September 25, 2011

The Metric of Time

Dear Dr. Craig,

My question is quite short. It's on the subject of time. I thought I would ask you, because it's something I've been thinking about, and you seem to know a thing or two about this area (pardon the understatement). We measure time through changes, correct? So we compare changes we observe with things that change at steady rates, like the earth's rotation and changes in the seasons, and get our measurements of time in that way. My question is, assuming that time is immeasurable in principle (There is necessarily no comparison point for the measurement) in the absence of change, would this fact have any bearing on the reality of time in a completely changeless state? (I'm talking about actual change, here, not any kind of MacTaggartian or "grue-like" sense.) More broadly, if things are immeasurable even in principle, does that always mean they certainly are not real? If not, why not?




This is an interesting question, Dan, which has bearing both on one’s doctrine of divine eternity and on the kalam cosmological argument.

Yes, we measure time through changes in physical things which we take as our standard. Notice the ultimate arbitrariness of such a procedure, however: for unless we assume that time itself has an intrinsic measure, we have no grounds for taking some changes to proceed “at steady rates.” We can judge that an atomic clock has a certain constant number of beats per second only if time has an intrinsic metric that allows one to compare non-overlapping intervals of time with respect to their length, so as to differentiate one-second intervals. That doesn’t mean that time is actually composed of seconds; rather what is meant is that if we take an interval which we call a second, then any other non-overlapping interval will be either longer than, shorter than, or equal to our second. In that case, it is a meaningful question to ask whether an atomic clock has a constant number of beats per second and so is a good measure of time.

By contrast, if time has no intrinsic metric, as metric conventionalists hold, then there just is no fact of the matter whether any non-overlapping temporal interval is either longer than, shorter than, or equal to our second. In that case, there is no answer to the question of whether our atomic clock really has a steady rate of change and so is a good measure of time. It is just a human convention that certain processes proceed at steady rates.

There are few philosophers of time who defend metric conventionalism. There are no good arguments for it, and it seems highly counter-intuitive to say, for example, that the duration of my lunch break was not really shorter than the Jurassic Age.

Still there is a trio of Christian philosophers, John Lucas, Richard Swinburne, and Alan Padgett, which I have dubbed the Oxford School, who embrace metric conventionalism and an attendant view of divine eternity. So let’s explore your question: “would this fact have any bearing on the reality of time in a completely changeless state?” Well, not directly. Whether time would exist in such a changeless state depends not on the metric of time but on whether you hold to a relational or a substantival view of time. If time can exist as a substance in its own right, independently of change, then there could be time prior to creation, even if there are no events. God would exist literally before creation. By contrast, on a relational view of time, “before” and “after” would not exist in the complete absence of any events. So God, existing changelessly sans creation, would on this view, it seems to me, be timeless.

The Oxford School holds that God exists literally prior to creation. Some might try to justify this even on a relational view of time by saying that creation itself is an event which determines a “before” and an “after.” That’s not at all clear to me. But let’s grant them God’s being temporal prior to creation to see how their view plays out. In the absence of any events whatsoever prior to creation, there is no metric of time that would allow one to compare the lengths of non-overlapping temporal intervals. So if God, existing alone sans the creation, were changeless, one could not differentiate one second from one trillion years in such a time. It would be meaningless to ask how long God existed prior to creating the world. So these thinkers hold that God has always existed in a non-metric time which transcends our conventional measures of time. Padgett refers to this state as “relative timelessness.” But it is, in fact, a real time.

A nice feature of this view is that it removes any perceived difficulty about the necessity of causes’ being temporally prior to their effects. Some people stumble at the idea of God’s creating the universe (or the Big Bang) because causes must be prior to their effects in time, and there is no time prior to the Big Bang. In fact, Stephen Hawking on the recent television program “Curiosity” presents this difficulty as a proof of atheism (see Question of the Week 226)! I’m inclined to say, with most philosophers, I think, that causes need not exist temporally prior to their effects. But for those who are hung up on this difficulty, relative timelessness provides a neat way out: God does exist temporally prior to causing the Big Bang—not in physical time, to be sure, but in His own time, the time in which God Himself endures.

It might be thought that the kalam cosmological argument would be incompatible with God’s existing in a beginningless, non-metric time. But this is not obvious. As I have formulated them, the kalam arguments against an infinite temporal regress of events concern events of equal temporal duration. These arguments would entail that metric time must have begun to exist, since there cannot have been an actually infinite number of past years, for example. But if we erase time’s intrinsic metric, then it is meaningless to talk about the number of years prior to creation. Thus, the kalam argument would show that metric time began to exist but allow that God could exist in non-metric time prior to creation. So the doubts of those who object to the kalam argument because they do not see, for example, how a timeless being could have a temporal effect or how a being with intentions could exist timelessly or how God’s state of existing without creation could be timeless should be completely allayed, since according to the Oxford School God is in time prior to creation.

Whether stripping time of its metric is sufficient to avoid the problems attending an infinite regress of events is debatable. One may need to strip time not only of its metrical properties but also of its topological properties as well, that is to say, its having the structure of a line. In that case an undifferentiated “before” prior to creation starts to look very much like a state of timelessness, which is my preferred view.