Part Two: Quantum Theory

Terry Bristol

Feynman insisted 'no one understands quantum theory'. Yet, experimentalists tell us quantum theory is the most successful theory in history. Quantum theory cannot be understood as a classical mechanical theory since it arose through the 'interpolation' of two highly successful but complementary classical mechanics: Newtonian particle mechanics and Maxwellian wave mechanics. The two-slit experiment illustrates that what is experienced depends on choice of experimental set-up. Quantum theory is properly understood within the more general framework of engineering thermodynamics. In Part One, I point to four essential characteristics of quantum theory that cannot be understood in any framework defined by the classical mechanical presuppositions of symmetry and conservation. These four characteristics are the participatory, the complementary, the indeterminate and the new non-commutative geometry. In Part Two, articulating engineering thermodynamics, I note there are two histories and two formulations of thermodynamics: Carnot's engineering thermodynamics and the 'rational mechanical' tradition of Clausius-Boltzmann. These four essential characteristics of quantum theory are also characteristics of engineering thermodynamics. In Part Three, I trace the precursors of Lazare Carnot's engineering thermodynamics to earlier insights of Huygens, d'Alembert, Leibniz and the Bernoullis. Leibniz brought these forth in his meta-paradigm shift from Statics to Dynamics. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.

Peter Atkins, Julio de Paula, James Keeler

Xin Guo

The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains diagonal elements of Fock space from the interacting terms, which is different from the standard procedure of previous perturbation method. In this letter, we use the adaptive perturbation theory to extract the solvable elements in the two-particle system and obtain the energy spectrum of the solvable part. Then, we diagonalize the Hamiltonian to obtain the numerical solution. Finally, we compare two kind of values. The results show that the adaptive perturbation theory can be well applied to the strong coupling regime of two-particle system, and on the whole, with the increase of quantum number, two values are closer.

Maurice Ebison

J Mehra and H Rechenberg 1982 Berlin: Springer Part 1 xlvii + 372 pp price DM75 ISBN 3 540 90642 8, Part 2 vi + 878 pp price DM85 ISBN 3 540 90667 3 These two volumes, which are the first of a massive ten-part enterprise, provide an exhaustive treatment of the foundation of quantum theory by Planck, Einstein, Bohr and Sommerfeld and the advent of its difficulties in the first quarter of the 20th century. The chief aim of the authors was to use the written resources and the recollections of leading physicists to describe the main ideas of and events in the birth of quantum theory.

Tom Purves