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A Summary of the Second Superstring Revolution
First, M-theory has eleven dimensions (ten space and one time).
The second feature of M-theory that has been discovered is that it contains vibrating strings, but it also includes other objects: vibrating two-dimensional membranes, undulating three-dimensional blobs (called "three-branes"), and a host of other ingredients as well.
An Approximation Method
Perturbation theory is an elaborate name for making an approximation to try to give a rough answer to a question, and then systematically improving this approximation by paying closer attention to fine details initially ignored.
A Classical Example of Perturbation Theory
A Perturbative Approach to String Theory
Is the Ballpark in the Ballpark?
Well, the mathematics underlying string theory shows that the dividing line between "small" and "large" is the number 1, in the following sense. If the string coupling constant has a value less than 1, then—like multiple strikes of lightning—larger numbers of virtual string pairs are increasingly unlikely to erupt momentarily into existence. If the coupling constant is 1 or greater, however, it is increasingly likely that ever-larger numbers of such virtual pairs will momentarily burst on the scene.
This realization leads us to the next crucial question: What is the value of the string coupling constant (or, more precisely, what are the values of the string coupling constants in each of the five string theories)? At present, no one has been able to answer this question. It is one of the most important unresolved issues in string theory.
The Equations of String Theory
Duality
The Power of Symmetry
Even without understanding intricate details of a theory, the fact that it has supersymmetry built in allows us to place significant constraints on the properties it can have.
Duality in String Theory
These strong coupling characteristics of Type I string theory exactly agree with known properties of Heterotic-O string theory, when the latter has a small value for its string coupling constant. That is, when the coupling constant of the Type I string is large, the particular masses and charges that we know how to extract are precisely equal to those of the Heterotic-O string when its coupling constant is small.
Related arguments gave equally persuasive evidence that the reverse is also true:
A Summary, So Far
Supergravity
Glimmers of M-Theory
Whatever the eleven-dimensional theory is, Witten has provisionally named it M-theory.
But even without having a firm grasp on its name or its properties, it is already clear that M-theory provides a unifying substrate for pulling together all five string theories.
M-Theory and the Web of Interconnections
The Overall Picture
A Surprising Feature of M-Theory: Democracy in Extension
Does Any of This Solve the Unanswered Questions in String Theory?
No.
Although we are far from a full understanding of the terra incognita of M-theory, there are no blank regions on the map.
As Witten has said, "Understanding what M-theory really is—the physics it embodies—would transform our understanding of nature at least as radically as occurred in any of the major scientific upheavals of the past."
Chapter 13
Black Holes: A String/M-Theory Perspective
Black Holes and Elementary Particles
John Wheeler has summarized by the statement "black holes have no hair." By this, Wheeler meant that except for a small number of distinguishing features, all black holes appear to be alike. The distinguishing features? One, of course, is the black hole's mass. What are the others? Research has revealed that they are the electric and certain other force charges a black hole can carry, as well as the rate at which it spins.
Does String Theory Allow Us to Go Forward?
Tearing the Fabric of Space—with Conviction
A Flurry of E-Mail
Returning to Black Holes and Elementary Particles
"Melting" Black Holes
Morrison, Strominger, and I showed that there is a tight mathematical and physical analogy between such phase transitions and the space-tearing conifold transitions from one Calabi-Yau shape to another. Again, just as someone who has never before encountered liquid water or solid ice would not immediately recognize that they are two phases of the same underlying substance, physicists had not realized previously that the kinds of black holes we were studying and elementary particles are actually two phases of the same underlying stringy material.
Black Hole Entropy
How Black Is Black?
Enter String Theory
Our understanding of string theory is still too coarse to be able to make direct and precise contact with experimental observations of, say, the mass of a quark or an electron. But we now see that string theory has provided the first fundamental explanation of a long-established property of black holes that has stumped physicists using more conventional theories for many years.
Even Sheldon Glashow—the archrival of string theory through the 1980s—has said recently, "when string theorists talk about black holes they are almost talking about observable phenomena—and that is impressive."
Almost doesn't really count here, Brian. "You can almost do an experiment" is not science.
The Remaining Mysteries of Black Holes
The bet remains unsettled, but Hawking has recently acknowledged that the newfound understanding of black holes from string theory, as discussed above, shows that there might be a way for the information to re-emerge.
In 2004, Hawking announced that he was conceding the bet, and that he now believed that black hole horizons should fluctuate and leak information, in doing so providing Preskill with a copy of Total Baseball, The Ultimate Baseball Encyclopedia.
Chapter 14
Reflections on Cosmology
The Standard Model of Cosmology
Friedmann's work, refashioned in a more systematic and efficient form by the physicists Howard Robertson and Arthur Walker, still forms the foundation of modern cosmology.
The temperature of the universe a mere 10-43 seconds after the bang, the so-called Planck time, is calculated to have been about 1032 Kelvin, some 10 trillion trillion times hotter than the deep interior of the sun.
