matter was well. Specifically, he proposed that electrons too have wave-like characteristics, and even suggested a formula for their wavelengths. Most of his colleagues ignored these wild and unsupported claims, but Einstein, who had a reliable intuition about physics, wrote "I believe it is the first feeble ray of light on this worst of our physics enigmas." Einstein turned out to be right" de Brogile had discovered the secret of matter. But as de Brogile himself admitted in his thesis, unless experimental proof could be found, his theory would remain useless speculation. The roaring twenties were a boisterous era of prosperity, fast cars, jazz, popular radio, and illegal drinking. Before they ended with the crash of the stock market in 1929, which triggered the Great Depression, the twenties produced such human and technological accomplishments as the invention of television and the jet engine, and the first transatlantic solo flight by Charles Lindbergh in 1927. Out of range of public clamor, this exhilaration atmosphere also produced what might be called the greatest achievement of quantum mechanics. Frustrated by the inconsistencies of the patchwork quantum theory pioneered by Einstein and Bohr, the 23 year old German physicist Werner Heisenberg started from scratch. In the summer of 1925 he decided that atoms should be described without assuming anything about unmeasurable quantities such as the positions and speeds of electrons inside atoms. instead, he arranged the measurable quantities, such as the discrete frequencies of light emitted by the atom, in arrays of number not unlike spreadsheets. By manipulating these spreadsheets, which mathematicians call matrices, Heisenberg was able to recover the successes of the older quantum theory, without encountering its contradictions. Heisenberg's matrices give the right answers, but convey no visual image of the interior of the atom. in the winter of 1925-26 the Austrian ...
