Archive for February, 2012

Where the randomness comes from

Tuesday, February 21st, 2012

For perhaps 200 years it was possible to believe that physics gave a picture of the world with no place for randomness. Newton’s laws prescribe a picture of nature that is completely deterministic – at any time, the future is completely specified by the present. For anyone attached to the idea that they have some control over their destiny, that the choices they make have any influence on what happens to them, this seems problematic. Yet the idea of strict physical determinism, the idea that free will is an illusion in a world in which the future is completely predestined by the laws of physics, remains strangely persistent, despite the fact that it isn’t (I believe) supported by our current scientific understanding.

The mechanistic picture of a deterministic universe received a blow with the advent of quantum mechanics, which seems to introduce an element of randomness to the picture – in the act of “measurement”, the state function of a quantum system discontinuously changes according to a law which is probabilistic rather than deterministic. And when we look at the nanoscale world, at least at the level of phenomenology, randomness is ever-present, summed up in the phenomenon of Brownian motion, and leading inescapably to the second law of thermodynamics. And, of course, if we are talking about human decisions (should we go outside in the rain, or have another cup of tea?) the physical events in the brain that initiate the process of us opening the door or putting the kettle on again are strongly subject to this randomness; those physical events, molecules diffusing across synapses, receptor molecules changing shape in response to interactions with signalling molecules, shock waves of potential running up membranes as voltage-gated pores in the membrane open and close, all take place in that warm, wet, nanoscale domain in which Brownian motion dominates and the dynamics is described by Langevin equations, complete with their built-in fluctuating forces. Is this randomness real, or just an appearance? Where does it come from?

I suspect the answer to this question, although well-understood, is not necessarily widely appreciated. It is real randomness – not just the appearance of randomness that follows from the application of deterministic laws in circumstances too complex to model – and its ultimate origin is indeed in the indeterminism of quantum mechanics. To understand how the randomness of the quantum realm gets transmitted into the Brownian world, we need to remember first that the laws of classical, Newtonian physics are deterministic, but only just. If we imagine a set of particles interacting with each other through well-known forces, defined through potentials of the kind you might use in a molecular dynamics simulation, the way in which the system evolves in time is in principle completely determined, but in practise any small perturbation to the deterministic laws (such as a rounding error in a computer simulation) will have an effect which grows with time to widen the range of possible outcomes that the system will explore, a widening that macroscopically we’d interpret as an increase in the entropy of the system.

To understand where, physically, this perturbation might come from we have to ask where the forces between molecules originate, as they interact and bounce off each other. One ubiquitous force in the nanoscale world is known to chemists as the Van der Waals force. In elementary physics and chemistry, this is explained as a force that arises between two neutral objects when a randomly arising dipole in one object induces an opposite dipole in the other object, and the two dipoles then attract each other. Another, perhaps deeper, way of thinking about this force is due to the physicists Casimir and Lifshitz, who showed that it arises from the way objects modify the quantum fluctuations that are always present in the vacuum – the photons that come in and out of existence even in the emptiest of empty spaces. This way of thinking about the Van der Waals force makes clear that because the force arises from the quantum fluctuations of the vacuum, the force must itself be fluctuating – it has an intrinsic randomness that is sufficient to explain the randomness we observe in the nanoscale world.

So, to return to the question of whether free will is compatible with physical determinism, we can now see that this is not an interesting question, because rules that govern the operation of the brain are fundamentally not deterministic. Of course, the question of how free will might emerge from a non-deterministic, stochastic system isn’t of course a trivial question either, but at least it starts from the right premise – we can say categorically that strict physical determinism, as applied to the operation of the brain, is false. The brain is not a deterministic system, but one in which randomness is central and inescapable to its operation.

One might go on to ask why some people are so keen to hold on to the idea of strict physical determinism, more than a hundred years after the discoveries of quantum mechanics and statistical mechanics that makes determinism untenable? This is too big a question for me to even attempt to answer here, but maybe it’s worth pointing out that there seems to be quite a lot of of determinism around – in addition to physical determinism, genetic determinism and technological determinism seem to be attractive to many people at the moment. Of course, the rise of the Newtonian mechanistic world-view occurred at a time when a discussion about the relationship between free will and a theological kind of determinism was very current in Christian Europe, and I’m tempted to wonder whether the appeal of these modern determinisms might be part of the lingering legacy of Augustine of Hippo and Calvin to the modern age.