# Would String Theory Truly Realize Einstein’s Dream?

When I reviewed Peter Woit’s book “Not Even Wrong,” Several readers of this blog were puzzled by my claim that string theory does not attempt to reconcile Einstein’s theory of gravity and quantum theory. After all, isn’t string theory supposed to be realizing Einstein’s dream of unifying gravity with the other forces, into a final theory of everything, as Brian Greene, the Columbia University string theorist, reminds us in a New York Times op-ed article today? And if not, have the string theorists — and all those who popularize their work — been fooling the public all along? Here I will try to help correct the misconception, and also guess how it may have arisen.

String theory — if it turns out to be a well-defined, experimentally verified theory — would achieve an astonishing feat among others: it would “quantize” gravity. This means that the force of gravity would become for the first time a bona fide part of quantum physics. But that is not the same as saying that string theory would include a “quantized” general relativity. The versions of string theory that physicists consider promising would only include a radically simplified version of general relativity, Einstein’s theory of gravity.

Einstein posited that the geometry of space is not fixed and immutable, but that it changes responding to the presence of matter and energy. The presence of a heavy object — say, a star like the Sun — creates a “depression” in the fabric of space (often pictured as a heavy ball resting on a rubber sheet — the analogy by the way is not entirely accurate, but hopefully it gives the idea).

In turn, how matter and energy move in space is affected by the changing structure of space itself. The “force” of gravity is in a sense apparent, just like the centrifugal forces you feel riding a rollercoaster are the result of the rollercoaster being curved. (Again, the analogy is not exact, but please bear with me.)

In string theory, on the other hand, space is static. The theory is not yet capable of predicting that heavy objects curve space. In particular, the theory cannot explain mesmerizing phenomena like the formation of black holes (when the depression becomes infinitely deep), or the gravitational lensing astronomers see around galaxies. This problem is known as “background dependence,” meaning that string theory has to assume the shape of the universe as a “background” known and assigned once and for all(1).

Strings also seem to be very fastidious about what universe you put them into. Initially, string theory only seemed compatible with a “flat” universe. When physicists showed in the late 1990s that there were a few other possibilities for string-compatible universes, that was seen as a huge breakthrough. Still, it was like saying, string theory takes not only vanilla ice cream, but also chocolate and strawberry — but forget about Wavy Gravy or Cherry Garcia. The other string-compatible universes would be curved and evolving (as opposed to flat and static), but still as a background. Their evolution would be unaffected by what the strings do.

All of this is true of the approaches to string theory that people have been working on for the last 20 years. A different, “background independent” approach to string theory, called string field theory, was proposed in the mid-1980s, but most physicists soon abandoned it after discovering that it seemed to be unworkable.

At the same time, it is true as Greene says that a successful string theory would be able for the first time to model gravity in the language and mathematics of quantum theory — a problem that’s been nagging physicists ever since quantum theory became seen as expressing the fundamental nature of physics laws. Hopefully, a “single equation” would be found that explains all forces of nature — gravity, the weak and strong nuclear forces, the electromagnetic force, and even the mysterious dark energy.

Gravity according to string theory would still keep some of the great achievements of Einstein’s theory. It would be a force that propagates at the speed of light, rather than instantaneously as in Newton’s spooky “action at a distance.” And it would fully be consistent with Einstein’s earlier, “special” relativity, with its slowing clocks, shrinking measuring sticks, paradoxes of the twins, and so on.

Such a theory could in principle be accurate within a wide range of applicability, namely as long as you do experiments far from massive objects, and if you forget about trying to predict anything about the universe as a whole.

Would this achieve Einstein’s dream? Yes and no. Einstein certainly wanted to unify physics, but his version of the dream involved wrestling the other forces off the grip of quantum theory — which he helped father and then despised — rather than letting quantum theory get its grip on gravity. In today’s article, Greene does warn the reader on this point. But he seems to gloss over the fact that the problem of fully recovering general relativity would remain open.

Why and how have a lot of people come to believe such a misconception about string theory, namely, that string theorists are working on fully integrating general relativity into a unified theory? I believe it’s due in large part due to the perils of popularizing science. While physicists who also act as science communicators could be more open on this point, part of the fault could also be ours — the science journalists’.

If you have to express what string theory is to someone who knows nothing about physics, and if you must do that in one or two sentences, it is imperative that you give your reader (or the listener or T.V. spectator) a lifesaver to grasp onto. At least some of the words you are going to say must be familiar to the reader, or else you’ve lost them. The only word that is guaranteed to sound familiar to most people is Einstein. The reader will ask, what is physics? Oh, it’s what Einstein did. At least I have a mental pigeonhole where to put this guy.

At the same time, the need to avoid overwhelming the reader almost always forces you to make stark choices on what to leave out, as all of us who write about science will attest. So Greene was right to somehow mention Einstein’s name in there, and probably also not to go too much into the details.

Still, all of us who communicate science could probably try harder to avoid misleading the reader. “Whenever you are translating mathematical work into natural language, there’s inevitably going to be some imprecisions,” New York Times science writer George Johnson once said to me in a telephone interview. However, he said, “I like to subtly work in a disclaimer, sometimes, just to remind people that — especially when you write about physics, and quantum mechanics particularly — a really precise description that would do complete justice to the phenomena is going to require differential equations.” That’s what Johnson often does in his books, and that’s some advice we science communicators could all try to follow. (Read the complete Q&A with George Johnson)

(1) Here’s how Stephon Alexander, a theoretical physicist at the University of Pennsylvania, explained this to me in more technical terms:

When one quantizes string theory, it is done on a fixed space-time background. This background is usually Minkowski space time. Therefore the metric is fixed. Most string theories have another symmetry which is called conformal invariance (observables are invariant under dilations (magnification)) In order for the quantum theory to respect this symmetry and be consistent, something called the Beta function must vanish -the Beta function is a quantum measure of the deviation from conformal invariance. It turns out that the condition for a vanishing beta function is exactly the Einstein Equations. However, even though the Einstein field equations are present, their solutions are only consistent with string theory for the background which gave the beta functions, Minkowski space. Other space-times are difficult to obtain in string theory because most usually break supersymmetry and the gravity theories are supergravity theories which only satisfy supersymmetric gravitational configurations.

## 2 thoughts on “Would String Theory Truly Realize Einstein’s Dream?”

1. Nice post, Davide. You certainly cleared up some of my misconceptions about what String Theory is doing.

I’m going to read it over again, and maybe we can talk about it next week. (I took off today to go skateboarding).

-Buzz Skyline

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2. Aaron Bergman says:

I’m sorry, but this is wrong. String perturbation theory makes sense (although can be difficult to quantize) on any background that satisfies the Einstein field equations, not just Minkowski space. Even in this context, string theory does explain “that heavy objects curve space”, at least perturbatively.

Within more nonperturbative approaches (the main example being AdS/CFT), one can go much further. In AdS/CFT, there is no background dependence except at the boundary of spacetime.

You also say that “Initially, string theory only seemed compatible with a “flat” universe. When physicists showed in the late 1990s that there were a few other possibilities for string-compatible universes, that was seen as a huge breakthrough”. The existence of multiple solutions was well-known back to the dawn of string theory; as mentioned above, string perturbation theory is compatible with any solution to the appropriate Einstein field equations. What was accomplished in the late 1990s was the issue of moduli fixing. The previous geometries all could deform continuously in such a way that led to massless fields that we do not observe. The accomplishment was to get rid of those fields and to make plausible that one could obtain solutions with a positive cosmological constant.

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