A couple years ago I had some interesting conversations with a colleague, Steve, in the philosophy department. He wanted to talk to a science person about determinism – are all future things predictable (in principle, at least) if we had perfect knowledge of the present. Apparently this is a conundrum that has kept philosophers busy for quite a while.
In a classical-mechanics viewpoint, determinism looks nice. We know that if we throw a stone upward at a certain angle and with a certain speed it will go in a certain trajectory and land at a well-defined area. If necessary, you can correct for air resistance and even the rotation of the earth under the flying rock to refine the landing point, a factor which is important to long-range artillery fire for example. And in chemistry, we certainly do a lot of labs that are basically deterministic – if you add X to Y you get Z.
But Steve’s philosophical need to fully define determinism collides with both chaos models and quantum mechanics and the inherent uncertainty they both generate. Determinism works far better in hindsight than in the real world. And it works fine for classical mechanics in simple systems. But it fails when moving to the real world.
A deterministic model of gas behavior, for instance, says that in a sample of air, if we know the exact position and motion of every gas molecule – that’s nine quantities per atom (3 coordinates of position, 3 vectors for motion, and 3 more for angular momentum) – we can predict where every single one of them will be an instant later, and an instant after that, and so forth. We’ll have to, for now, neglect the ludicrous amount of computing power that would require.
The chemist would say, who cares. Since one nitrogen molecule is just like another, all we really need are the macro parameters of the sample. But that’s ducking the determinism question. Positing a computer capable of doing the calculations, does it work?
I suggest that the answer is NO. Suppose just one of those atoms in the air sample was radon, which is radioactive. If the atom decays, it will spit out an atom of polonium and an alpha particle. Those will have different trajectories and energies than the radon atom did. But if it doesn’t decay, it continues along the same path at least for a few more microseconds.
The determinist answers, “But, how do we know radioactive decay is not itself deterministic?” In that case, given the correct data about the subatomic particles, we should be able to predict not just the exact moment of decay but the velocities of the decay products which gives us new information for the future state of the system. Okay, so now the computation problem has been expanded by several orders of magnitude.
Einstein famously hated quantum uncertainty. “God does not play dice with the universe” Most likely, he suspected that there was something deterministic behind the randomness and wave-function models of quantum. So far, nobody has been able to find it and the truly random model seems to work the best.
Perhaps in a future post I’ll think about the information theory issues with the computation problems described – particularly the self-referential paradox of Gödel.