Wednesday, May 25, 2011

Time is Partly Ontologically Ineffable

I start with a trivial-sounding argument.

Suppose x denotes the position of a particle through time, x(t). The worldline of the particle can be plotted on a spacetime diagram. Now I want to highlight a trivial-sounding observation that many have made,

(1)  it's possible to imagine (epistemologically) a point moving along the worldline

The (philosophical) problem is that the worldline was supposed to represent the particle moving "through time" in the first place. But the worldline is a mathematical object that's timeless/eternal/ static/etc., in the way all mathematical objects are, so there's really no chance it could account for the behavior of the point in (1). But then what kind of space-'time' diagram would be appropriate if it's going to account for everything we know about time?

One can model a person performing (1) in/along his own worldline through spacetime. The problem now takes the form that the person (call him p1) moving in/along his world line imagines that his spacetime diagram is independent of his own temporal experience. That's not the case if both of the following are true:

(2)  what's true of the universe is what's true in the universe

(3)  what's true in the universe is the information carried by it's extant "information-bearers" 

The information-bearers are the objects that exist in the ontology. The each bearer's information can be thought of as the maximum amount of information each can have about the universe at that (bearer's) time.

One way to proceed is to say that it's inconsistent to suppose the particle's behavior has been completely specified by the spacetime diagram in the ontology of the spacetime diagram. In support of this is that, by (2) and (3), temporal flow is itself a prerequisite for any theory or information purporting to model the universe through time. But we know these facts. 1. the person p1 experiences a temporal flow. So, 2. If the particle is not ontologically distinct, it's a part of person p1, so is equally associated with p1's temporal flow. This suggests the hypothesis 

(4)  each ontologically distinct element of a theory that satisfies the above conditions evolves in it's own ontologically distinct dimension of time

of course these dimensions are closely correlated. But the point is there does not exist "a time" at which there is a fact as to the state of both objects p1 and particle p2. Suppose we pick a p1-time at which things could be true of p2. But p2's evolution (history) is temporally independent of p1. So there is no p1-time at which p2 exists in a particular state, until they recombine (and vice versa).

Imagine two particles in R3. Put a unit sphere around each. All that's true is the information carried by each particle in it's own timeline. Since each has no information about "what time" the other finds itself to be in, they have to take into account all possible timelines until they actually interact. Moreover, there is only the information about p2's location relative to p1, i.e., p2's location projected onto p1's sphere (and vice versa). There is no objective location for both of them in R3. And along the two timelines there are the possibilities for the other particle's state at it's different possible time values projected to the sphere surrounding each.

Instead of the combined system s = (p1, p2) evolving according to an objective time parameter t in tcrossR3, there is

(tp1crossS2)cross(tp2crossS2).

and a particular state is given by values of the two time parameters. Form the space R3-minus-spheres, etc.


More philosophically, what's going on looks like: part of what we mean by "time" is ontologically ineffable. We can't communicate to someone on Alpha Centuri what it's like to exist in the present temporal flow, because for all we know Alpha Centuri was destroyed 3 years ago, in terms of our present, even though it'll be another year before our region of the universe receives the information. 

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