In Feynman’s Footsteps

Howard Burton, Nima Arkani-hamed A

Canizaro, Nicholas

We are not particles falling into a black hole, we are one wave, falling forever, and the light we see in the sky is only the interference of our own footsteps.

Daisuke Fujiwara

Richard F. W. Bader

A reading of the book of Dirac's life entitled The Strangest Man is a most stirring experience, bringing one back to the beginnings of quantum mechanics where every attempt was made "to establish a basis for theoretical quantum mechanics founded exclusively on relationships between quantities which are in principle observable." The prime movers in this quest were Heisenberg and Dirac. One of Dirac's most important contributions in the passage from classical to quantum mechanics, a passage that consumed much of his early efforts, was unfortunately published in an obscure Russian journal where it remained largely unread until it was found by Feynman while a graduate student at Princeton. The paper posed the question, "what corresponds in the quantum theory to the Lagrangian method of classical mechanics?", a method that, as Dirac pointed out, is clearly superior in the simplicity of its structure to that of the classical Hamiltonian approach. Dirac's partial answer to this question provided the key to solving the problem of introducing the action integral into quantum mechanics that occupied Feynman's mind, leading to his formulation of the path integral technique. His contribution was followed two years later by Schwinger's independently derived statement of the quantum action principle, each contribution providing a complete formulation of quantum mechanics stated in terms of single principle. The present paper points out that the successful introduction of the action principle into quantum mechanics made possible by Dirac, enables one to proceed still further by extending Schwinger's quantum action principle to an open system, to an atom in a molecule. Thus the quantum theory of an atom in a molecule has its roots in the question posed by Dirac in 1933. The paper proposes a return to a greater use of the theorems of quantum mechanics in interpretive chemistry from that begun by Slater in 1933, a staunch advocate of theory following in the footsteps of observation.

Etienne K. Klein

A Western woman takes up Chinese painting and discovers another way of being in the world through learning how to paint and about perspective in painting. Following in the footsteps of Shitao, one of the greatest Chinese painters, she embraces the world of mountains and water, allowing herself to gradually be transformed by what she sees.