Curvature and Free will (part 1)
Posted: Wed Jul 23, 2008 5:48 am
I posted this a MA&D but it must have been a boring topic. Oh well. I'll try it here.
First a caveat. I am all for free will and I have felt the existential rush of an open future. But, physics seems to present a problem.
It starts off something like the following but gets more and more subtle as various philosophical points are raised and also as more physics is brought to the table.
Part of the point of the physics/philosophy that follows is that it seems to threaten our sense of free will and the sense that the future is open.
To start things off, let’s try and encapsulate some folk wisdom about time. It is usually thought, if only implicitly, that for every event (say the event of me seeing an explosion or deciding to sin), there is a division of time into the past, present and future relative to that event. It is also thought that there are three levels of reality here:
1. Real (0) The present is most definitely and clearly real. All events simultaneous with the explosion are completely real and definite.
2. Real (-1) The past is also real but in a weaker sense. Lincoln really was shot and the Berlin Wall really did fall. Those are real historical facts nestled solidly in the real past.
3. Real (+1) The events in the future are not real in that they do not (yet) exist. Furthermore, the set of future events is supposed to be open. There is, rather, a set of possible events and none are determined or yet real. Thus in this standard view, Real(+1) is actually unreal or at least not actual. It is thought that the structure of possible futures has a branching structure and depending in part on our choices we will go down one series of branches making those events first present, Real (0), and then past and thus Real (-1).
Now, it turns out that according to the highly successful special theory of relativity, the set of all events simultaneous with a given event (my “now”) is relative to my state of motion. In other words , there is no absolute fact of the matter about which events are in the past of a given reference event and which are in the present or future of the reference event.
But then the 3-fold ontological dichotomy above breaks down. There is no absolute present dividing past from future. It is also possible to show under mild assumptions, that the future must be just as real as the past. Real (-1) has the same definiteness as Real (+1). In fact, it looks like we are committed to a block universe picture of spacetime wherein the future is just as real as the past.
Another way of saying things is that there is no preferred way of slicing up the 4-d spacetime continuum into a series of “nows”, some of which are future and some of which are past. Such a slicing (think about space-time like a 4D loaf of bread) is called a foliation by space-like submanifolds (sorry for the jargon).
Now several other things must come in to play. One is quantum mechanics. Does it make a difference? (It seems not actually—at least not in a way that sounds anything less than bizarre). Second, it turns out that once gravitation is taken into account, the situation is mitigated slightly. This has to do with possibility of picking out a preferred notion of “now” intersecting any event and thus preferred notions of future and past. A curved spacetime that is symmetric enough can end up having a special foliation which could serve as our preferred way of reckoning what is past present and future and maybe allow some kind of resurrection of the notions of actual past and potential future. However, a closer look reveals that we don’t get off so easy.
First a caveat. I am all for free will and I have felt the existential rush of an open future. But, physics seems to present a problem.
It starts off something like the following but gets more and more subtle as various philosophical points are raised and also as more physics is brought to the table.
Part of the point of the physics/philosophy that follows is that it seems to threaten our sense of free will and the sense that the future is open.
To start things off, let’s try and encapsulate some folk wisdom about time. It is usually thought, if only implicitly, that for every event (say the event of me seeing an explosion or deciding to sin), there is a division of time into the past, present and future relative to that event. It is also thought that there are three levels of reality here:
1. Real (0) The present is most definitely and clearly real. All events simultaneous with the explosion are completely real and definite.
2. Real (-1) The past is also real but in a weaker sense. Lincoln really was shot and the Berlin Wall really did fall. Those are real historical facts nestled solidly in the real past.
3. Real (+1) The events in the future are not real in that they do not (yet) exist. Furthermore, the set of future events is supposed to be open. There is, rather, a set of possible events and none are determined or yet real. Thus in this standard view, Real(+1) is actually unreal or at least not actual. It is thought that the structure of possible futures has a branching structure and depending in part on our choices we will go down one series of branches making those events first present, Real (0), and then past and thus Real (-1).
Now, it turns out that according to the highly successful special theory of relativity, the set of all events simultaneous with a given event (my “now”) is relative to my state of motion. In other words , there is no absolute fact of the matter about which events are in the past of a given reference event and which are in the present or future of the reference event.
But then the 3-fold ontological dichotomy above breaks down. There is no absolute present dividing past from future. It is also possible to show under mild assumptions, that the future must be just as real as the past. Real (-1) has the same definiteness as Real (+1). In fact, it looks like we are committed to a block universe picture of spacetime wherein the future is just as real as the past.
Another way of saying things is that there is no preferred way of slicing up the 4-d spacetime continuum into a series of “nows”, some of which are future and some of which are past. Such a slicing (think about space-time like a 4D loaf of bread) is called a foliation by space-like submanifolds (sorry for the jargon).
Now several other things must come in to play. One is quantum mechanics. Does it make a difference? (It seems not actually—at least not in a way that sounds anything less than bizarre). Second, it turns out that once gravitation is taken into account, the situation is mitigated slightly. This has to do with possibility of picking out a preferred notion of “now” intersecting any event and thus preferred notions of future and past. A curved spacetime that is symmetric enough can end up having a special foliation which could serve as our preferred way of reckoning what is past present and future and maybe allow some kind of resurrection of the notions of actual past and potential future. However, a closer look reveals that we don’t get off so easy.