When physicists are asked about “parallel worlds” or ideas along those lines, they have to be careful to distinguish among different interpretations of that idea. There is the “multiverse” of inflationary cosmology, the “many worlds” or “branches of the wave function” of quantum mechanics, and “parallel branes” of string theory. Increasingly, however, people are wondering whether the first two concepts might actually represent the same underlying idea. (I think the branes are still a truly distinct notion.)

At first blush it seems crazy — or at least that was my own initial reaction. When cosmologists talk about “the multiverse,” it’s a slightly poetic term. We really just mean different regions of spacetime, far away so that we can’t observe them, but nevertheless still part of what one might reasonably want to call “the universe.” In inflationary cosmology, however, these different regions can be relatively self-contained — “pocket universes,” as Alan Guth calls them. When you combine this with string theory, the emergent local laws of physics in the different pocket universes can be very different; they can have different particles, different forces, even different numbers of dimensions. So there is a good reason to think about them as separate universes, even if they’re all part of the same underlying spacetime.

The situation in quantum mechanics is superficially entirely different. Think of Schrödinger’s Cat. Quantum mechanics describes reality in terms of wave functions, which assign numbers (amplitudes) to all the various possibilities of what we can see when we make an observation. The cat is neither alive nor dead; it is in a superposition of alive + dead. At least, until we observe it. In the simplistic Copenhagen interpretation, at the moment of observation the wave function “collapses” onto one actual possibility. We see either an alive cat or a dead cat; the other possibility has simply ceased to exist. In the Many Worlds or Everett interpretation, both possibilities continue to exist, but “we” (the macroscopic observers) are split into two, one that observes a live cat and one that observes a dead one. There are now two of us, both equally real, never to come back into contact.

These two ideas sound utterly different. In the cosmological multiverse, the other universes are simply far away; in quantum mechanics, they’re right here, but in different possibility spaces (i.e. different parts of Hilbert space, if you want to get technical). But some physicists have been musing for a while that they might actually be the same, and now there are a couple of new papers by brave thinkers from the Bay Area that make this idea explicit.

Physical Theories, Eternal Inflation, and Quantum Universe, Yasunori Nomura

The Multiverse Interpretation of Quantum Mechanics, Raphael Bousso and Leonard Susskind

Related ideas have been discussed recently under the rubric of “how to do quantum mechanics in an infinitely big universe”; see papers by Don Page and another by Anthony Aguirre, David Layzer, and Max Tegmark. But these two new ones go explicitly for the “multiverse = many-worlds” theme.

After reading these papers I’ve gone from a confused skeptic to a tentative believer. This happened for a very common reason: I realized that these ideas fit very well with other ideas I’ve been thinking about myself! So I’m going to try to explain a bit about what is going on. However, for better or for worse, my interpretation of these papers is strongly colored by my own ideas. So I’m going to explain what I think has a chance of being true; I believe it’s pretty close to what is being proposed in these papers, but don’t hold the authors responsible for anything silly that I end up saying.

There are two ideas that fit together to make this crazy-sounding proposal into something sensible. The first is quantum vacuum decay.

When particle physicists say “vacuum,” they don’t mean “empty space,” they mean “a state of a theory that has the lowest energy of all similar-looking states.” So let’s say you have some scalar field filling the universe that can take on different values, and each different value has a different potential energy associated with it. In the course of normal evolution the field wants to settle down to a minimum of its potential energy — that’s a “vacuum.” But there can be the “true vacuum,” where the energy is really the lowest, and all sorts of “false vacua,” where you’re in a local minimum but not really a global minimum.

The fate of the false vacuum was worked out in a series of famous papers by Sidney Coleman and collaborators in the 1970′s. Short version of the story: fields are subject to quantum fluctuations. So the scalar field doesn’t just sit there in its vacuum state; if you observe it, you might find it straying away a little bit. Eventually it strays so far that it climbs right over the barrier in the direction of the true vacuum. That doesn’t happen everywhere in space all at once; it just happens in one tiny region — a “bubble.” But once it happens, the field really wants to be in the true vacuum rather than the false one — it’s energetically favorable. So the bubble grows. Other bubbles form elsewhere and also grow. Eventually all the bubbles crash into each other, and you successfully complete a transition from the false vacuum to the true one. (Unless the universe expands so fast that the bubbles never reach each other.) It’s really a lot like water turning to steam through the formation of bubbles.

This is how everyone talks about the fate of the false vacuum, but it’s not what really happens. Quantum fields don’t really “fluctuate”; that’s poetic language, employed to help us connect to our classical intuition. What fluctuates are our observations — we can look at the same field multiple times and measure different values.

