More is Different

The reductionist hypothesis does not by any means imply a “constructionist” one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.

Earlier, I mentioned Anderson’s idea of more is different. This is a really important idea, although in some sense rather obvious. Obviously we can’t derive biology from quantum electrodynamics (obvious to anyone who knows biology or quantum electrodynamics). Obviously there is a huge gap between these subjects, despite the assumption of the reductionist hypothesis. Understanding where this gap comes from is about understanding how a quantitative difference (the difference in number between the handful of particles in a particle physics experiment compared to the many, many particles in a cat) creates qualitative differences (entirely different concepts, laws, and equations are needed to describe many-particle systems (the cat) than to describe the particles the cat is made of). In solid-state physics (many-electron physics), these qualitative differences arise through the process of spontaneous symmetry breaking. This transition is well-understood, but other transitions (between neuroscience and cognitive science, for example) are not understood in such neat terms. More is different is also true at the transition from the quantum world to the classical world. As I understand it, decoherence provides the mechanism for spontaneous symmetry breaking in many-particle systems. This is important stuff. Anyone who thinks they want to study particle physics or cosmology because they are more fundamental should consider how small the domain of “fundamental” science really is.

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