What a mouthful!
But it’s an important theorem, so let me give a brief introduction.
First, you may have heard of entropy, but in case it’s not a clear concept, let’s review.
Entropy basically means disorder, and in particular, it means the disorder that energy gets into when work is done. You drive your car, burning the gas. After you drive the car, the world has just as much energy as before, but it’s all scattered around the countryside as heat and fumes, and you can’t use it to drive your car unless you collect it back again, which would take far more energy than you could obtain by that collection. For all practical purposes, the energy is gone, not because it does not exist, but because it is too scattered to do anything for anybody.
This particular kind of disordering of energy is called entropy, and one of the characteristics of the universe as a whole is the increase in entropy. The whole universe is, like my house, getting messier every day. Fortunately, I can eat a good meal, read a good book, get some orderly energy into myself, and clean house, but the universe has nowhere to turn for a new input of order, so it is running down. We have conservation of mass and energy, but not of order, and without order, all the energy in the world – or in the universe — won’t do any work. It’s like those fumes and heat from my car; scattered energy may as well not be there at all.
Entropy means time has an arrow.
What does that mean?
Well, some things, like the rolling of a ball, could go either way. If you took a video of a gently rolling ball and ran it backwards, it would look just as real – at least for a while. If you took a photo of a light turning on and off, you could run it backwards; same thing. Even if you took a picture of sunrise or moonrise and ran it backwards, most people would just think you had a picture of sunset or moonset.
But a video of a falling egg would be very funny backwards, because it’s not possible. Or get one of those time-lapse pictures of a flower unfolding from a bud; not the same backwards, eh?
A universe with increasing entropy is like that egg that falls on the floor; you always know which way the arrow of time is going. In one place or another, the universe might be like the rolling ball, which looks the same for a while, but if you see the entire roll, you generally know where the start and finish are.
Because entropy is increasing in the universe as a whole, it follows that the universe cannot be infinite in time. It cannot have an infinite history because when you go back far enough, the energy is in the best possible order for doing stuff, and any change would be more entropy, not less. By the same token, the universe cannot have an infinite future because when the disorder is total nothing meaningful can happen.
What would that look like?
It would look like a puff of smoke, only the smoke is so thin and the puff is so broad that there’s really nothing to see, and as you approach the end, even though some particles have enough oomph to drift, they still cannot make a difference in how it looks. It’s not that energy and mass are gone; it’s just that they can’t do anything noticeable – my father would say that the power to pass information is gone. The universe as an intelligible system is ended; there’s nothing to know. (And, of course, no place to stand and watch it!)
The multiverse is subject to entropy
We’re almost there.
Father Spitzer has a new book out, (New Proofs for the Existence of God) explaining that there is now (since 2003) a theorem – the Borde-Vilenkin-Guth Theorem — which shows that even if Hawking’s multiverse were real (there is no specific evidence for it), the laws of entropy would still prevail and the multiverse would come to an end — and would, for that matter, need a beginning. Thus Hawking’s multiverse does not open up the possibility for a universe infinite in time; it just offers a universe context that can hang around unimaginably (which is not the same as infinitely) longer than the one we know.
I have not read Spitzer’s book; I have only heard him talk about it. You can listen too by going to http://www.magisreasonfaith.org/ and choosing the video clip from EWTN. Around the 18th minute, he gets to the Borde-Vilenkin-Guth theorem. Note that there are also clips that say something about Larry King Live. These are not from the TV show but are follow-ups to such a show, and interesting in their own right. Enjoy yourself!