About a year ago, CVM and I exchanged a series of emails on the fruitless topic of free will and determinism. It transpired that I argued that, well, determinism is inconsistent not just with quantum mechanics (as any sophomore philosopher knows), but also relativity in an inflationary universe. I thought I should post the key paragraphs for posterity.
Well, the reference to Kant at the end of my last message was not flippant. The free-will/determinism antinomy is interesting but I think lies in the same category as our intuitions that the universe is infinite and that it has an intelligent designer. Which is to say, from the standpoint of ‘pure reason’ one might make the argument that there is a contradiction between free will and determinism but in light of the nature of the universe we live in, it’s not much of a paradox.
Have you ever read Alan Lightman’s book, Einstein’s Dreams? It’s a delightful little book. He tells 30 stories describing the experience of time in different possible, or at least imaginable, universes. One of those happens to coincide with the way our universe actually is, i.e. objects moving quickly experience time dilation. What you are proposing as “that annoying apparent contradiction between determinism and free will” pertains to some universe other than the one we inhabit.
Just in case you are thinking I am getting back to quantum mechanics being the camel’s nose that enables free will to sneak back into the ontological tent, let me point out that, as I see it, relativity provides just as much of a challenge to determinism as does quantum mechanics. The reason is thus: I propose that the principle of determinism states that if the initial states of all the particles and fields composing a system can be measured precisely, the future state of the system will be determined. Set aside quantum mechanical uncertainty for the moment. This determinism principle is not consistent with relativity. As you know, special relativity dictates that there are three topologically distinct regions of spacetime associated with any point in 4-space: the absolute future, the absolute past, and the absolute elsewhere. These regions are separated by the light cones forward and back attached to the point. Now, any state that is to be “predicted” must lie in our absolute future, that is, it must be contained in the forward part of our light cone. The crucial point is this: that future state will be influenced by particles and fields that lie in our absolute elsewhere, that is, outside our current light cone.There is no way — not even in principle — to ascertain the states of those particles and fields because we have never been in contact with them before. When you look up at night and see starlight (well, you might have to leave the City), those photons were traveling on a light cone that merged with your worldline only in the instant they entered your eye, not before — until that instant you could not have accounted for their existence in calculating a deterministic future. Of course, the photons are on the light cone, but the reasoning also applies to any massive particle traveling towards you at nearly the speed of light (say, the solar neutrinos that left the sun eight minutes ago and are only now weakly interacting with your electrons). And a curious footnote to this observation is that all those massive ‘elsewhere’ particles, because of the relativity of simultaneity, could be in the future or in the past, depending on the frame of reference you choose.
So I believe relativity is at least as insurmountable an obstacle as quantum mechanics to a principle of determinism.
I challenge you to come up with a reasonable formulation of the principle of determinism that is consistent with the universe we live in. Until then, I don’t see what the problem is. We don’t live in a deterministic universe.
Monday, 12 July 2010 at 17:27
I would say that your relativistic indeterminism is not the same thing as quantum mechanical indeterminism. The difference is that even though one observer cannot, in principle, determine an event in his future if it will also be influenced by events outside his past light cone, the requirement for consistency means that only one future is possible, even though it is not determinable, because the future event has to be consistent with all of the influences from its past light cone, which includes those events in spacetime not accessible to the predictor at the time of the prediction.
Suppose I am aware of event A and predict from it that either event B or event C will happen, but which one will happen is not then determinable by me, because I do not know which of event D of event E (assume they are mutually exclusive), separated from me by a spacelike interval at the time of my prediction, will influence the result. However, the result must be consistent with whichever of event B or event C has happened in its past.
Only one result is actually possible. It is predetermined by the state of the universe before event D or E, but it is not determinable by me because my local nature restricts my access to information (here, I discount the function of quantum mechanics and speak a universe which is only relativistic).
This is why I would say that a relativistic universe is indeterminable rather than indeterminate.
Now there is a requirement for consistency with quantum mechanics as well, in that the result of an observation at A affects the wavefunction of all entangled entities everywhere, so that observations involving them must be consistent with the observation at A.
But in this case, knowledge of the state of the entire universe in the past of event A (rather than just locally accessible information) would still not allow a prediction to be made.
So I would say that a QM universe is indeterminate, whereas a relativistic universe is indeterminable.