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<p><b>New page</b></p><div>{{Audience_Sidebar<br />
| difficulty = Foundational<br />
| reading_time = 8 minutes<br />
| prerequisites = [[Psionics_Primer]]; [[Kaluza-Klein_Theory]]; basic quantum mechanics.<br />
| if_too_advanced_see = [[Psionics_Primer]]<br />
| if_you_want_the_math_see = [[Kaluza-Klein_Theory]]; [[Klein-Gordon_Equation]]<br />
}}<br />
<br />
{{Person_Vital_Stats<br />
| name = Oskar Benjamin Klein<br />
| birth = 15 September 1894 (Danderyd, Sweden)<br />
| death = 5 February 1977 (Stockholm)<br />
| nationality = Swedish<br />
| field = Theoretical physics; quantum mechanics; mathematical physics<br />
| affiliation = Niels Bohr Institute (Copenhagen) → Lund → University of Stockholm<br />
| key_works = Klein 1926a; Klein 1926b; Klein-Nishina 1929<br />
| era = Early-to-mid 20th century<br />
}}<br />
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== Summary ==<br />
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'''Oskar Klein''' was a Swedish theoretical physicist who made foundational contributions across multiple areas of 20th-century physics:<br />
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* The '''Klein-Gordon equation''' (1926) — the first relativistic quantum wave equation.<br />
* '''Compactification of the fifth dimension''' (1926) — the geometric mechanism that completes [[Kaluza-Klein_Theory|Kaluza-Klein theory]].<br />
* The '''Klein-Nishina formula''' (1929, with Yoshio Nishina) — quantum electrodynamic Compton scattering cross-section.<br />
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Klein's compactification mechanism is the structural basis for all later higher-dimensional unification, and his Klein-Gordon equation is the natural starting point for any scalar field theory — including the [[Psi_Field|ψ field]] of the [[Psionics|psionic framework]].<br />
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== Life ==<br />
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Klein was born in 1894, son of the chief rabbi of Stockholm. He studied at the Stockholm University and received his doctorate in 1921. He spent formative years at Niels Bohr's institute in Copenhagen, then short positions in Lund and Michigan, before settling at the University of Stockholm in 1931, where he remained until retirement in 1962.<br />
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== Key Contributions ==<br />
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=== Klein-Gordon equation (1926) ===<br />
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Klein independently formulated (with Vladimir Fock, Walter Gordon, Erwin Schrödinger, Theodor de Donder, and Louis de Broglie all contributing variants) the relativistic scalar wave equation:<br />
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:<math>(\Box + m^2)\,\psi = 0</math><br />
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where □ = ∂<sup>μ</sup>∂<sub>μ</sub> is the d'Alembertian. The equation describes a relativistic scalar (spin-0) particle of mass m. It is the starting point for all scalar field theories.<br />
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=== Compactified fifth dimension (1926) ===<br />
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Klein's contribution to Kaluza-Klein theory: identifying the fifth dimension with a small circle of radius R. This explains why the fifth dimension is not directly observed (its scale is too small) and provides a quantisation mechanism: the Fourier modes around the compact dimension give a tower of states with masses m<sub>n</sub> = n/R.<br />
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This compactification mechanism is the conceptual ancestor of all modern higher-dimensional unification — string theory, M-theory, brane-world cosmology.<br />
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=== Klein-Nishina formula (1929) ===<br />
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With Yoshio Nishina, Klein derived the quantum-electrodynamic cross-section for photon-electron scattering (Compton scattering), one of the earliest predictions of relativistic QED.<br />
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=== Klein paradox ===<br />
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In 1929 Klein analysed relativistic-quantum scattering off a step potential, finding the apparent "Klein paradox" — transmission of particles into classically-forbidden regions, later understood as pair creation.<br />
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== Reception ==<br />
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Klein's work was foundational across multiple fields. He is considered one of the major theoretical physicists of the early 20th century; his absence from the Nobel Prize list reflects more the depth of competition than any judgment on his work.<br />
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The Oskar Klein Memorial Lectures, established 1988 in Stockholm, honour his legacy and have been given by Roger Penrose, Stephen Hawking, Edward Witten, and others.<br />
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== Bibliography ==<br />
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* Klein, O. (1926a). "Quantentheorie und fünfdimensionale Relativitätstheorie." ''Zeitschrift für Physik'' 37: 895–906.<br />
* Klein, O. (1926b). "The atomicity of electricity as a quantum theory law." ''Nature'' 118: 516.<br />
* Klein, O., Nishina, Y. (1929). "Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac." ''Zeitschrift für Physik'' 52: 853–868.<br />
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== See Also ==<br />
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* [[Theodor_Kaluza]]<br />
* [[Kaluza-Klein_Theory]]<br />
* [[Klein-Gordon_Equation]]<br />
* [[Paul_S_Wesson]]<br />
* [[Psi_Field]]<br />
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== External Links ==<br />
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* [https://en.wikipedia.org/wiki/Oskar_Klein Wikipedia: Oskar Klein]<br />
* [https://www.okc.albanova.se/ Oskar Klein Centre, Stockholm]<br />
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== References ==<br />
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* Klein 1926a, 1926b (above).<br />
* Klein, O., Nishina, Y. 1929 (above).<br />
* Ekspong, G. (ed.) (1991). ''The Oskar Klein Memorial Lectures, Vol. 1.'' World Scientific.<br />
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[[Category:Psionics biographies]]<br />
[[Category:Theoretical physicists]]<br />
[[Category:Kaluza-Klein founders]]</div>JonoThora