FIGURE 1-3: Strings wrap around extra dimensions to create particles with different masses.

      A string has two ways to wrap once around this shape.

      It’s even possible (though harder to visualize) for a string to wrap in both directions simultaneously — which would, again, give us yet another particle with yet another mass. Branes can also wrap around extra dimensions, creating even more possibilities.

      Defining space and time

      In many versions of string theory, the extra dimensions of space are compactified into a very tiny size, so they’re unobservable to our current technology. Trying to look at space smaller than this compactified size would provide results that don’t match our understanding of space-time. (As you see in Chapter 2, the behavior of space-time at these small scales is one of the reasons for a search for quantum gravity.) One of string theory’s major obstacles is attempting to figure out how space-time can emerge from the theory.

      As a rule, though, string theory is built upon Einstein’s notion of space-time (see Chapter 6). Einstein’s theory has three space dimensions and one time dimension. String theory predicts a few more space dimensions but doesn’t change the fundamental rules of the game all that much, at least at low energies.

      Some proposals for how to address this have been developed, mainly focusing on space-time as an emergent phenomenon — that is, the space-time comes out of the sum total of all the string interactions in a way that hasn’t yet been completely worked out within the theory.

      However, these approaches don’t meet some physicists’ bar for compelling scientific evidence, leading to criticism of the theory. String theory’s biggest competitor, loop quantum gravity, uses the quantization of space and time as the starting point of its own theory, as Chapter 19 explains. Some believe that this will ultimately be another approach to the same basic theory.

Appreciating the Theory’s Amazing (and Controversial) Implications

      Although string theory is fascinating in its own right, what may prove to be even more intriguing are the possibilities that result from it. These topics are explored in greater depth throughout the book and are the focus of Parts 3 and 4.

      Landscape of possible theories

      One of the most unexpected and disturbing discoveries of string theory is that instead of one single model of the universe, it turns out that there may be a huge number of possible models (or, more precisely, possible solutions to the theory) — maybe as many as 10⁵⁰⁰ different solutions! (That’s a 1 followed by 500 zeroes!) While this huge number has prompted a crisis among some string theorists, others have embraced it as a virtue, claiming it means that string theory is very rich.

      In order to wrap their minds around so many possible models, some string theorists have turned toward the anthropic principle, which tries to explain properties of our universe as a result of our presence in it. Others instead argue that the vast number of possible string models is to be expected — or even that it’s a feature, not a bug, so to say. For them, it’s just a matter of nailing down the particular string solution that does describe our universe.

      With such a large number of theories available, the anthropic principle allows a physicist to use the fact that we’re here to choose among only those theories that have physical parameters that allow us to be here. In other words, our very presence dictates the choice of physical law — or is it merely that our presence is an observable piece of data, like the speed of light?

      As anthropic-principle skeptics are quick to point out, physicists adopt the anthropic principle only when they have no other options, and they abandon it if something better comes along. It remains to be seen if string theorists will find another way to maneuver through the string theory landscape. (Chapter 12 has more details about the anthropic principle.)

      The universe as a hologram

      In the mid-1990s, two physicists came up with an idea called the holographic principle. In this theory, if you have a volume of space, you can take all the information contained in that space and show that it corresponds to information “written” on the surface of the space. As odd as it seems, this holographic principle may be key in resolving a major mystery of black holes that has existed for more than 30 years!

      Many physicists believe that the holographic principle will be one of the fundamental physical principles that will allow insights into a greater