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.

About Aron Wall

I am a Lecturer in Theoretical Physics at the University of Cambridge. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my postdocs at UC Santa Barbara, the Institute for Advanced Study in Princeton, and Stanford. The views expressed on this blog are my own, and should not be attributed to any of these fine institutions.
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8 Responses to Reparameterizing Time

  1. I am not a Physics graduate or anything, but I really enjoyed and appreciated this. Thanks.

  2. Charlie says:

    Why are so many of the best physicists and philosophers of physics atheists? And relatively few theists. Sometimes I feel like I'm completely deluding myself if I believe in God when so many smarter people sound like they've already figured it out.

  3. Matthew G says:

    Don't feed the troll.

  4. TY says:

    Good teaser but here a better question. Physicists like fishermen are part of the human population. Why do we find theists far outnumber atheists? And, in fact, those are considered atheists are really agnostics if they are logical.. But: Is atheism new? Hardly. In Psalm 14, we read “The fool hath said in his heart, There is no God.” See Alvin Platinga in a New York Times interview Gary Gutting (professor of philosophy at the University of Notre Dame).

    “Is Atheism irrational?”


  5. David says:

    I think you forgot to put the "st" in Charles Misner, he's a Christian. I think.

    [It appears so. Corrected above, and prior credit given to St E.A. Milne---AW]

  6. Aron Wall says:

    Thanks for your comment. I also enjoyed looking at several posts on your blog.

    I especially appreciated your ability to articulate the actual distinctions between different non-Christian religions, not painting them all with a broad brush, but also clarifying what is really unique about Christ.

    I don't think there's enough evidence yet to accuse Charlie of being a troll, i.e. somebody who deliberately posts insincere comments to a web forum in order to inflame controversy. He's made one seemingly legit comment previously, there are indeed real people who sincerely think what he is saying, and his comment is not completely off-topic given my mention of Hawking and Smith. So I think we need to be charitable and give him the benefit of the doubt. In any case, people don't troll in order to receive reasonable and calm replies to their comments. And as moderator, I can always delete comments later if things turn out badly!

    It sounds like mostly you do believe in God, but that you worry sometimes about all the smart people who seem so confident it's not true. But truth is not decided by majority rule. That's why you have to look past the bluster and see what their actual arguments are. If they don't have good reasons, it doesn't matter how smart they are.

    You can be an expert in physics, or even the philosophy of physics, without being trained in how to properly evaluate theological arguments. The majority of philsophers of religion are in fact theists, although this may in part be because atheists don't want to devote their time to thinking about it. Similar selection effects may exist the other way around with people who go into science or certain kinds of philosophy. That's why it's dangerous to just go by the numbers, when there are so many confounding cultural factors.

    The mere fact that they are cocksure unfortunately tells you nothing. In poker, if you want the other person to fold, you have to act like you have a good hand even if you don't. Has it ever occured to you that maybe these people sometimes feel insecure too, but put up a front in order to look more confident than they are?

    Concentrate on your own relationship with God, and that will give you a channel of information which they don't have access to.

  7. Steve says:

    Hi Aron,

    I have a question for you, You say that the universe must have an explanation even infinite, I guess you are familiar with the argument from contingency he says in his first premise that everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause, but critics say the Copenhagen interpretation of quantum mechanics has removed determinism. But do you really no explanation of quantum events?

  8. Aron Wall says:


    Quantum mechanics is a nondeterministic theory, in the sense that if you start with a given initial condition, and you know the laws of physics, there is generally more than one possible final outcome, and you can only predict probabilities.

    But that doesn't mean that events have no explanation at all. For example, if a radioactive atom decays, you can't predict exactly when it will decay, but you can still explain why it can decay with reference to the forces and particles in the nucleus. It's not like the decay occurs in an explanatory void.

    So I think in a quantum mechanical theory, we need to generalize our notions of "explanation" and "causation" to be nondeterministic. Just because you can't predict exactly what happens, doesn't mean there isn't a set of circumstances which causes whatever happens to happen. It's just that there's more than one possible outcome that set of circumstances could have produced. That's different from something happening without any causes at all.

    Even before QM, philosophers who believed in free will would have had to say something similar. If a person has the free choice to e.g. either obey God or disobey God, then the outcome is caused by them (they are the responsible agent) but not determined by their situation (since they could have picked the other choice). So the person would be a nondeterministic cause of what they do, on this viewpoint.

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