Likewise, when we say “a bubble forms and grows,” that’s not exactly right. What really happens is that there is a quantum amplitude for a bubble to exist, and that amplitude grows with time. When we look at the field, we see a bubble or we don’t, just like when we open Schrödinger’s box we see either a live cat or a dead cat. But really there is a quantum wave function that describes all the possibilities at once.

Keep that in mind, and now let’s introduce the second key ingredient: horizon complementarity.

The idea of horizon complementarity is a generalization of the idea of black hole complementarity, which in turn is a play on the idea of quantum complementarity. (Confused yet?) Complementarity was introduced by Niels Bohr, as a way of basically saying “you can think of an electron as a particle, or as a wave, but not as both at the same time.” That is, there are different but equally valid ways of describing something, but ways that you can’t invoke simultaneously.

For black holes, complementarity was taken to roughly mean “you can talk about what’s going on inside the black hole, or outside, but not both at the same time.” It is a way of escaping the paradox of information loss as black holes evaporate. You throw a book into a black hole, and if information is not lost you should (in principle!) be able to reconstruct what was in the book by collection all of the Hawking radiation into which the black hole evaporates. That sounds plausible even if you don’t know exactly the mechanism by which happens. The problem is, you can draw a “slice” through spacetime that contains both the infalling book and the outgoing radiation! So where is the information really? (It’s not in both places at once — that’s forbidden by the no-cloning theorem.)

Susskind and Gerard ‘t Hooft suggested complementarity as the solution: you can either talk about the book falling into the singularity inside the black hole, or you can talk about the Hawking radiation outside, but you can’t talk about both at once. It seems like a bit of wishful thinking to save physics from the unpalatable prospect of information being lost as black holes evaporate, but as theorists thought more and more about how black holes work, evidence accumulated that something like complementarity is really true. (See for example.)

According to black hole complementarity, someone outside the black hole shouldn’t think about what’s inside; more specifically, everything that is happening inside can be “encoded” as information on the event horizon itself. This idea works very well with holography, and the fact that the entropy of the black hole is proportional to the area of the horizon rather than the volume of what’s inside. Basically you are replacing “inside the black hole” with “information living on the horizon.” (Or really the “stretched horizon,” just outside the real horizon. This connects with the membrane paradigm for black hole physics, but this blog post is already way too long as it is.)

Event horizons aren’t the only kind of horizons in general relativity; there are also horizons in cosmology. The difference is that we can stand outside the black hole, while we are inside the universe. So the cosmological horizon is a sphere that surrounds us; it’s the point past which things are so far away that light signals from them don’t have time to reach us.

So then we have horizon complementarity: you can talk about what’s inside your cosmological horizon, but not what’s outside. Rather, everything that you think might be going on outside can be encoded in the form of information on the horizon itself, just like for black holes! This becomes a fairly sharp and believable statement in empty space with a cosmological constant (de Sitter space), where there is even an exact analogue of Hawking radiation. But horizon complementarity says that it’s true more generally.

So, all those pocket universes that cosmologists talk about? Nonsense, say the complementarians. Or at least, you shouldn’t take them literally; all you should ever talk about at once is what happens inside (and on) your own horizon. That’s a finite amount of stuff, not an infinitely big multiverse. As you might imagine, this perspective has very deep consequences for cosmological predictions, and the debate about how to make it all fit together is raging within the community. (I’m helping to organize a big meeting about it this summer at Perimeter.)

Okay, now let’s put the two ideas together: horizon complementarity (“only think about what’s inside your observable universe”) and quantum vacuum decay (“at any point in space you are in a quantum superposition of different vacuum states”).

The result is: multiverse-in-a-box. Or at least, multiverse-in-an-horizon. On the one hand, complementarity says that we shouldn’t think about what’s outside our observable universe; every question that it is sensible to ask can be answered in terms of what’s happening inside a single horizon. On the other, quantum mechanics says that a complete description of what’s actually inside our observable universe includes an amplitude for being in various possible states. So we’ve replaced the cosmological multiverse, where different states are located in widely separated regions of spacetime, with a localized multiverse, where the different states are all right here, just in different branches of the wave function.

That’s a lot to swallow, but hopefully the basics are clear. So: is it true? And if so, what can we do with it?

Obviously we don’t yet know the answer to either question, but it’s exciting to think about. I’m kind of inclined to think that it has a good chance of actually being true. And if so, of course what I’d like to do is to ask what the consequences are for cosmological initial conditions and the arrow of time. I certainly don’t think this perspective provides an easy answer to those questions, but it might offer a relatively stable platform from which definite answers could be developed. It’s a very big universe, we should expect that understanding it will be a grand challenge.