Swedish theoretical physicist of the 20th century, and also an International authority on quantum mechanics in his time but even more recognised after his death for his pioneering work in several fields. Oskar Klein studied very fundamental theoretical questions. He was Niels Bohr's (1885-1962) closest associate when both the correspondence and complementarity principles in quantum mechanics were developed. Klein is today perhaps most known for his pioneering work trying to unite gravity and electromagnetism. Klein found similarities between Einstein's theory of gravity and Maxwell's theory of electromagnetism when five dimensions (four spatial plus time) are applied instead of four. This Kaluza-Klein theory constitutes one of the fundamental pillars in today's theoretical physics, and is especially relevant in string theory. Klein was also one of the first who understood, and developed Paul Dirac's (1902-1984) relativistic electron theory. Klein’s interests in theoretical physics were broad and he also introduced physics to the Swedish general public through his newspaper articles, radio talks and his popular science books.

**Oskar's father Gottlieb** Klein (1852-1914) was born close to the Carpathian Mountains, in Humenné (present Slovakia), He was both theologically and scientifically educated. During his time as Rabbi in Elbing, Germany, he married Toni Levy (1857-1940) in 1879. He then moved to Stockholm in 1883 to become chief rabbi. Oskar’s father, Gottlieb Klein, was liberal in his role as rabbi and had contacts with the Swedish King Oscar II. He was awarded an honourable professorship by the King for his for his scientific research in the theological sciences.

Oskar was the second youngest child in his family, and had a gift for studying. He became interested in science after reading popular scientific newspaper articles. As a young man, Oskar became involved in chemistry in Stockholm and served as assistant to the well-established **Svante Arrhenius** (1859-1927) at the chemical Nobel Institute in Stockholm. Arrhenius (who had received the Nobel Prize in chemistry in 1903) helped Oskar (who was 16 years of age) to publish an article about the solvability of Zinc hydroxide with radioactive substances. When he reached 20 years of age, in 1914, Oskar Klein was successful in his university examination at the "Stockholm University College".

Shortly afterwards, Arrhenius sent Klein to Jean-Baptiste Perrin (1870-1942) at the University of Paris. But the First World War intervened and Oskar was forced to return to Sweden to fulfil his military duties (1915-1916). After 1916, Oskar continued his research on electrolytes with Arrhenius (Debyean theory for dielectricity). **Physical chemistry** was at this time still regarded as theoretical physics. He then met Hendrik Kramers (1894-1952) who was on a lecture tour in Sweden in 1917 to convince the Swedes about the new theory of the atom. Kramers was a Dutch student and collaborator to Niels Bohr (1885-1962) in Copenhagen from 1916. Oskar, who already had an interest in atomic theory, became more enthusiastic about the subject after meeting Kramers. The visit made Oskar want to go to work with Bohr in **Copenhagen**. Klein wrote to Bohr, describing his limited knowledge in theoretical physics, his work with electrolytes that he wanted to complete, and explained that he wanted to learn more of Bohr's theories and way of working. Klein was "ordentlig velkommen" (really welcome) and started out as a trainee with Bohr in Copenhagen before the summer of 1918, thus becoming and the second collaborator after Kramers. Klein now started to become acquainted with the theoretical physics that Bohr explored. When Bohr didn't have time to teach Klein, Kramers taught him. Kramers and Bohr also helped Oskar with his treatise on electrolytes.

Oskar left Copenhagen to ski in Sweden in the end of 1918. Because of the **Spanish disease** (Influenza) that ravaged in Scandinavia, and that he contracted, the journey back was considerably delayed. In the beginning of the Summer of 1919, Klein was back with Bohr in Copenhagen as his assistant. Among other things they both attended a conference in atomic physics in Lund, Sweden, arranged by Professor Manne Siegbahn (1886-1979). In November the same year (1919), Klein returned to Sweden to work on his doctoral thesis that he wanted to finish so that he would have more time to plunge deeper into the new physics of the atom. Supervisor for the thesis was Carl Wilhelm Oseen (1879-1944), who at this time was the best physicist in Sweden (in hydrodynamics).

