As a result, in a move called "the second string revolution" in the middle 1990s, string theorists postulated that all the different string theories so far discovered plus an infinite number of so-far-undiscovered theories are but approximations to one unified theory. This theory has been called M theory, but there is no general agreement as to what its principles are or what mathematical form it takes. The idea is that M theory, if it exists, would be background-independent and have all the different background-dependent string theories as different solutions to it.
Many string theorists now say that the main problem in string theory is to find M theory and give string theory a background-independent form. But the funny thing is that not many string theorists have tried to work on this problem. The problem is that all their intuition and tools are based on background-dependent theories. When I bother string theorists about this, they tell me it's premature—not time to work on this problem yet.
I've had a lot of interesting conversations with the leaders of string theory—Edward Witten, Leonard Susskind, Renate Kallosh, David Gross, John Schwarz, Michael Green, Andrew Strominger, and many others. We clearly disagree about methodology. They tell me I have the wrong idea about how science works. They tell me one cannot hope to solve fundamental problems by attacking them directly. Instead one must follow the theory where it goes. A leading string theorist has said to me several times that "I learned a long time ago that string theory is smarter than I am" and that to try to tell the theory where to go would be to presume that you are "smarter than the theory." Another tells me that string theory works because it is "a very disciplined community" in which the leaders impose an order on the community of researchers to insure that only a few problems are worked on at any one time.
I have huge respect for the string theorists as people and for what they have accomplished. Some of them are good friends. At the same time, I think they're wrong about how science works. I certainly don't want to say that I'm smarter than string theory, or than string theorists. But I disagree about the methodology, because I'm sure that fundamental scientific problems are not solved in such an accidental way. Einstein used to complain that many scientists limit themselves to easy problems—"drilling where the wood is thin," as he put it. On one of the few occasions when I talked to Richard Feynman, he said that many theoretical physicists spend their careers asking questions that are only of mathematical interest. "If you want to discover something significant," he told me, "only work on questions whose answers will lead to new experimental predictions."
I also learned from the philosopher Paul Feyerabend the importance of conflict and pluralism in science. I read him in graduate school and I felt imediately that, unlike other philosophers I had been reading, he really understood what we scientists actually do. He pointed out that science often develops out of the tension that arises when competing research programs collide. He advised that in such situations one should always work on the weakest part of each of the competing programs. He also emphasized that pluralism in science is good, not bad. According to him, and I agree, science moves fastest when there are several healthy competing approaches to a problem, and stagnates when there is only one approach. I think this is true on every level—in the scientific community as a whole, in a research center or group, and even in each one of us.
So while I disagree with the leading string theorists about methodology, this hasn't kept me from working on string theory. After all, they don't own it; its open problems are there for anyone to try to solve. So I decided a few years ago to ignore their advice and try to construct the background independent form of M theory. In the process of inventing loop quantum gravity, we gained a lot of knowledge about how to make quantum theories of space and time that are background-independent. We have a mathematical language, we have a conceptual language, we know what questions to ask, and we know how to do calculations. It turns out that there is a lot of loop quantum gravity that can be generalized and extended by adding extra dimensions and extra symmetries in order to make it a suitable language for M theory.
At first some of my friends and collaborators were shocked that I was working on string theory. However, I had an idea that maybe string theory and loop quantum gravity were different sides of the same theory, much like the parable of the blind men and the elephant. I spent about two years working on string and M theory, with the goal of making them background-independent and thus unifying string theory and loop quantum gravity. I did find some very interesting results. I was able to build a possible background-independent formulation of string theory.
The most interesting results I found use some beautiful mathematics, having to do with a kind of number called an octonion. These are numbers that you can divide, but they fail to satisfy the other rules, such as commutativity and associativity. Feza Gürsey, from Yale University and his students, especially Murat Gunyadin, have for years been exploring the idea that the octonions might be connected to string theory. Using octonions, I was able to develop an attractive idea (from Corrine Manogue and Tevian Dray of Oregon State University) that explains why space may look three-dimensional while being, in a certain mathematical sense, nine-dimensional. I don't know if the direction I took is right, but I did find that it is indeed not so hard to use background-independent methods to formulate and study conjectures about what M theory is.
Working on string theory using the methods from loop quantum gravity was a lot of fun. I was out there with just a few friends, as it had been in the early days of loop quantum gravity, and I made real progress. However, in the last year I put this work aside because of the new experimental developments. As soon as I understood what Giovanni Amelino-Camelia was saying, I realized that this was science and that's what we had to focus on. Since then, it's been a lot harder to wake up and go to work in the morning to an imaginary world with six or seven extra dimensions.
There was another piece of shocking news from the experimenters that took me away from string theory—the discovery over the last couple of years that most of the energy in the universe is in a form that Einstein called the cosmological constant.. The cosmological constant can be interpreted as indicating that empty space has a certain intrinsic energy density. This is a hard thing to believe in, but the cosmological data cannot now be explained convincingly unless one assumes that most of the energy of the universe is in this form. The problem is that string theory seems to be incompatible with a world in which a cosmological constant has a positive sign, which is what the observations indicate. This is a problem that string theorists are thinking and worrying very hard about. They are resourceful people, and maybe they'll solve it; but as things stand at the moment, string theory appears to be incompatible with that observation.
Meanwhile, loop quantum gravity incorporates a positive cosmological constant extremely well. In fact it's our best case: If there's a cosmological constant, we're able find a candidate for the quantum state of the universe and show that it predicts that the universe at large scales is governed by general relativity and quantum theory. So in the last several months, I've mostly been studying how to make predictions about the new experiments from a version of loop quantum gravity that incorporates a positive cosmological constant.
The good thing about science is that you get these shocks from the real world. You can live for a few years in an imaginary world, but in the end the task of science is to explain what we observe. Then you look in the mirror and ask yourself, "Do I want to be out there in eleven dimensions, playing with beautiful math, when the experiments start coming in?"