The Conceptual Development of Early Quantum Theory

          @misc{ pirsa_PIRSA:25100070,
            doi = {10.48660/25100070},
            url = {https://pirsa.org/25100070},
            author = {},
            keywords = {Quantum Foundations},
            language = {en},
            title = {The Conceptual Development of Early Quantum Theory},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100070 see, \url{https://pirsa.org}}
          }
          

Abstract

I will review conceptual advances which paved the way for the emergence of the mature form of quantum theory (quantum mechanics) in 1925-27, focusing on the contributions of Albert Einstein [1,2]. I argue that Einstein’s 1905 paper on light quanta was motivated by his firm belief that equipartition of energy was inescapable within classical statistical mechanics. Moreover, his rejection of the ether in his work on Special Relativity freed physicists to accept the possibility of wavelike phenomena not supported by a medium. Einstein in his 1907 paper on the specific heat of solids, became the first important physicist to embrace clearly the quantization of energy, strengthening his conclusion that a radical revolution in all of physics (not just electromagnetism) was upon us. In 1909 Einstein was able to derive the first rigorous result in quantum statistical mechanics, his energy/momentum fluctuation formula, which strongly supported the necessity of wave/particle duality in the new physics. Bohr in 1913 was able to explain the hydrogen spectrum in terms of quantization of electron orbits, but at the expense of accepting the possibility of accelerating charges which do not radiate, a result that Einstein found puzzling. In 1916-7 Einstein introduced fundamental randomness into quantum theory via the hypothesis of spontaneous emission. Shortly thereafter he generalized the Bohr-Sommerfeld quantization rules by putting them in a topological form but noticed that they didn’t seem to work for what we now call chaotic systems [3]. When Heisenberg eventually replaced the semiclassical quantization rules with a discrete generalization in matrix mechanics in 1925 he unwittingly escaped this limitation, something which does not appear to have been appreciated in the historical literature. Independently of these developments, De Broglie and Bose inspired Einstein in 1925 to develop a quantum statistical mechanics of indistinguishable atoms with wave-particle duality. This work directly motivated Schrodinger to investigate a wave equation describing electrons and eventually to discover his equation for the complex wave function of the electron at the beginning of 1926, which resolved the puzzle of non-radiating charges in hydrogen