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Person: Klein (2), Oskar

Oskar Klein was a Swedish theoretical physicist whose ideas were important in the development of string theory.

Mathematical Profile (Excerpt):

• Gottlieb Klein received his doctorate from Heidelberg and moved to Sweden in 1883.
• He evidently instilled an interest in learning in his young son, as Oskar became quite fond of biology at an early age.
• This interest changed to chemistry around the age of 15 and soon after, in 1910, Svante Arrhenius, at what seems to be the behest of Gottlieb, invited Oskar to work in his laboratory at the Nobel Institute.
• Arrhenius wanted to send Klein to work with Jean-Baptiste Perrin in his laboratory at the University of Paris but the plan was foiled by the outbreak of World War I.
• Klein found himself caught up in the tempest and saw military service in 1915 and 1916.
• Kramers and Klein met several times during the next few years both in Stockholm and in Copenhagen, which was to be Klein's next destination.
• In 1917 Klein received a fellowship to study abroad and, subsequently, arrived in Copenhagen in 1918.
• Bohr traveled to Stockholm in 1920 to visit Klein and convinced him to return to Copenhagen once more to work at Bohr's Institute.
• Klein agreed and began what would prove to be quite a fruitful relationship that eventually would lead him to his first teaching position.
• After his successful defence, Klein returned to Copenhagen, later assisting Bohr on a trip to Göttingen.
• Around this time Klein turned to publishing semi-popular writings on physics.
• For the time (1923), this was a fairly large problem to tackle, but Klein did not stop there.
• Klein chose to solve the problem by essentially extending his work to a fifth dimension, though his early unification ideas centred around quantum physics as the catalyst.
• After a time Klein argued less and less that quantum physics could lead to a unified picture, in fact he later abandoned the idea entirely.
• At this time, Klein apparently was unaware of the work of Theodor Kaluza.
• In 1925, Klein returned to Copenhagen and contracted hepatitis.
• Klein's results were published in Nature in the autumn of 1926 and generated interest from such eminent theorists as Vladimir Fock, Leon Rosenfeld, Louis de Broglie, and Dirk Struik.
• Unfortunately, despite a lot of initial interest in unification, most physicists eventually went on to more promising and experimentally testable research leaving Kaluza-Klein theory to be explored by another generation of physicists nearly half a century later.
• 1926 was a banner year for Klein.
• In a paper in which he determined the atomic transition probabilities (prior to Dirac), he introduced the initial form of what would become known as the Klein-Gordon equation.
• The Klein-Gordon equation was the first relativistic wave equation.
• However, Bethe and Jackiw's Intermediate Quantum Mechanics, originally written in 1964, does refer to the same equation as the Klein-Gordon equation.
• Klein and Walter Gordon were thus eventually honoured with having the equation named after them, though it seems to have taken over a quarter of a century to receive the honour.
• Oddly enough, Schrödinger himself privately developed a relativistic wave equation from his original wave equation, which, in reality, was not that difficult to do, and did so prior to Klein and Gordon, though he never published his results.
• But, nonetheless, it was an important point in quantum theory and, along with his unification theory, was to ensure a lasting legacy for Klein and cemented 1926 as a pivotal year in his life.
• In the years following 1926, Klein turned to teaching and continued his research, though possibly at a reduced pace.
• In 1927, Klein was appointed Lektor in Copenhagen but nonetheless continued his research working with Pascual Jordan on the second quantization in quantum mechanics.
• It was known that second quantization guarantees that photons obey Bose-Einstein statistics, but Klein showed that second quantization is not confined to free particles only.
• He and Jordan showed that one can quantize the non-relativistic Schrödinger equation and, in honour of this work, he was the recipient of yet another named mathematical tool, the Jordan-Klein matrices.
• Despite the so-called Klein paradox, that being that the positron was not completely understood by physicists, he was able to convince physicists of the soundness of Dirac's relativistic wave equation.
• His continued work included the quantum mechanics of the second law of thermodynamics and Klein's lemma.
• During the 1930s, Klein helped many refugee physicists who were expelled from Germany and other nations largely due to their Jewish heritage.
• Of the many he helped, one included Walter Gordon who would later join Klein in being the beneficiaries of the named equation we have just discussed.
• In 1943, Klein also aided in Bohr's escape from Copenhagen.
• During the 1930s Klein also found time to attend conferences, not the least of which included the 1938 Warsaw Conference where he spoke on (almost) non-Abelian gauge theories.
• It was at this conference that Klein suggested that a spin -1 particle mediated beta decay and played a role in weak interactions in a similar manner to the photon in electromagnetism.
• Klein's hypothesis was yet another crack at a unified field theory, this time in attempt to unify the strong, weak, and electromagnetic forces.
• In the 1940s Klein worked on a wide variety of subjects including superconductivity (with Jens Lindhard in 1945), biochemistry, universal ppp-decay, general relativity, and stellar evolution.
• In the 1950s and 1960s Klein remained active, addressing the 11th Solvay Conference in 1958, developing a new model for cosmology in conjunction with Hannes Alfven in 1963, and tackling Einstein's General Relativity in a paper published in Astrophisica Norvegica in 1964.
• Oskar Klein died in Stockholm, one of the finest theoretical physicists of the twentieth century.

Born 15 September 1894, Mörby, Stockholm, Sweden. Died 5 February 1977, Stockholm, Sweden.

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive