Laplace's Demon

In 1814, Laplace proposed that the future is already written, and that all you need is a sufficiently large une intelligence (the demon is a later invention) and a sufficiently large piece of paper.

Nothing is uncertain. The future is not unknown, merely uncomputed. Free will is, at best, a rounding error.

Poincaré then showed that the solutions the demon is supposed to track are exponentially sensitive to initial conditions. Two states that differ by less than an atom diverge until they are, for all practical purposes, different universes. The demon requires infinite precision. The universe, one suspects, is not in the business of providing it. It has never once been in the business of providing it.

Heisenberg then showed that the two quantities the demon needs most (position and momentum, the very coordinates it would need to start) cannot be simultaneously specified. Not because our instruments are crude. Because the classical initial conditions the demon is asking for do not exist as a pair. The demon is handed an equation with missing variables and asked to call the gap uncertainty. One imagines it finding this mildly insulting.

But hasn't quantum mechanics slain the demon? Well, under the many-worlds interpretation, the wavefunction evolves deterministically, and the demon is alive and well. It simply cannot tell you which branch you are on. Under Bohmian mechanics, the particles have definite positions at all times, and the demon survives, though its paper now has to encode non-local correlations that have no classical analogue. Under Copenhagen, the demon opens the paper and finds it blank. The answer is not uncomputed. It does not exist until someone asks. The question of whether the universe is deterministic is not a settled question. It is an interpretation question, and the interpretations disagree.

The second law of thermodynamics gives the universe an arrow of time that the microscopic equations do not. And this is the part that is slightly embarrassing for the demon, because the microscopic equations are time-reversible. The demon can run them backwards. It will. It will produce a perfectly valid solution in which the cup of tea uncools, the steam reassembles itself, and the whole thing becomes, to anyone who actually wants to know what happens next, absolutely useless. The arrow of time is not in the equations. It is in the fact that you are not tracking every molecule. The demon's answer is correct. The demon's answer is also no answer.

Seth Lloyd did the arithmetic. The observable universe, over its entire history, could have performed at most 10¹²⁰ elementary operations on 10⁹⁰ bits. The demon, being a physical object, is subject to the same limit. It does not have enough paper. It does not have enough time. It does not, in fact, have enough of anything.

The question, then, is whether determinism and predictability are the same thing. A universe can be fixed in every detail and still be, to every observer inside it, a complete mystery. Is determinism a property of the universe, or a property of our models? That is the question we will be arguing about.

Location will be announced next. Possibly West End, and not too far from the CBD.

Join the chat: https://smp18.simplex.im/g#mgR_AjYqVsxwGX5A1mmT-7rc2wWmNC9ROLw3Q0qFKYY