Klein had also time to write a popular science article about relativity before he returned to Copenhagen in the autumn of 1920. While in Copenhagen, he wrote an article with the Norwegian astronomer Svein Rosseland (1894-1985) about **collisions of the second kind in atomic physics. ** Franck and Hertz had experimentally showed (in 1919) that the velocity of electrons can be absorbed by atoms and excite the atom as a result of the collision (collision of the first kind). Klein and Rosseland showed that this collision that excited atoms can also transfer surplus energy to passing electrons (collision of the second kind), and increase the velocity of the electron in the process, in accordance with the laws of thermodynamics. Klein and Rosseland’s article, which was submitted in 1920, was the **first article** ("Zeitschrift für Physik", 1921, Vol 4, p. 46) published under the new name of the institute that Bohr founded, even though the **Institute for Theoretical Physics**** **(called the Niels Bohr institute after 1965) was not completed until 1921. It was also Klein's first article in theoretical physics. The results of the article were experimentally verified a few years later.

Oskar defended his thesis and **was awarded his doctoral degree** in 1921 for his work in physical chemistry about strong electrolytes, at **Stockholms Högskola** (Univeristy College, renamed Stockholm University later). His examiner was Ivar Fredholm (1866-1927), professor in mechanics and mathematical physics, and Kramers was his opponent. The grades were so good ("med beröm godkänt" (very good) for the writing and "med utmärkt beröm godkänt" (excellent) for his defence) that he directly could apply for a degree as "docent" (equivalent to reader in the UK / associate professor in the US) in physics.

With the help of a scholarship from the Rask-Örsted foundation Oskar became the **assistant of Bohr** in the academic year of 1921/22. He was offered a "docentur" (readership) in Lund but rejected it despite that it was considerably better paid than the position at the Institute for Theoretical Physics in Copenhagen. Being Bohr’s assistant meant taking a lot of dictation from Bohr, who was very thorough in his authoring. Among the papers Bohr dictated to Klein was the famous article about the principle of correspondence. In June of 1922 Klein followed Bohr to Göttingen for what later would be called the "Bohr Festspiele". Klein spent autumn of 1922 at the Stockholm University College as an unpaid docent. He complemented his doctoral degree with a licentiate degree in mathematical physics and mechanics. For the spring semester of 1923, Klein was interested in a readership (docent) in Lund and was appointed for one semester at an allowance of 2500 Swedish Kronor for the whole semester. Much of Klein’s time in the years of 1922 and 1923 was spent writing extensive compilations of Bohr's atom theories on assignment by the Swedish Society of Physicists. These writings were presented in the 1922 and 1923 editions of its yearbook "Kosmos" and gave Klein a good overview of the atomic physics of the time.

Klein derived the quantum mechanic energy calculation of a molecule that is not rotationally symmetric. The solution, that used Bohr's principle of correspondence, was a significant advance considering that the classical version is already complex. The formula is primarily used in microwave spectroscopy.

Klein also improved Rydberg's calculation of how the force between the molecules of an atom depends on the observable energy levels of the atom. The RKR method (Rydberg-Klein-Rees) is primarily used for spectrum analysis of diatomic molecules.

In the spring of 1923, Klein accepted a position as "instructor" at the University of Michigan at Ann Arbor, USA. The United States wanted to develop their knowledge of the new physics of the atom, by not only by sending students to Europe, but also by recruiting good teachers from Europe. Bohr had been consulted to recommend someone as a teacher. So Niels recommended Oskar, and Oskar later accepted. This appointment provided an economic security that Oskar had not had in Lund (from where he took sabbatical leave), or in Copenhagen where, during Oskar’s time, there was a lack of academic jobs. Oskar needed this security to support his family. Oskar married the Dane Gerda Agnete Koch the same year (1923) and required a larger and more stable income in anticipation of children to support. In 1924 he was appointed assistant professor. His salary was now almost twice as much as his previous income from Lund (the equivalent to 9600 Swedish crowns per year).

In Ann Arbor, Klein taught a course in electromagnetic field theory in 1924 and analysed a charged particle exposed to both an electromagnetic and a gravitational field with the so called Hamilton-Jacobi equation. He saw similarities in the equation between the potentials for Einstein's gravitational theory and Maxwell's electromagnetic theory. This was the start of his work on unified field theory, which much later would become one of the key ideas within string theory. It became Klein's favourite subject and he pursued the goal of finding a general theory, almost like Albert Einstein (1879-1955) the 1930s onwards in pursuit of his goals. Klein tried to solve the problem by adding a fifth dimension and obtain quantum mechanics equations that can be described with both waves and particles. After some time he came to the conclusion that it was not feasible. However, Klein stuck to the idea that more dimensions were a possible solution.

Soon Klein started to feel scientifically isolated in USA; being away from the swift development in atomic physics that was taking place, with Copenhagen as the centre. He wanted to go back to Copenhagen as fast as possible. His family went back to Denmark, but Oskar was contracted to Ann Arbor for the rest of the academic year of 1924/25. In May of 1925 Klein returned to Sweden and was able to resume his employment as docent (associate professor) at University of Lund. He acquired jaundice soon after his return, and regular visits to the Institute in Copenhagen could not start until the month of March the following year (1926).

