Epilogue

Summary

Heisenberg's research style was to seek a new theory through correspondence-limit procedures to extend the concept of intuition into ever-smaller spatial domains. This approach had been incredibly successful in 1925 (invention of quantum mechanics), 1932 (invention of exchange forces in nuclear theory), and in 1934 it provided optimism (density-matrix formalism). Developments of Heisenberg's 1943 S-matrix formalism, particularly by Dyson (1949a,b), would lead to far-reaching results.

By 1943 Heisenberg judged the situation in physics as serious enough to warrant return to his strategy of 1925 in combination with the ‘fundamental length’ (Heisenberg 1943a). He proposed to replace the existing quantum electrodynamics with the S-matrix formalism based on only measurable quantities like cross-sections that could be calculated from the initial and final states of scattering processes. He hoped that the S-matrix could provide the means to penetrate interaction distances less than the fundamental length.

In Heisenberg's opinion the crux of basic problems in elementary particle physics was the Hamiltonians from classical physics which were essentially for point particles. We have seen this opinion surface in Heisenberg's letters of 12 March 1934 to Bohr (Section 4.7.3), and 5 February 1934 to Pauli, where Heisenberg proposed a new Hamiltonian that contains ‘measurable quantities’. It is also part of the view of Heisenberg and Pauli which appears from time to time according to which correspondence-limit arguments between quantum electrodynamics, quantum mechanics and classical physics fail (for example, letters of Pauli to Peierls, 18 June 1929 in Section 3.2 and Heisenberg, 1930, analyzed in Section 4.2).