Reparameterizing Time

In recent posts I've been discussing whether the universe began or not.

Perhaps the most important issue which I have not yet discussed, is the idea (I think originally due to Charles Misner, first pointed out by St. Edward Arthur Milne, and independently by St. Charles Misner) that it may not be well-defined whether time has a beginning or not.  That is, suppose you have a model in which there is a time coordinate $t$, and time has a beginning in the sense that the only allowed times are $t > 0$.  Well, in General Relativity we are free to use whatever time coordinate we like, and nothing stops us from defining a new time coordinate in terms of the old one, let's say $\tau = \log(t)$.  If you look at a plot of the log function, you'll see that $\tau$ ranges from $-\infty$ to $+\infty$.

However, this type of time reparameterization may not be very physical once you get down to the Planck time, about $10^{-43}$ seconds, when quantum gravity effects become important.  Times less than that might not be well-defined.  In any case, the Misner argument suggests that we need to be more careful to define what we mean by time having a beginning.

Similarly, atheist philosopher Quentin Smith has argued that the standard Big Bang Model is inconsistent with divine creation, due to it not really having a beginning, even though the past is finite.  Smith argues that because the time $t = 0$ is singular, technically it shouldn't be included in the spacetime, so actually only times with $t > 0$ exist.  That means that there is no initial moment of creation, and therefore, he claims, God cannot have created the universe.

This is somewhat reminiscent of Hawking's claim that the no boundary proposal doesn't have the right sort of beginning, and it seems to me that my Fuzzing into Existence post is also applicable.  If God is like an author, then he can make a story in which time works in whatever way he pleases.

According to Smith, each time $t$ exists because the preceding times exist, and indeed the laws of physics hold at a given time $t$ (according to him) because they hold at earlier times.  Since each moment of time is fully explained by those before, he claims that the universe is therefore self-caused and therefore fully explained, with no more explanation possible.  (Of course, if time is continuous, then we could make a similar infinite regress of times going back closer and closer to any finite time $t$.  Smith has to struggle a bit to explain why his argument doesn't apply there...)

Now to me, this seems like the sort of explanation which is really no explanation at all.  A satisfying worldview should explain as much as possible with as few assumptions as possible.  If the laws of physics have some property $X$ (e.g. having an electron field, or whatever) now because they were like $X$ a minute ago, and so on all the way back arbitrarily close to the beginning, that doesn't in any way satisfy my curiosity about why they are like $X$ instead of some other way $Y$ (say, having no charged particles).  For if they had been $Y$ for all time, I could have made the same argument.  So it seems that there is a potentially meaningful question "Why are the laws of physics like $X$ rather than like $Y$", which Smith's statements do not really explain.  Maybe there is no explanation, and we have to take $X$ being the way it is as a fundamental fact.  But to say that there could not possibly be an explanation seems rather dogmatic.

And if God exists, then he can explain this fact.  God's will chooses what the laws of physics will be for all time.  So he can choose for the universe to be like $X$ instead of like $Y$.  This would be the fundamental explanation.  Whether or not it is a useful explanation for us as human beings, would depend on whether our puny minds can identify the actual reasons why God might prefer $X$ over $Y$.

The Kalam argument has some intuitive appeal if you think that the universe could not have begun without some causal reason.  Evaluating this claim requires an analysis of what causation is, and why one would think in various situations that a cause is necessary.  But the first preliminary question is whether there are any facts to be explained by the putative cause.  It seems to me that there are.

All of the same reasoning about $X$ and $Y$ would also apply if time stretches back to $-\infty$.  There would still be various timeless facts about the universe which would not really be explained by the infinite regress.  This suggests that the Kalam argument may be misguided to the extent that it attempts to prove God from a temporal beginning a finite time in the past.  The most important issues are the same whether time goes back finitely or infinitely.

But having said all this, it does seem a little bit weirder that the universe should exist for a finite amount of time with no external explanation, than that it should exist for an infinite time with no explanation.   Historically, many materialists (such as Lucretius) have believed that time is infinite, due to their belief that it is impossible for something to come from nothing.  Conversely, monotheists have mostly believed that the universe has a beginning, either for philosophical reasons or because the Bible says so.  (St. Thomas Aquinas argued that God could have created an infinite past, but that divine revelation tells us he didn't.) To that extent, Big Bang cosmology appears to vindicate the standard religious view over the standard nonreligious one.

(Of course, the same cannot be said if—unlike St. Thomas or St. Augustine—one also takes the 6 day creation about 6,000 years ago literally.  Some fundamentalists have argued that this problem can be solved by reparameterizing our coordinate system, but that just seems silly to me.  Also, the days are not in the right order to correspond to the scientific chronology.)

But a Theist could believe that God created time going back infinitely, without contradicting themselves, so long as they are prepared to be flexible about what "creation" means.  Similarly, an Atheist could believe that the universe just started existing 13.8 billion years ago for no reason, without contradicting themselves, so long as they are prepared to be flexible when deciding when explanations are called for.  All four views are logically consistent; the real question is which viewpoint explains the most with the least.