On the Quantum Theory of Molecules: Rigour, Idealization, and Uncertainty

TL;DR

This paper defends the quantum mechanical validity of Born-Oppenheimer methods in molecular theory, addressing philosophical claims about their inconsistency with fundamental quantum principles.

Contribution

It provides a rigorous analysis showing Born-Oppenheimer methods are consistent and fully quantum, countering philosophical criticisms about their validity.

Findings

Born-Oppenheimer methods are mathematically rigorous.

They are consistent with Heisenberg uncertainty relations.

The paper proposes a philosophy of quantum chemistry aligned with scientific practice.

Abstract

Philosophers have claimed that: (a) Born-Oppenheimer approximation methods for solving molecular Schr\"odinger equations violate the Heisenberg uncertainty relations; therefore, (b) `quantum chemistry' is not fully quantum; and (c) therefore chemistry does not reduce to physics. This paper analyses the reasoning behind Born-Oppenheimer methods and shows that they are internally consistent and fully quantum mechanical, contrary to (a)-(c). Our analysis addresses important issues of mathematical rigour, physical idealization, reduction, and classicality in the quantum theory of molecules, and we propose an agenda for the philosophy of quantum chemistry more grounded in scientific practice.