Justin du Coeur (jducoeur) wrote,
Justin du Coeur

The Turtle-Free Universe: Chance and Time

Commentary on the first and second installments of this article pointed out an imprecision in my thinking: I've been tossing the word "probable" around too casually. Okay -- on some thought, it seems closely bound up with the notion of Time, which I was going to discuss in this chapter anyway. So let's examine both concepts, and how they relate to each other.

The error I made was referring to a universe as "probable". On some reflection, that isn't really what I intended: I'm really talking about particular states of a specific universe as being probable or improbable. That's still a slightly iffy concept, but we'll explore it more below.

Probability, in the sense that I'm thinking of, really arises from causation. Therefore, it is something of a non-sequiteur to refer to the "probability" of a universe, since nothing "causes" a universe in this model. Indeed, this may be a good way to define "universe" for purposes of this model: A universe is a set of mathematical laws and states that are causally related to each other. That is, if state A can lead to state B, then we can say that they exist within the same universe.

This definition explicitly assumes that it is not meaningful to talk about the principles of a single universe changing over time -- the constants might alter, but I'm assuming (based on what I know of our reality) that the underlying laws don't. It does mean that worlds-of-if style parallel worlds are counted as part of the same universe, so this definition includes some common definitions of a multiverse. Indeed, alternate futures and alternate pasts also count within the same universe, so it's a more expansive definition of universe than the usual. But I think that it's the only reasonable definition, once we think carefully about time.

For causation (and thus probability) to make sense, a given universe must have a time dimension. Note that some universes in this model have no time dimension: they are simply a single static state, eternal and unchanging, so probability is a non-issue. (Conceivably, a universe might have multiple time dimensions. I'm not sure exactly what that would mean, but it's worth thinking about as fodder for an exceptionally odd science fiction story.)

Less obviously, probability requires uncertainty at the mathematical level. What we normally call "probability" on the human-level macro scale isn't really anything of the sort: it's simply a matter of not understanding the state thoroughly enough to predict things accurately. If we lived in a truly Newtonian universe, there would be no such thing as probability: everything would ultimately be deterministic, even if we didn't understand it well enough to know how to predict it. Uncertainty appears to be deeply bred into our quantum-mechanical universe, however, with the result that it isn't a simple straight-line progression of states. Personally, I find that unpredictability comforting; however, it does mean that we need to wrestle with uncertainty as an integral part of any discussion of this sort.

Okay, now let's talk about time. What is time? Our perception of time is the progression of the universe through a series of states. Intuitively, we think of that progression as monotonic: time is constantly moving forward, carrying us with it. (Hence, the common metaphor of time as a river.)

Of course, things aren't actually that simple. Relativity has demonstrated that time isn't nearly as intuitive as we would like to believe. Different objects in the same universe can move through time at different rates if their frames of motion are different.

That's terribly easy to say, but we tend to mentally skirt around the implication: time is simply another mathematical construct. Many of the questions that often arise in casual philosophical discussion, such as "where did the universe come from?" are arguably nonsensical when we realize that there *is* no necessary concept of "before" and "after" outside the bounds of our reality.

Let's make this point a little sharper, by separating the "man's-eye" and "God's-eye" views of reality. By this, I don't mean to take a stand on the existence of God (I'll get to that subject later), but it's a convenient way of thinking about the "outside" view. For purposes of this essay, when I say "the God's-eye view", I mean what the multiverse would look like if you could view it in its entirety from the outside. (And please, don't try to take that statement too literally -- I know that words like "view" and "outside" are meaningless in this case.)

From the God's-eye view, then, time doesn't exist. If our universe is simply a set of states related by causation, then all of those states exist equally from the view outside time. Hold that idea in your mind for a while, and try to internalize it. Many of our mental assumptions are rooted in the notion of time as an absolute. I'll be getting back to some of the implications here.

So back to probability. For purposes of this discussion, probability is the likelihood that a universe in state A will give rise to state B. Related to this, when we say that a particular state is "improbable", what we mean is that the sum of the probabilities leading from every other state to this one is relatively low; there is no high-probability pathway leading from the beginning of the universe to that state.

In principle, at least within our universe, it appears that every state is at least remotely possible, due to quantum effects. If we take quantum tunneling painfully literally, then every flight of fantasy is possible within our universe. However, many (including pretty much every superhero comic book) are extremely improbable, requiring fantastically unlikely quantum effects to arrive at those states. (It may be possible to conceive of fantasies that are not possible within our universe, but I suspect that they would be so removed from our experience as to be interesting only on an intellectual level.)

Enough for today. Next time, we take a look at the really nasty issue of Consciousness.

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