George Ellis is the Emeritus Distinguished Professor of Complex Systems in the Department of Mathematics and Applied Mathematics at the University of Cape Town in South Africa. He co-authored The Large Scale Structure of Space-Time (1973) with Stephen Hawking.

The French mathematician Pierre-Simon Laplace (1749-1827) believed that the Universe was a piece of machinery, and that physics determines everything. Napoleon, who had read up on Laplace’s work, confronted him about the conspicuous absence of a creator in his theory. ‘I had no need of that hypothesis,’ came the reply. Laplace might have said the same thing about free will, which his mechanistic universe rendered superfluous.

Since Laplace’s day, scientists, philosophers and even neuroscientists have followed his lead in denying the possibility of free will. This reflects a widespread belief among theoretical physicists that if you know the initial values of the variables that characterise a physical system, together with the equations that explain how these variables change over time, then you can calculate the state of the system at all later times. For example, if you know the positions and velocities of all the particles that make up a gas in a container, you can determine the positions and velocities of all those particles at all later times. This means that there should be no freedom for any deviation from this physically determined trajectory.

Consider, then, that everything we see around us – rocks and planets, frogs and trees, your body and brain – is made up of nothing but protons, electrons and neutrons put together in very complex ways. In the case of your body, they make many kinds of cells; in turn, these cells make tissues, such as muscle and skin; these tissues make systems, such as the heart, lungs and brain; and these systems make the body as a whole. It might seem that everything that’s happening at the higher, ‘emergent’ levels should be uniquely determined by the physics operating beneath them. This would mean that the thoughts you’re having at this very moment were predetermined at the start of the Universe, based on the values of the particle physics variables at that time.

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At very small scales, quantum theory underlies what’s happening in the world. Heisenberg’s uncertainty principle introduces an unavoidable fuzziness and an irreducible uncertainty in quantum outcomes. You might know the value of one variable, such as a particle’s momentum, but that means you can’t accurately detect another, such as its position. This seems to fundamentally undermine the allegedly iron-clad link between initial data and physical results. However, this is controversial, so I’ll set it aside for now, as important as it is. Instead, I’ll focus on key aspects of causation that occur in the molecular biology of neurons in the brain.

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