We assume the world is made of particles, but this is mistaken at even the most fundamental levels of science, argues Olimpia Lombardi, a leading philosopher of science and critic of the idea of “a theory of everything.” The interactions and transformations of chemical substances cannot be explained in terms of the sub-atomic particles that make them up. Quantum mechanics, our best theory of these particles, cannot account for what happens when substances interact, from rusting to combustion. The realm of chemical transformations appears to be independent of the realm of physical things.

Physics describes the dynamics of material bodies. It studies objects, and asks why they move around in the ways that they do, relying on properties like position, velocity and mass. Chemistry, on the other hand, focuses on the behavior and reactions of so-called “substances.” Substances are not objects—they are the stuff that macroscopic objects are made of. They are characterized in terms of certain observable properties, such as color, melting point and boiling point, and the ways that they interact with—transform and are transformed by—other substances. Thus, instead of asking about the position, velocity and mass of objects, chemists ask about the transformations induced by chemical reactions between substances, such as combustion and oxidation, and they explain these transformations in terms of the structure of the molecules that make up the substances.

Are chemical transformations between substances ultimately explicable in terms of the dynamics of material bodies that physics studies? Is chemistry just the physics of complex objects? One might think so. After all, chemical substances are composed of molecules, studied by molecular chemistry, and molecules are composed of atoms, and atoms in turn are composed of subatomic particles studied by quantum mechanics. Therefore, molecules and the substances they compose should be describable in quantum‑mechanical terms—how could it be otherwise? However, when one examines the technical details of these two scientific domains, matters prove to be far less straightforward: the descriptions offered by molecular chemistry and quantum mechanics are not fully compatible, and they exhibit tensions that cannot be ignored.

Chemistry is not just complex physics

There is a heated debate about the relationship between chemistry and physics. Although chemistry developed historically as a discipline independent from physics, the spectacular success of quantum mechanics led to the widespread belief that chemistry can ultimately be completely explained by physics. Paul Dirac’s famous remark has become emblematic of this perspective:

"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry [are] completely known from quantum mechanics."

From this viewpoint, the chemical world is made up of physical items, whose peculiarity is only that they are highly complex. Unfortunately, the situation is not that simple, in part because quantum items exhibit peculiarities that render them entirely different from classical objects, whereas chemistry continues to use a classical framework. Although the field of quantum chemistry makes extensive use of standard quantum mechanics, it combines it with classical assumptions that underlie its most successful models.

This is especially clear when it comes to the nature of molecular structure. In chemistry, molecular structure is the main factor used to explain the chemical properties of substances and the reactivity between substances. The structure that matters is largely geometrical, defined by the relative spatial relations between the nuclei of the molecule’s atoms.