When he finally returned to Copenhagen, Oskar was informed by Wolfgang Pauli (1900-1958) that Theodor Kaluza (1885-1954) had published a similar theory a couple of years earlier. Reading Kaluza's article Klein realized that he had moved one step further than Kaluza. Klein had demonstrated that the extra dimensions were rolled up like a ball with a size of the Planck length (10-35 m). He modified his five dimensional theory when Erwin Schrödinger (1887-1961) published his wave mechanics in 1926, and thus managed to get a relativistic wave equation. Klein's result was published in "Nature" in the autumn of 1926.

Klein now became deeply involved in merging Werner Heisenberg's (1901-1976) matrix mechanics with Schrödinger's wave mechanics and doing it in terms of the correspondence principle. In 1926 he determined the probabilities for the atomic transitions on a form now called the **Klein-Gordon equation** (after Walter Gordon (1893-1939) who was a refugee to Stockholm from Hamburg, after being dismissed by the nazis in 1933, and later died in Stockholm in 1939). This was the first relativistic wave equation. The equation was a success because the Compton effect, that until this time had been described from a particle perspective, could now also be described using wave mechanics. The Klein-Gordon equation is only valid for bosons, i.e. particles with integer spin, and cannot for example explain the right fine structure constant of the hydrogen atom or the Zeeman effect.

Dirac had proposed that an uncertainty should be introduced in the electromagnetic field theory concerning the relation between the value of the field in a position and its time derivative; similar with the uncertainty principle of Heisenberg. Klein realized together with Pascual Jordan (1902-1980) that the particles shall be described as fields, that in its turn should be considered with the uncertainty laws of quantum mechanics. This so called **second quantification** was a success and resolved many unsolved problems in relativistic quantum mechanics. The Klein-Jordan field quantization is valid for particles that follow Bose-Einstein statistics, i.e. with integer spin. Jordan soon afterwards published a field quantification for particles with half integer spin with Eugene Wigner (1902-1995). Each particle type corresponds to a field type and vice versa. This soon led to the discovery of new particles and the Klein-Jordan second quantification idea is now also used in solid state physics, except in elementary particle physics.

Klein summarized his **five dimensional theory** in the winter of 1927 to 28, because he no longer believed it would lead to a complete theory. He abandoned his theory in 1928 when Dirac discovered his relativistic wave equation for the electron, that is both relativisticly invariant and contains spin.

Klein was Bohr's closest associate in the development of the **complementary principle** and he got Heisenberg to realize in 1927 that his uncertainty principle was a special case of the more general complementary principle. Niels Bohr had hesitated to publish his, in his own opinion, incomplete thoughts about complementary, but his brother Harald persuaded him to write a speech at the conference in Como, Italy, on the occasion of his 100th birthday of Alessandro Volta in September of 1927. Oskar assisted him in writing it.

Bohr convinced Oskar to take over after Heisenberg as **associate professor at the Institute** from January of 1928 when Heisenberg became professor in Leipzig. Here the Swedish Klein, for the first time, introduced quantum mechanics into teaching in Copenhagen.

In October 1928, in collaboration with Yoshio Nishina (1890-1951), Oskar formulated the **Klein-Nishina formula**, which describes the distribution of the scattering angle between a highly energetic photon and an electron when these collide with each other. The formula considers effects such as radiation pressure and relativistic quantum mechanics. The Klein-Nishina formula was an improvement over J. J. Thomson's (1856-1940) classical equation that had considerable flaws compared to experiments. The Klein-Nishina formula was one of the first successful applications of Dirac's new theory on the Compton effect, and was published in "Zeitschrift für Physik" (1929, Vol 52, p. 853, 869).

Nishina was an experimentalist, and the collaboration resulted in conclusions that were unusually evident for the theoretical physics that reigned in Copenhagen, and for Oskar. Afterwards, alone and without Nishina, Klein soon drew more theoretical conclusions about Dirac's equation for the electron. Klein noticed an apparently unreasonable consequence of Dirac's relativistic theory for the electron that is called **Klein's (pseudo) paradox**. This thought experiment tells us that when electrons are sent towards an electrical potential, more electrons are reflected than were sent towards the potential when the electrical potential exceeds a curtain value (E + m_0*c^2). The article was sent to "Zeitschrift für Physik" in December of 1928 (1929, Vol 53, p. 157). Thus the Klein-Nishina formula was an early indication that the Dirac’s relativistic theory of the electron was correct. The first time this apparently contradictive pseudo paradox was observed was after the discovery of graphene by Andre Geim (1958- ) and Konstantin Novoselov (1974- ) in the year of 2004, for which they were awarded with the Nobel Prize in physics for 2010. The reason for the observation is because pseudo particles can get energy from the one dimensional material, graphene, and reflect parts of these pseudo particles with the same mechanism as with **Hawking radiation** at black holes. Thus, mechanism with the graphene could be called **Klein radiation** instead. One of the four valence electrons of carbon in the chicken wire structure has no mass and contributes to the phenomenon.

