The fact that there are innumerably many different solutions of the standard model does not, of course, mean that the standard model of particle physics—this triumph of human thinking—is somehow unbelievably complicated, or that it’s a theory of anything, or that it has no predictive power. It just means that it’s rich enough to accommodate the rich phenomenology we actually see in nature, while at the same time starting from a very simple setup. There are only certain quarks. There is only one kind of electron. There are only certain ways you can put them together, and you cannot make arbitrary materials with them. There are statistical laws that govern how very large numbers of atoms behave, so even though things look like they get incredibly complicated, they start simplifying again when you get to really large numbers.
In string theory, we’re doing a different kind of building of iron blocks. String theory is a theory that wants to live in ten dimensions—nine spatial dimensions and one of time. We live in three spatial dimensions and one of time, or at least so it seems to us. And this used to be viewed as a little bit of an embarrassment for string theory—not fatal, because it’s actually fairly easy to imagine how some of those spatial dimensions could be curled up into circles so small that they wouldn’t be visible even under our best microscopes. But it might have seemed nicer if the theory had just matched up directly with observation.
It matches up with observation very nicely when you start realizing that there are many different ways to curl up the six unwanted dimensions. How do you curl them up? Well, it’s not like they just bend themselves into some random shape. They get shaped into a small bunch of circles, whatever shape they want to take, depending on what matter there is around. Similar to how the shape of your Lego car depends on how you put the pieces together, or the shape of this chair depends on how you put the atoms in it together, the shape of the extra dimensions depends on how you put certain fundamental string-theory objects together.
Now, string theory actually is even more rigorous about what kind of fundamental ingredients it allows you to play with than the Lego company or the standard model. It allows you to play with fluxes, D-branes, and strings. And these are objects that we didn’t put into the theory; the theory gives them to us and says, “This is what you get to play with.” But depending on how it warps strings and D-branes and fluxes in the extra six dimensions, these six dimensions take on a different shape. In effect, this means that there are many different ways of making a three-dimensional world. Just as there are many ways of building a block of iron or a Lego car, there are many different ways of making a three-plus-one dimensional-seeming world.
Of course, none of these worlds are truly three-plus-one dimensional. If you could build a strong enough accelerator, you could see all these extra dimensions. If you could build an even better accelerator, you might be able to even manipulate them and make a different three-plus-one dimensional world in your lab. But naturally you would expect that this happens at energy scales that are currently, and probably for a long time, inaccessible to us. But you have to take into account the fact that string theory has this enormous richness in how many different three-plus-one dimensional worlds it can make.
Joe Polchinski and I did an estimate, and we figured that there should be not millions or billions of different ways of making a three-plus-one dimensional world, but ten to the hundreds, maybe 10500 different ways of doing this. This is interesting for a number of reasons, but the reason that seemed the most important to us is that it implies that string theory can help us understand why the energy of the vacuum is so small. Because, after all, what we call “the vacuum” is simply a particular three-plus-one dimensional world—what that one looks like when it’s empty. And what that one looks like when it’s empty is basically, it still has all the effects from all this stuff you have in the extra dimensions, all these choices you have there about what to put.
For every three-plus-one dimensional world, you expect that in particular the energy of the vacuum is going to be different—the amount of dark energy, or cosmological constant, is going to be different. And so you have 10500 ways of making a three-plus-one dimensional world, and in some of them, just by accident, the energy of the vacuum is going to be incredibly close to zero.
The other thing that’s going to happen is that in about half of these three-plus-one dimensional worlds, the vacuum is going to have positive energy. So even if you don’t start out the universe in the right one—where by “right one” I mean the one that later develops beings like us to observe it—you could start it out in a pretty much random state, another way of making a three-dimensional world. What would happen is that it would grow very fast, because positive vacuum energy needs acceleration, as we observed today in the sky. It will grow very fast and then by quantum mechanical processes it would decay, and you would see changes in the way matter is put into these extra dimensions, and locally you would have different three-plus-one dimensional worlds appearing.
This is not something I made up. This is actually an effect which predates string theory, which goes back to calculations by Sidney Coleman and others in the ’70s and ’80s, and which doesn’t rely on any fancy gravity stuff. This is actually fairly pedestrian physics, which is hard to really argue with. What happens is, the universe gets very, very large; all these different vacua, three-dimensional worlds that have positive weight, grow unboundedly and decay locally; and new vacua appear that try to eat them up but don’t eat them up fast enough. So the parents grow faster than the children can eat them up, and so you make everything. You fill the universe with these different vacua, these different kinds of regions in which empty space can have all sorts of different weights. Then you can ask, “Well, in such a theory, where are the observers going to be?” To just give the most primitive answer to this question, it’s useful to remember the story about the holographic principle that I told you a little bit earlier.
