Copenhagen Quantum Mechanics

TL;DR

This paper revisits Copenhagen quantum mechanics, integrating modern measurement theory and decoherence to present a more satisfying interpretation that explains wave function collapse as a bookkeeping device and explores the emergence of classicality.

Contribution

It offers a reinterpretation of Copenhagen quantum mechanics by combining early ideas with decoherence and measurement theory, providing new insights into wave function collapse and classical emergence.

Findings

Wave functions spread rapidly in chaotic systems, making Schrödinger cat states common.

Conditioned states depend on measurement type, illustrating quantum jumps and smooth behaviors.

Classical mechanics and thermodynamics emerge from quantum principles through decoherence.

Abstract

In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.