The paradox was discussed at the workshop in quantum mechanics held in Copenhagen in April of 1928. Paul Ehrenfest (1880-1933) concluded the discussions that unfortunately did not succeed in solving the paradox, with "God knows what Psi is, man knows h". This soon resulted in the **Copenhagen interpretation** that is a restriction of the freedom of the interpretations of the new quantum mechanics. Klein's pseudo paradox was later resolved when it was shown that a particle-antiparticle pair is created at the potential, in the form of an electron and a positron, that has a tendency to move towards opposite potentials when the passing electron is passing by. The positron (the most common anti particle) was not fully understood at this time, which complicated the interpretation. The positron was experimentally confirmed in 1932 by Carl Anderson (1905-1991) during studies of cosmic radiation.

In competition with mainly Ivar Waller (1898-1991), Klein was awarded **professorship in mechanics and mathematical physics at "Stockholm’s Högskola"** in 1930. He succeeded Ivar Fredholm, that died three years earlier and had been Klein’s opponent of his doctoral dissertation. No doctoral award in physics had been made at the university since 1920, so the appointment of Klein was important for the university and for the subject of theoretical physics of Sweden. Klein retained his professorship until his retirement in 1962. In 1961, the name of the professorship was changed to "theoretical physics".

In 1932 Oskar Klein, using his deep understanding for both quantum and statistical mechanics, succeeded in solving the ten year old question of whether the quantum statistics on molecular level can explain how the entropy increases with time in accordance with the second law of thermodynamics. The problem in classical statistical mechanics had been already noticed by Gibbs in 1902.. Oskar's proof, that uses the notion that only the diagonal elements in the density matrix for the phase space of the particles are relevant for the entropy, is now called **Klein's lemma**. With Klein's lemma, the entropy can increase in the formula of Ludwig Boltzmann's (1844-1906) microscopic definition, where it is described with the number of states in the phase space. The results were published in the article "Zur quantenmechanischen begründung des zweiten Hauptsatzes der Wärmelehre" ("Zeitschrift für Physik", p.226, 1932).

At the physics conference in Warsaw in 1938, Oskar was back again on unified field theory when he proposed that a particle with spin 1 mediated beta decay has the same role as the photon in electromagnetism. This hypothesis was not recognized fully until 1957 when Abdus Salam (1926- ), Steven Weinberg (1933- ) and Sheldon Glashow (1932- ) used it on a fundamental level in their work on weak interactions in unification with electrodynamics.

In the 1940ies, Klein worked in several areas such as superconductors, biochemistry, proton decay, general relativity and the physics of stars. In 1947 he realized that both the electron and the µ meson are weakly interacting particles and that the µ meson decays into the electron.

In 1943 Niels Bohr stayed at Klein's house in Sweden for some days when fleeing from Denmark to Great Britain to escape the Nazis that had planned for his arrest in occupied Copenhagen.

In 1945 Klein realized, together with G Beskow and L Treffenberg, that the **chemical elements were all created in the stars**. This is still true in combination with the chemical elements that were created at the Big Bang, a conclusion that George Gamow (1904-1968), Ralph Alpher (1921- ) and Robert Herman (1914-1997) arrived at approximately the same time.

Oskar Klein died the fifth of February in 1977 in Danderyd, Stockholm. There is now an annual lecture series in his memory called Oskar Klein Memorial Lecture, held in Stockholm University since 1988, and is delivered by some of the greatest physicists. In 1994 a special symposium was held to commemorate what would have been Klein’s 100th birthday. The great auditorium for the physical sciences at Albanova/Stockholm University is named in his honour.

This biography was kindly provided by Christian Målmark on www.kosmologika.net/Cosmologica.html

På svenska: http://kosmologika.net/Scientists/Klein.html

More information about Oskar Klein in an article by Ian T Durham can be found here

**Updated:** 2013-02-06

**To be updated before:** update

**Author:** Serena Nobili