## Sunday, March 8, 2015

### A wacky metaphysics of time for deterministic physics

Consider a deterministic physical theory on which for each t>0 there is a time-evolution operator Ut on set of all instantaneous states of the universe (i.e., global phase space), so that if u is the state of the universe at time t1, then Utu is the evolved state of the universe at t1+t. For example, Everett-style no-collapse quantum mechanics or Newtonian physics without situations like Norton's dome.

Suppose there is a first moment of time, call it time 0. Here, then, is an odd metaphysics to go with the theory. The universe fundamentally has some initial state. Then what it is for the universe to be in state v at a time t>0 is nothing else than for v to equal Utu0, where u0 is the initial state.

For a simple example, suppose that we have a simple Newtonian theory with point particles and no forces. Then what it is for a particle to be at location x at time t>0 just is for the particle to have an initial momentum p0, initial location x0 and initial mass m0 such that x=x0+(p0/m)t.

On this wacky metaphysics, later states are not caused by the initial state, but are metaphysically grounded in the initial state.

What are the merits of this kind of a weird theory? Well, it has a lot of fundamental simplicity:

• Fundamental reality is only three dimensional, and facts about later times are just mathematically derivative from the fundamental facts.
• At the fundamental level of description there is no such thing as time.
• There is no need for causation, laws of nature or nomic simplicity. Temporal evolution just is a matter of metaphysical necessity. Later states reduce to earlier ones.
Yet, we can have genuine explanatory relations between times. If the Ut operator has the right kind of mathematical definition in terms of differential equations, we will be able to say that the state of the universe at time t2 is explained by the state of the universe at an earlier t1 which in turn is explained by the state at time 0. The explanation is reductive or metaphysical rather than nomic. Thus the number of types of explanation is reduced.

This is, of course, very wacky. But if one doesn't take our intuitions about modality (say, the metaphysical possibility of miracles, which is ruled out on this account), the fundamental existence of persons, free will, and the like, and one has a deterministic theory, it is hard to avoid falling into a theory like this. Simplicity does, after all, strongly favor it.

The above formulation assumes an initial moment of time, but I think one can formulate it in terms of limiting conditions if one's deterministic theory doesn't have an initial moment.

I've noticed that for a while I've been unconsciously pursuing a curious research project. The research question is something like this: If one throws anthropocentric intuitions to the winds, what sort of interpretations of physics would one take seriously? Call this the estrangement (ostranenie) project. The point of the project is to take estranging approaches to their logical conclusion, and see where they lead. The lesson I am drawing is that when one abandons the kinds of anthropocentric approaches that Aristotelian metaphysics uses, one must go much further, and much stranger, than most people are willing to go.

Heath White said...

I will agree that this is very far and very strange.

But is observation, "the way things look," one of your shuffled-off anthropocentric coils? Because surely the best argument that things are not the way you describe, now at t>>>0, is that they don't seem to be that way.

Or am I missing something?

Alexander R Pruss said...

I am not sure what you mean by saying things don't seem that way. On this interpretation particles are where they seem to be. But what grounds the statement that they are there are the "initial" conditions. But grounding facts are not meant to be apparent.

Heath White said...

I think I misunderstood your intent. I had the idea that the universe was a single frozen 3D timeslice, with an extra metaphysical "law of nature", so that "later" states of the universe were just mathematical functions of the "initial" state.

Alexander R Pruss said...

Yes, that was my intent. But this doesn't affect the truth of any physics statements about later times. It only affects what makes these statements be true.

Alexander R Pruss said...

I suspect that the theory will require something like multiple worlds. There are many Ut-style operators, corresponding to different physical theories. Which one is the one that defines our four-dimensional universe? It seems that the only satisfactory answer on the theory is: they all do. And each one corresponds to a different world.