(say) half the size of its successor. That way, as you worked back, each oscillation would be smaller than its successor, but there would be no beginning. If our oscillation reached a size of x light-years, the previous one would have reached x/2 light-years, the one before x/4, and so on. However far back you went, there would be no “infinitely small” oscillation.
leslie
But wouldn’t each cycle also be shorter than its successor? Moreover, radiation from each cycle would accumulate, and by now there would be huge amounts of it in the universe—maybe an infinite amount. There isn’t. Nor is there the high or infinite degree of entropy (roughly, disorder) that there ought to be after so many oscillations.
geoffrey
That may be. But in any case it seems that you might have a “crunch” in which the whole system of laws of nature was dissolved and took shape again in (quite possibly) some totally different form; and in that case you couldn’t conclude that the cycles would die down.
leslie
But could you talk of a “cycle” at all in such a case? If the new universe has nothing at all in common with the previous one—matter has been crunched into a state where its former laws no longer apply—I don’t see what meaning there can be in saying that it’s the same universe bouncing back. It would be simpler just to say that there are other universes besides this one, and keep the beginning of time. And if the laws change so much, how can we be sure that there will be any more oscillating?
geoffrey
Even if we pass over all that, there is my second possibility: something like what Stephen Hawking seemed to be saying in A Brief History of Time. That is, that there is no boundary to space-time, and hence no need to appeal to God to set boundary conditions at its beginning. Or, as others have put it, as you get nearer the “bang,” ordinary notions of space and time cease to apply; there is no need to think in terms of an absolute beginning, a “singularity” where the whole of space and its contents were infinitely compressed.
leslie
Don’t forget that this “no boundary” idea is only a “proposal” (Hawking’s word); it isn’t implied by anything we actually know. As Hawking himself presents it, it turns on the use of what he calls “imaginary time”—which elsewhere he describes as “merely a mathematical device or trick to calculate answers about real time.” It seems funny to use a “mathematical trick” to decide such important matters as the reality or non-reality of a God.
geoffrey
But you don’t need to stress the idea of imaginary time; other presentations of this point have not done so. And I am told that while using “imaginary time” is indeed only a trick when one is dealing with special relativity, it becomes more serious when you get on to general relativity.
leslie
Ah. Perhaps I was being unfair to Hawking—or perhaps he wasn’t doing himself justice.
myra
If I have followed him, which is not at all certain, you can use either “real time” or “imaginary time” to describe the history of the universe. One yields a beginning, the other doesn’t. And it seems to me that if either of them does, then we have to treat the world as having a beginning. To adapt an analogy Hawking himself uses, you can go round the earth in circles indefinitely, and you can’t fall off the edge; but the earth is limited, and to someone approaching it from space there is a point where it begins.
geoffrey
The point is not that Hawking’s proposal is proven truth; it is simply that it is a possibility. And if it is possible, then your argument from an alleged beginning is not a proof.
leslie
There is of course another approach, which goes back to the Middle Ages but has been revived in recent years—the attempt to show that there must be a beginning to time, whatever physical theories may happen to be in fashion at the moment. An infinite stretch of time in the future may perhaps be possible—you don’t after all have to complete it. You never actually reach a point infinitely far in the future; it is just that whatever finite length of time you suggest lies ahead, there is more beyond it. There is no end to the time-series. But an infinite past time is another matter altogether; it implies that an infinite number of days and events has actually come to an end. And this seems impossible, literally unimaginable.
geoffrey
Unimaginable, maybe; but all that says is that our imaginations are limited. I can’t imagine a start to time with no moment preceding it either.
leslie
Perhaps I shouldn’t have used the word “unimaginable.” What we can or cannot imagine hardly matters if infinite past time is impossible anyway.
geoffrey
But why should it be impossible? You theists should of all people be reluctant to say this; why shouldn’t your omnipotent and eternal God have created a universe with no beginning (or end)?
leslie
Not even God can create an impossibility.
geoffrey
But either God is in time, in which case presumably he has no beginning himself, or he is not in time at all, in which case questions of ending an infinite series don’t arise; he simply creates an infinite universe which from our point of view goes back for ever. Either way, where is the impossibility?
myra
This seems very queer, Geoffrey. You seem to have suddenly turned theist.
geoffrey
Only ad hominem, to make Leslie see that an infinite past was possible after all. (As many theist philosophers have held, even when, like Maimonides or Aquinas, they thought it wasn’t actually the case.) But in any case, I do not think we need a God, whether there is a beginning or not.
leslie
Yet Hawking himself seems to think that if there was a beginning, there probably would have to be a God,
geoffrey
If he really did mean that, he was wrong. Let me explain.
Firstly, the beginning, if there was one, was not an event. It was not in time in the way that the events that followed it were; it was the start of time. The events in a novel may follow one from the other, but the novel’s opening doesn’t. The various features of a painting have proportions one to another; the corners of the canvas don’t. If the beginning had something before it, you could perhaps treat it as an event which needed a cause (though, by the way, it would surely be a physical cause, not a divine one!); but it didn’t.
leslie
If you insist that causes must be events, yes; but must they? Put it another way: the beginning calls for an explanation. Why did this beginning take place?
geoffrey
No, it doesn’t call for an explanation: indeed, I’m not sure it could have an explanation. An explanation must include, surely, an “If A, then B” at some point. My jumping is explained by the loud explosion just before, because it is our
