Wednesday, February 22, 2023

From a determinable-determinate model of location to a privileged spacetime foliation

Here’s a three-level determinable-determinate model of spacetime that seems somewhat attractive to me, particularly in a multiverse context. The levels are:

  1. Spatiotemporality

  2. Being in a specific spacetime manifold

  3. Specific location in a specific spacetime manifold.

Here, levels 2 and 3 are each a determinate of the level above it.

Thus, Alice has the property of being at spatiotemporal location x, which is a determinate of the determinable of being in manifold M, and being in manifold M is a determinate of the determinable of spatiotemporality.

This story yields a simple account of the universemate relation: objects x and y are universemates provided that they have the same Level 2 location. And spatiotemporal structure—say, lightcone and proper distance—is somehow grounded in the internal structure of the Level 2 location determinable. (The “somehow” flags that there be dragons here.)

The theory has some problematic, but very interesting, consequences. First, massive nonlocality, both in space and in time, both backwards and forwards. What spacetime manifold the past dinosaurs of Earth and the present denizens of the Andromeda Galaxy inhabit is partly up to us now. If I raise my right hand, that affects the curvature of spacetime in my vicinity, and hence affects which manifold we all have always been inhabiting.

Second, it is not possible to have a multiverse with two universes that have the same spacetime structure, say, two classical Newtonian ones, or two Minkowskian ones.

To me, the most counterintuitive of the above consequences is the backwards temporal nonlocality: that by raising my hand, I affect the level 2 locational properties, and hence the level 3 ones as well, of the dinosaurs. The dinosaurs would literally have been elsewhere had I not raised my hand!

What’s worse, we get a loop in the partial causal explanation relation. The movement of my hand affects which manifold we all live in. But which manifold we all live in affects the movement of the objects in the manifold—including that of my hand.

The only way I can think of avoiding such backwards causation on something like the above model is to shift to some model that privileges a foliation into spacelike hypersurfaces, and then has something like this structure:

  1. Spatiotemporality

  2. Being in a specific branching spacetime

  3. Being in a specific spacelike hypersurface inside one branch

  4. Specific location within the specific spacelike hypersurface.

We also need some way to handle persistence over time. Perhaps we can suppose that the fundamentally located objects are slices or slice-like accidents.

I wonder if one can separate the above line of thought from the admittedly wacky determinate-determinable model and make it into a general metaphysical argument for a privileged foliation.


William said...

If some hypothetical versions of quantum gravity work out, my arm movement's influence on the continuum might drop off over distances quickly enough (inverse square?) so my movement of my arm cannot change the continuum at some sufficient distance. This would be due to the fact that the continuum requires some quantum sized influence to change, which is not sufficiently large at some sufficient distance. This would mean that there is some limit to nonlocality, for simple changes in momentum at least.

All speculative, but it dissolves part of your backwards temporality problem, at least at sufficiently large (meters? kilometers? light-seconds?) distance and time interval.

Alexander R Pruss said...

I think you still have nonlocality, because it is literally true that if you move your arm, the stuff in the distance is in a different manifold from what it would have been. The continuum in the neighborhood of the distant point may be qualitatively unchanged, but it is a part of a different manifold.

Alexander R Pruss said...

It has occurred to me this morning that the problems with backwards causation may evaporate if in the initial model we just replace "manifold" with a forward branching manifold structure, and posit that all the substances travel together down the same branches. We don't need to bother with a determinable that specifies which branch we're in, and so we don't have to posit slices.

There are mathematical technicalities, of course, that I don't know much about how to handle.

I suspect that the nonlocality might also disappear if this is handled right.