When Heisenberg met Einstein
A mere 24 years old, Werner Heisenberg (1901-76) in 1925 developed a treatment of electron behavior based solely on directly observable quantities such as the frequencies of light that atoms absorb and emit. Recovering from hay fever on the island of Heligoland, "still very uncertain about it", Heisenberg in July 1925 sent his manuscript to Max Born (1882-1970) for review. Upon reading Heisenberg’s paper, Born realized that in Heisenberg’s new formulation, the classical variables of position and momentum could be represented by matrices which can be multiplied together like numbers, albeit with the crucial difference that the order of multiplication matters. The first conceptually autonomous and logically consistent formulation of quantum mechanics had been born. Heisenberg’s formulation accounted for quantum jumps, thereby supplanting Niels Bohr (1885-1962)’s model of electron orbits by interpreting the physical properties of particles as matrices that evolve over time.