In quantum theory, distance is inverse to energy, because you need particles of very high energy to probe very short distances. The inverse of the Planck energy is the Planck length. It is where the classical picture of space as smooth and continuous is predicted by our theories to break down, and it is some twenty powers of ten smaller than an atomic nucleus. Because the Planck scale is so remote from experiment, people began to put great trust in mathematics and theory. There were even some string theorists who said silly things like "From Galileo to 1984 was the period of modern physics, where we checked our theories experimentally. Since then, we work in the age of postmodern physics, in which mathematical consistency suffices to demonstrate the correctness of our theories and experiment is neither possible nor necessary. "I'm not exaggerating; people really said things like this.
The idea that you could do experiments to test the quantum theory of gravity was mentioned from time to time by a few people through the 1990s, but to our shame we ignored them. One person who proposed the idea forcefully is a young man in Rome called Giovanni Amelino-Camelia. He just ignored everybody who said, "You'll never probe scales that small. You'll never test these theories." He told himself that there must be a way, and he examined many different possible experiments, looking for ways that effects of quantum gravity could appear. And he found them. Now we know more than half a dozen different experiments we can do to test different hypotheses about physics at the Planck scale. Indeed, in the last year, several proposals about Planck scale physics have been ruled out by experiment.
The key thing that Amelino-Camelia and others realized is that we can use the universe itself as an experimental device to probe the Planck scale. There are three different ways the universe gives us experimental probes of the Planck scale. First, there are accelerators in distant galaxies that produce particles with energies much higher than we can produce in even the largest human-made accelerators. Some of these ultra-high-energy cosmic rays have been observed hitting our atmosphere with energies more than 10 million times those we have ever produced. These provide us with a set of ready-made experiments, because on their way to us they have traveled great distances through the radiation and matter that fill the universe. Indeed, there are already surprises in the data which, if they hold up, can be interpreted as due to effects of quantum gravity.
Second, we detect light and particles that have traveled billions of light years on their way across the universe to us. During the billions of years they travel, very small effects due to quantum gravity can be amplified to the point that we can detect them.
Finally, the postulated inflation by which the universe expanded very rapidly at early times serves as a kind of microscope, blowing up Planck scale features to astronomical scales, where we can see them in small fluctuations in the cosmic microwave radiation.
So what are the theories we will be testing with these effects? One is loop quantum gravity.
Loop quantum gravity started in the early 1980s with some discoveries about classical general relativity by Amitaba Sen, then a postdoc at the University of Maryland. These were made into a beautiful reformulation of Einstein's theory by Abhay Ashtekar, then at Syracuse University and now director of the Center for Gravitational Physics at Penn State—a reformulation that brought the mathematical and conceptual language we use to describe space and time closer to the language used in particle physics and quantum physics. My colleague Ted Jacobson of the University of Maryland and I then found in 1986 that we could use this new formalism of Ashtekar's to get real results about quantum spacetime. Since the 1950s, the key equation of quantum gravity has been one called the Wheeler-DeWitt equation. Bryce DeWitt and John Wheeler wrote it down, but in all the time since then, no one had been able to solve it. We found we could solve it exactly, and in fact we found an infinite number of exact solutions. They revealed a microscopic structure to the geometry of space and told us that space, at the Planck scale, looks like a network with discrete edges joined into graphs. The next year, I was joined by Carlo Rovelli (now of the Centre de Physique Théorique in Marseille), and we were able to make a full-fledged quantum theory of gravity out of these solutions. This became loop quantum gravity. We were quickly joined by many others, and now it is a rather large field of research.
Loop quantum gravity differs from other approaches to quantum gravity, such as string theory, in that apart from using Ashtekar's formalism we made no modifications to the principles of relativity and quantum theory. These principles are well tested by experiment, and our theory is based on their consistent unification, nothing more. Our approach joins relativity in the world as we see it, with three spatial dimensions and matter more or less as we see it, with quantum mechanics more or less in the form presented to us by Paul Dirac, Werner Heisenberg, and their friends. While most people had given up and were seeking to modify the principles of either relativity or quantum theory, we surprised ourselves (and many other people) by succeeding in putting them together without modifying their principles.
This has led to a detailed theory that gives us a new picture of the nature of space and time as they appear when probed at the Planck scale. The most surprising aspect of this picture is that on that scale, space is not continuous but made up of discrete elements. There is a smallest unit of space: Its minimum volume is given roughly by the cube of the Planck length (which is 10-33 cm). A surface dividing one region of space from another has an area that comes in discrete units, the smallest of which is roughly the Planck length squared. Thus, if you take a volume of space and measure it to very fine precision, you discover that the volume can't be just anything. It has to fall into some discrete series of numbers, just like the energy of an electron in an atom. And just as in the case of the energy levels of atoms, we can calculate the discrete areas and volumes from the theory.
When we first worked out the predictions for these smallest units of area and volume, we had no idea that they would be observable in real experiments in our lifetime. However, a number of people—beginning with Rodolfo Gambini, of the University of the Republic in Montevideo, and Jorge Pullin, then at Penn State—showed that there are indeed observable consequences. At about the same time, Amelino-Camelia and others were pointing out that if there were such effects, they would be detectable in experiments involving cosmic rays and gamma-ray bursts. These effects are caused by light scattering off the discrete structure of the quantum geometry, analogous to diffraction and refraction from light scattering off the molecules of the air or liquid it passes through. The quantum gravity effect is tiny—many orders of magnitude smaller than that due to matter. However, we observe light from gamma-ray bursts—huge explosions, possibly caused by mergers of binary neutron stars or black holes—that has traveled across the universe for some 10 billion light-years. Over such long distances, the small effects amplify to the point where they can be observed. Because elementary particles travel as waves in quantum theory, the same thing happens to such particles—protons and neutrinos, for example. It is possible that these effects may be responsible for the surprises I mentioned in the observations of very-high-energy cosmic rays.