page_title: Fine-structure constant
section_title: History
hierarchical_section_title: Fine-structure constant / History
caption_attribution_description: Deutsch: Büste Arnold Sommerfeld, München, LMU, Theresienstr. 37
context_page_description: In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted by α, is a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity related to the elementary charge e, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4πε₀ħcα = e². As a dimensionless quantity, its numerical value, approximately, is independent of the system of units used.
  While there are multiple physical interpretations for α, it received its name from Arnold Sommerfeld introducing it in extending the Bohr model of the atom: α quantifies the gap in the fine structure of the spectral lines of the hydrogen atom, which had been precisely measured by Michelson and Morley.
context_section_description: Based on the precise measurement of the hydrogen atom spectrum by Michelson and Morley in 1887, Arnold Sommerfeld extended the Bohr model to include elliptical orbits and relativistic dependence of mass on velocity. He introduced a term for the fine-structure constant in 1916. The first physical interpretation of the fine-structure constant α was as the ratio of the velocity of the electron in the first circular orbit of the relativistic Bohr atom to the speed of light in the vacuum. Equivalently, it was the quotient between the minimum angular momentum allowed by relativity for a closed orbit, and the minimum angular momentum allowed for it by quantum mechanics. It appears naturally in Sommerfeld's analysis, and determines the size of the splitting or fine-structure of the hydrogenic spectral lines.  This constant was not seen as significant until Paul Dirac's linear relativistic wave equation in 1928, which gave the exact fine structure formula.
  With the development of quantum electrodynamics (QED) the significance of α has broadened from a spectroscopic phenomenon to a general coupling constant for the electromagnetic field, determining the strength of the interaction between electrons and photons. The term  is engraved on the tombstone of one of the pioneers of QED, Julian Schwinger, referring to his calculation of the anomalous magnetic dipole moment.
caption: Sommerfeld memorial at University of Munich
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