If you have a lot of vacuum energy, then even though the universe globally grows and grows and grows, if you sit somewhere and look around, there’s a horizon around you. The region that’s causally connected—where particles can interact and form structure—is inversely related to the amount of vacuum energy you have. This is why I said earlier that just by looking out the window and seeing that the universe is large, we know that there has to be very little vacuum energy. If there’s a lot of vacuum energy, the universe is a tiny little box from the viewpoint of anybody sitting in it. The holographic principle tells you that the amount of information in the tiny little box is proportional to the area of its surface. If the vacuum energy has this sort of typical value that it has in most of the vacua, that surface allows for only a few bits of information. So whatever you think observers look like, they probably are a little bit more complicated than a few bits.
And so you can immediately understand that you don’t expect observers to exist in the typical regions. They will exist in places where the vacuum energy happens to be unusually small due to accidental cancellations between different ingredients in these extra dimensions, and where, therefore, there’s room for a lot of complexity. And so you have a way of understanding both the existence of regions in the universe somewhere with very small vacuum energy, and also of understanding why we live in those particular, rather atypical regions.
What’s interesting about this is the idea that maybe the universe is a very large multiverse with different kinds of vacua in it; this was actually thrown around independently of string theory for some time, in the context of trying to solve this famous cosmological-constant problem. But it’s not actually that easy to get it all right. If you just imagine that the vacuum energy got smaller and smaller and smaller as the universe went on, that the vacua are nicely lined up, with each one you decay into having slightly smaller vacuum energy than the previous one, you cannot solve this problem. You can make the vacuum energy small, but you also empty out the universe. You won’t have any matter in it.
What was remarkable was that string th
eory was the first theory that provided a way of solving this problem without leading to a prediction that the universe is empty—which is obviously fatal and immediately rules out that approach. That, to me, was really remarkable, because the theory is so much more rigid; you don’t get to play with the ingredients, and yet it was the one that found a way around this impasse and solved this problem.
I think the things that haven’t hit Oprah yet, and which are up and coming, are questions like, “Well, if the universe is really accelerating its expansion, then we know that it’s going to get infinitely large, and that things will happen over and over and over.” And if you have infinitely many tries at something, then every possible outcome is going to happen infinitely many times, no matter how unlikely it is. This is something that predates this string-theory multiverse I was talking about. It’s a very robust question, in the sense that even if you believe string theory is a bunch of crap, you still have to worry about this problem, because it’s based on just observation. You see that the universe is currently expanding in an accelerated way, and unless there’s some kind of conspiracy that’s going to make this go away very quickly, it means that you have to address this problem of infinities. But the problem becomes even more important in the context of the string landscape, because it’s very difficult to make any predictions in the landscape if you don’t tame those infinities.
Why? Because you want to say that seeing this thing in your experiment is more likely than that thing, so that if you see the unlikely thing you can rule out your theory, the way we always like to do physics. But if both things happen infinitely many times, then on what basis are you going to say that one is more likely than the other? You need to get rid of these infinities. This is called, at least among cosmologists, the measure problem. It’s probably a really bad name for it, but it stuck.
That’s where a lot of the action is right now. That’s where a lot of the technical work is happening, that’s where people are, I think, making progress. I think we’re ready for Oprah, almost, and I think that’s a question where we’re going to come full circle, we’re going to learn something about the really deep questions, about what the universe is like on the largest scales, how quantum gravity works in cosmology. I don’t think we can fully solve this measure problem without getting to those questions, but at the same time, the measure problem allows us a very specific way in. It’s a very concrete problem. If you have a proposal, you can test it, you can rule it out, or you can keep testing it if it still works, and by looking at what works, by looking at what doesn’t conflict with observation, by looking at what makes predictions that seem to be in agreement with what we see, we’re actually learning something about the structure of quantum gravity. So I think that it’s currently a very fruitful direction. It’s a hard problem, because you don’t have a lot to go by. It’s not like it’s an incremental, tiny little step. Conceptually it’s a very new and difficult problem. But at the same time it’s not that hard to state, and it’s remarkably difficult to come up with simple guesses for how to solve it that you can’t immediately rule out. And so we’re at least in the lucky situation that there’s a pretty fast filter. You don’t have a lot of proposals out there that have even a chance of working.
The thing that’s really amazing, at least to me, is in the beginning we all came from different directions at this problem, we all had our different prejudices. Andrei Linde had some ideas, Alan Guth had some ideas, Alex Vilenkin had some ideas. I thought I was coming in with this radically new idea that we shouldn’t think of the universe as existing on this global scale that no one observer can actually see—that it’s actually important to think about what can happen in the causally connected region to one observer. What can you do, in any experiment, that doesn’t actually conflict with the laws of physics and require superluminal propagation. We have to ask questions in a way that conforms to the laws of physics if we want to get sensible answers.
I thought, “OK, I’m going to try this.” This is completely different from what these other guys are doing, and it’s motivated by the holographic principle that I talked about earlier. I was getting pretty excited, because this proposal didn’t run into immediate catastrophic problems like a lot of other simple proposals did. When you go into the details, it spit out answers that were really in much better agreement with the data than what we had had previously from other proposals. And I still thought that I was being original.
