However there is some fine print. For string theory to work, we need to hypothesize that there are six or seven unobservable dimensions of space. We must also hypothesize that there are new kinds of symmetries called supersymmetries, which have not so far been observed. These symmetries tie together particles usually considered constituents of matter (like quarks and electrons) with the quanta of forces (like photons and gluons).

Supersymmetry is a beautiful idea—and, indeed, it stands independent of string theory as an intriguing conjecture about the elementary particles. Unfortunately, it is not observed. Were it observed directly, then for every particle there would be a supersymmetric partner, which is a partner with the same mass and the same charges and interactions but a spin differing by one- half. This is certainly not observed! If supersymmetry is true, then it is realized in nature only indirectly; we say, in physicist talk, that the symmetry is broken. Another way to say this is that the forces have a symmetry, but the state of the world does not obey it. (For example, looking around your living room, you see that the fact that space has three dimensional symmetry is broken by the effects of the gravitational field, which points down.)

There is some indirect evidence that some people take as an indication that supersymmetry is present and will be seen in future experiments in accelerators. But so far no direct evidence for supersymmetry has been found. Nor has there been any experimental evidence for the extra dimensions that string theory requires.

The interesting—and unfortunate—upshot of this is that in the absence of experimental check, different communities of people have focused on different questions and invented different imaginary worlds. Those who work on loop quantum gravity still live in the world we see, where space has three dimensions and there is no need for more symmetries than are observed. Many string theorists live—at least, imaginatively—in a universe that has ten or eleven dimensions. A standard joke is that a string theorist hearing a talk about loop quantum gravity says, "That's a very beautiful theory, but it has two big faults: Space only has three dimensions and there is no supersymmetry!" To which the speaker replies, "You mean, just like the real world?" Actually this is not a joke—I've heard it. (And, by the way, if the world does have higher dimensions and supersymmetry, that could be incorporated into loop quantum gravity.)

The extent to which people can invent imaginary worlds when science gets decoupled from experiment is quite extraordinary. They follow a certain aesthetic of mathematical elegance out there as far as it takes them. If you buy all that—the extra dimensions and symmetries and so forth—string theory does succeed to a certain limited approximation in unifying gravity and quantum theory. However, even if it's right, string theory can be only an approximation to the real theory. One reason is that there turns out to be an enormous number of string theories. And so far, while many of them have been studied, no single string theory has been discovered that agrees with all the observations of our universe. There are three features of the world that no string theory can so far reproduce: the absence of supersymmetry at low energies, the presence of a cosmological constant with positive sign (more on this later), and the complete absence of a certain kind of field—called a massless scalar field—that string theories predict in abundance. Thus it seems likely that even if string theory is true in some generalized sense, the actual theory describing our universe must differ significantly from all string theories so far invented.

Another reason that string theory cannot be the final word is that in string theory one studies strings moving in a fixed classical spacetime. Thus, string theory is what we call a background-dependent approach. It means that one defines the strings as moving in a fixed space and time. This may be a useful approximation, but it cannot be the fundamental theory. One of the fundamental discoveries of Einstein is that there is no fixed background. The very geometry of space and time is a dynamical system that evolves in time. The experimental observations that energy leaks from binary pulsars in the form of gravitational waves—at the rate predicted by general relativity to the unprecedented accuracy of eleven decimal places—tells us that there is no more a fixed background of spacetime geometry than there are fixed crystal spheres holding the planets up. The fundamental theory must unify quantum theory with a completely dynamical description of space and time. It must be what we call a background-independent theory. Loop quantum gravity is such a one; string theory is not.

The debate between proponents of background-dependent and background independent theories is in fact just the modern version of an ancient debate. Since the Greeks, the argument has raged between those who believed that space and time have an eternally fixed, absolute character and those who thought space and time are no more than relations between events that themselves evolve in time. Plato, Aristotle, and Newton were absolutists. Heraclites, Democritus, Leibniz, Mach, and Einstein were relationalists. When we demand that the quantum theory of gravity be background-independent, we are saying we believe that the triumph that general relativity represented for the relational point of view is final and will not be reversed.

Much of the argument between string and loop theorists is a continuation of this debate. Most string theorists were trained as elementary-particle physicists and worked their whole lives in a single fixed spacetime. Many of them have never even heard of the relational/absolute debate, which is the basic historical and philosophical context for Einstein's work. Most people who work in loop quantum gravity do so because at some point in their education they understood the relational, dynamical character of spacetime as described in general relativity, and they believe in it. They don't work on string theory because they cannot take seriously any candidate for a quantum theory of gravity that is background-dependent and hence loses (or at best hides) the relational, dynamical character of space and time.

Similarly, at first string theorists were resistant to the idea that the fundamental theory must be background-independent. However, I think that by now almost all string theorists have come around. They did so because there are reasons internal to string theory to believe that the fundamental theory must be background-independent. This is because string theory turned out to be non-unique. While the original hope, back in the 1980s, was that mathematical consistency would suffice to determine the unified theory, it turns out that in fact there are a huge number of equally consistent string theories. Each is as consistent as any other and each depends on a different choice of fixed background. Further, in spite of the huge numbers of string theories we know about, none of them agree with observations on the three points I mentioned above.

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