Throwing Einstein for a Loop
By Amanda Gefter – Scientific American December 2002
She talks about physics like it's cooking. "My strength is to put things together out of nothing," she says, "to take this ingredient and another one there and stick something together." The art is figuring out which ones to use and how to combine them so that when the oven bell dings, the universe comes out just right.
At 31 years old, Fotini Markopoulou Kalamara is hailed as one of the world's most promising young physicists. She recently accepted a position at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario (Canada's answer to the Institute for Advanced Study in Princeton, N.J.). There she works alongside such prominent physicists as Robert Myers and Lee Smolin, hoping to blend Einstein's general relativity with quantum theory to explain the nature of space and time.
This unification is probably the single greatest challenge of modern physics. String theory has been the predominant contender. It proposes that the building blocks of matter are tiny, one-dimensional strings and that various vibrations of strings play the familiar medley of particles as if they were musical notes.
Although string theory finds a way to incorporate gravity into a quantum description of matter, some physicists believe that it has shortcomings that prevent it from being the ultimate theory of everything. For one, the theory presupposes up to 26 spatial dimensions, many more than have yet to be experimentally discovered. More fundamental still, whereas strings are fine for describing matter, they do not explain the space in which they wiggle. Newer versions of string theory may fix this problem. But a small band of physicists, including Smolin, Abhay Ashtekar of Pennsylvania State University and Carlo Rovelli of the Theoretical Physics Center in Marseilles, France, place greater stock in a different approach: loop quantum gravity, or LQG.
In LQG, reality is built of loops that interact and combine to form so-called spin networks-- first envisioned by English mathematician Roger Penrose in the 1960s as abstract graphs. Smolin and Rovelli used standard techniques to quantize the equations of general relativity and in doing so discovered Penrose's networks buried in the math. The nodes and edges of these graphs carry discrete units of area and volume, giving rise to three-dimensional quantum space. But because the theorists started with relativity, they were still left with some semblance of a space outside the quantum networks.
[PICTURE: LIGHT CONES, generated by plotting the speed of light against time and three dimensions of space (x, with y and z together), define all past and future connections to an event.
That was the state of LQG in the late 1990s, when Markopoulou Kalamara began tackling it. Serendipity actually led her to the subject. "I only decided on physics when I was 16 or 17," says the theorist, who is from Athens, Greece. "Before that, I wanted to be all sorts of things: an archaeologist, an astronaut, a painter." While she was an undergraduate at the University of London, a friend taking theoretical physics recommended lectures being given by quantum-gravity theorist Chris Isham of Imperial College London. "It was on my way home, so I went once a week, and I loved it." She convinced Isham to be her adviser and wound up with a Ph.D. in quantum gravity. She then joined Smolin at Penn State as a postdoctoral fellow.
Markopoulou Kalamara approached LQG's extraneous space problem by asking, Why not start with Penrose's spin networks (which are not embedded in any preexisting space), mix in some of the results of LQG, and see what comes out? The result was networks that do not live in space and are not made of matter. Rather their very architecture gives rise to space and matter. In this picture, there are no things, only geometric relationships. Space ceases to be a place where objects such as particles bump and jitter and instead becomes a kaleidoscope of ever changing patterns and processes.
Each spin network resembles a snapshot, a frozen moment in the universe. Off paper, the spin networks evolve and change based on simple mathematical rules and become bigger and more complex, eventually developing into the large-scale space we inhabit.
By tracing this evolution, Markopoulou Kalamara can explain the structure of spacetime. In particular, she argues that the abstract loops can produce one of the most distinctive features of Einstein's theory-- light cones, regions of spacetime within which light, or anything else, can reach a particular event. Light cones ensure that cause precedes effect. We can understand this concept by gazing upward and knowing that there are countless stars we cannot see because not enough time has passed since the birth of the universe for their light to shine our way; they are beyond our light cone.
It is not so obvious, though, where light cones fit into the spin networks. Those networks are subject to quantum mechanics. In that wonderland of uncertainty, any network has the potential to evolve into infinite new ones, leaving no trace of a causal history. "We didn't know how, in the language we were working in, to put in the notion of causality" in LQG, Smolin says. Markopoulou Kalamara found that by attaching light cones to the nodes of the networks, their evolution becomes finite and causal structure is preserved.
But a spin network represents the entire universe, and that creates a big problem. According to the standard interpretation of quantum mechanics, things remain in a limbo of probability until an observer perceives them. But no lonely observer can find himself beyond the bounds of the universe staring back. How, then, can the universe exist? "That's a whole sticky thing," Markopoulou Kalamara says. "Who looks at the universe?" For her, the answer is: we do. The universe contains its own observers on the inside, represented as nodes in the network. Her idea is that to paint the big picture, you don't need one painter; many will do. Specifically, she realized that the same light cones she had used to bring causal structure into quantum spacetime could concretely define each observer's perspective.
Because the speed of light is finite, you can see only a limited slice of the universe. Your position in spacetime is unique, so your slice is slightly different from everyone else's. Although there is no external observer who has access to all the information out there, we can still construct a meaningful portrait of the universe based on the partial information we each receive. It's a beautiful thought: we each have our own universe. But there's a lot of overlap. "We mostly see the same thing," Markopoulou Kalamara explains, and that is why we see a smooth universe despite a quantized spacetime. "I actually think theoretical physics is very much like art," concludes Markopoulou Kalamara, the daughter of two sculptors. "Putting these things together is like taking clay and making something out of nothing, and it should work from every side. I like the creative part, but I also like that you can check."
The time to check is fast approaching. There are details to work out, such as how to derive the usual one-dimensional time from the quantum causality, but she figures that if observations can confirm the basics of spin networks, she'll smooth out the kinks. One experiment could be to track gamma-ray photons from billions of light-years away. If spacetime is in fact discrete, then individual photons should travel at slightly different speeds, depending on their wavelength. Markopoulou Kalamara is trying to decipher the form of that dispersion.
If true, her predictions could forever change the way we think about the structure of space. Several tests of quantum gravity could take place within the next few years. "I always told myself that if it doesn't turn into real physics, if it doesn't get in touch with experiment, I'm getting a really well paying job in New York. For all I know, it may work easily. There's always that possibility," Markopoulou Kalamara says. In the meantime, she's hard at work, and waiting for the oven bell.
Amanda Gefter is based in New York City.
Last updated 16/02/2003