But then we discovered—and actually my student I-Sheng Yang played a big role in this discovery—that there’s a duality, an equivalence of sorts, and a very precise one, between this global way of looking at the universe that most cosmologists had favored and what we thought was our radical new local causal connected way of thinking about it. In a particular way of slicing up the universe in this global picture in a way that’s, again, motivated by a different aspect of the holographic principle, we found that we kept getting answers that looked exactly identical to what we were getting from our causal-patch proposal. For a while we thought, “OK, this is some sort of approximate, accidental equivalence,” and if we asked detailed enough questions we were going to see a difference. Instead, what we discovered was a proof of equivalence—that these two things are exactly the same way of calculating probabilities, even though they’re based on what mentally seemed like totally different ways of thinking about the universe.
That doesn’t mean we’re on the right track. Both of these proposals could be wrong. Just because they’re equivalent doesn’t mean they’re right. But a lot of things have now happened that didn’t have to happen. A lot of things have happened that give us some confidence that we’re on to something, and at the same time we’re learning something about how to think about the universe on the larger scales.
17
Quantum Monkeys
Seth Lloyd
Quantum mechanical engineer, MIT; author, Programming the Universe
It’s no secret that we’re in the middle of an information-processing revolution. Electronic and optical methods of storing, processing, and communicating information have advanced exponentially over the last half-century. In the case of computational power, this rapid advance is known as Moore’s Law. In the 1960s, Gordon Moore, the ex-president of Intel, pointed out that the components of computers were halving in size every year or two, and consequently the power of computers was doubling at the same rate. Moore’s law has continued to hold to the present day. As a result, these machines that we make, these human artifacts, are on the verge of becoming more powerful than human beings themselves, in terms of raw information-processing power. If you count the elementary computational events that occur in the brain and in the computer—bits flipping, synapses firing—the computer is likely to overtake the brain in terms of bits flipped per second in the next couple of decades.
We shouldn’t be too concerned, though. For computers to become smarter than us is not really a hardware problem; it’s more a software issue. Software evolves much more slowly than hardware, and indeed much current software seems designed to junk up the beautiful machines we build. The situation is like the Cambrian explosion—a rapid increase in the power of hardware. Who’s smarter, humans or computers? is a question that will get sorted out some million years hence—maybe sooner. My guess would be that it will take hundreds or thousands of years until we actually get software we could reasonably regard as useful and sophisticated. At the same time, we’re going to have computing machines that are much more powerful quite soon.
Most of what I do in my everyday life is to work at the very edge of this information-processing revolution. Much of what I say to you today comes from my experience in building quantum computers—computers where you store bits of information on individual atoms. About ten years ago, I came up with the first method for physically constructing a computer in which every quantum—every atom, electron, and photon—inside a system stores and processes information. Over the last ten years, I’ve been lucky enough to work
with some of the world’s great experimental physicists and quantum mechanical engineers to actually build such devices. A lot of what I’m going to tell you today is informed by my experiences in making these quantum computers. During this meeting, Craig Venter claimed that we’re all so theoretical here that we’ve never seen actual data. I take that personally, because most of what I do on a day-to-day basis is try to coax little superconducting circuits to give up their secrets.
The digital information-processing revolution is only the most recent revolution, and it’s by no means the greatest one. For instance, the invention of movable type and printing has had a much greater impact on human society so far than the electronic revolution. There have been many information-processing revolutions. One of my favorites is the invention of the so-called Arabic—actually Babylonian—numbers, in particular, zero. This amazing invention, very useful in terms of processing and registering information, came from the ancient Babylonians and then moved to India. It came to us through the Arabs, which is why we call it the Arabic number system. The invention of zero allows us to write the number 10 as “one, zero.” This apparently tiny step is in fact an incredible invention that has given rise to all sorts of mathematics, including the bits—the binary digits—of the digital computing revolution.
Another information-processing revolution is the invention of written language. It’s hard to argue that written language is not an information-processing revolution of the first magnitude.
Another of my favorites is the first sexual revolution—that is, the discovery of sex by a living organism. One of the problems with life is that if you don’t have sex, then the primary means of evolution is via mutation. Almost 99.9 percent of mutations are bad. Being from a mechanical engineering department, I would say that when you evolve only by mutation, you have an engineering conflict: Your mechanism for evolution happens to have all sorts of negative effects. In particular, the two prerequisites for life—evolve, but maintain the integrity of the genome—collide. This is what’s called a coupled design, and that’s bad. However, if you have sexual selection, then you can combine genes from different genomes and get lots of variation without, in principle, ever having to have a mutation. Of course, you still have mutations, but you get a huge amount of variation for free.
The Universe_Leading Scientists Explore the Origin, Mysteries, and Future of the Cosmos Page 29