going to make it down for Easter; there’s just too much to do here at Caltech. The last few weeks have been extremely exciting. I’m working with a couple of other people and we really don’t want to break off our calculations, even for a holiday in Baja. I’m really sorry about it as I was looking forward to getting together with you both again (if you take my meaning!). I shall miss the prickly cactus and the delicious dry heat, too. Sorry, and maybe next time. Tell Linda I’ll call her for a chat in the next few days if I can find time. Any chance of you people coming up here for a day (or better yet, a night)?
After breaking a promise like this I suppose I ought to tell you what’s stirred me up so. Probably a marine biologist like you won’t think this is of such great concern—cosmology doesn’t count for a lot in the world of enzymes and titrated solutions and all that, I suppose—but to those of us working in the gravitational theory group it looks as though there’s a genuine revolution around the corner. Or maybe it’s already arrived.
It’s related to a problem that’s been hanging around astrophysics for a long time. If there is a certain quantity of matter in the universe, then it has a closed geometry—which means it will eventually stop expanding and begin to contract, pulled back together by gravitational attraction. So people in our line of work have been wondering for some time if there is enough matter in our universe to close off the geometry. So far, direct measurements of the matter in our universe have been inconclusive.
Just counting the luminous stars in the universe gives a small quantity of matter, not enough to close off space-time. But there’s undoubtedly a lot of unseen mass such as dust, dead stars, and black holes.
We’re pretty sure that most galaxies have large black holes at their centers. That accounts for enough missing matter to close off our universe. What’s new is the recent data on how distant galaxies are bunched up together. These galactic-scale clumps mean there are large fluctuations in matter density throughout our universe. If galaxies bunch up together somewhere in our universe, and their density gets high enough, their local space-time geometry could wrap around on itself, in the same way that our universe might be closed.
We now have enough evidence to believe Tommy Gold’s old idea—that there are parts of our universe which have enough clustered galaxies to form their own closed geometry. They won’t look like much to us—just small areas with weak red light coming out of them. The red is from matter still falling into those clumps. The shocker here is that these local density fluctuations qualify as independent universes. The time for forming a separate universe is independent of the size. It goes like the square root of Gn, where G is the gravitational constant and n the density of the contracting region. So it’s independent of the size of the miniuniverse. A small universe will close itself off just as fast as a large one. This means all the various-sized universes have been around for the same amount of “time.” (Defining just what time is in this problem will drive you to drink, if you’re not a mathematician—maybe if you are, too.)
The point here is that there may be closed-off universes inside our own. In fact, it would be a remarkable coincidence if our universe was the largest of all. We may be a local lump inside somebody else’s universe. Remember the old cartoon of a little fish being swallowed by a slightly larger one, in turn about to be swallowed by another bigger one, and so on, ad infinitum? Well, we may be one of those fishes.
The last few weeks I’ve been working on the problem of getting information about—or out of—these universes inside our own. Clearly, light can’t get out of one universe into the next. Neither can matter. That’s what a closed geometry means. The only possibility might be some type of particle that doesn’t fit into the constraints set by Einstein’s theory. There are several candidates like this, but Thorne (the grand old man around here) doesn’t want to get into that morass. Too messy, he says.
I think tachyons are the answer. They can escape from smaller “universes” inside our own. So the recent discovery of tachyons has enormous implications for cosmology. It’s hard to detect