Gravity Gets Loopy

December 15, 2008

A few years ago, at a meeting of the American Physical Society in Tampa, Florida, I attended a press conference on loop quantum gravity (LQG), the leading contender to string theory for a unified Theory of Everything (i.e., a theory that merges general relativity with quantum mechanics). The press conference speakers included Abhay Ashtekar, currently director of the Center for Gravitational Physics at Penn State University. He was one of LQG's founders in the early 1980s (along with Lee Smolin and Carlo Rovelli, among others), and is still among its strongest proponents.

Max Planck spawned the quantum revolution when he introduced the notion of quanta: atoms could only emit or absorb energy in specific amounts -- much like how currency comes in specific denominations. (You can have a $1 bill or a $5 bill, but not a bill for exactly $2.43, for instance.) In LHQ, essentially space itself becomes quantized. Per Smolin, "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."

It just so happened that Brian Greene -- author of the bestselling book (and NOVA series) The Elegant Universe, and string theory's most prominent ambassador -- was also at the meeting. After a bit of arm-twisting, he agreed to sit in on the press conference, offering his take on the pros and cons of the rival schools. But if any of the assembled journalists were expecting the fur to fly, they were disappointed: the two men were perfectly cordial and reasonable -- in short, they behaved like the professional scientists they are.

The two approaches certainly have their differences. String theory starts at the quantum level and builds upward to incorporate general relativity, while loop quantum gravity starts out at the top with general relativity and seeks to incorporate quantum mechanics.

But both involve some kind of loop -- loops of string in string theory, and the mathematical equivalent to loops of space in loop quantum gravity. Who knows? As Greene pointed out at that press conference, maybe the two camps could turn out to be a weird sort of duality: opposite ends of the same Theory of Everything. Theorists of the future might end up with something that combines elements of both.

Loop quantum gravity does have at least one advantage over string theory: it is a "background-independent formulation." See, string theory makes one very big assumption: the pre-existence of the fabric of spacetime. Think of the master painter who produces great works, but never stop to wonder where the canvas came from. We talk about the "fabric" of spacetime routinely, but it isn't any kind of tangible material, despite the fact that physicists speak of curving and twisting space-time as if it were. It's more of a mathematical construct on which to drape the master equations of the universe. So explaining where it came from is one of the criteria for a bona fide Theory of Everything. String theorists are in hot pursuit of their own background-independent formulation, but loop quantum gravity already has it: the fabric of space-time emerges directly from the equations.

LQG might be string theory's lesser known cousin, but it's had its share of success (mathematically, at least), such as correctly computing the entropy of a black hole -- a must for any successful theory of quantum gravity. It's yielded some intriguing theoretical possibilities: for instance, last year another Penn State physicist, Martin Bojowald, published a paper in wich he claimed that, unlike Einstein's theory of general relativity, LQC doesn't break down at the point of the Big Bang.

In fact, per Bojowald and Ashtekar, there might not have been so much of a Big Bang, as more of a "big bounce." In their model, the universe eventually stops expanding and contracts, except instead of contracting down to the dreaded singularity, it bounces back, reborn -- literally. Just like the mythical phoenix rising from its own ashes, an old, dying universe gives birth to a new one. The sticking point: all the experimental data so far indicates that the universe is accelerating, expanding outward at an increasing rate because of dark energy, which is the exact opposite of a contraction.

We mere mortals can only grasp the outlines of these deep mathematical theories, of course, so I won't be so presumptuous as to make a call as to whether LQG or string theory will emerge victorious. Maybe we'll never know for sure. Physicists of a more experimental bent tend to dismiss theories that are mostly pretty math with few predictions and/or any means of experimentally testing those predictions. It's a valid criticism. But I like Greene's more laissez-faire attitude. Asked how he'd feel if string theory was proven wrong after devoting most of his career to its advancement, he responded, "Don't you want to know? I do!" Right or wrong, knowing is better. That's what science is all about.

Photo: 3D model of the "loopy" structure of space predicted by loop quantum gravity at very short scale. Source: Carlo Rovelli, Centre de Physique Theorique de Luminy.

Comments

[Freiddie]

Is it just me, or am I seeing LHQ, LQG, and LQC? What do the abbreviations LHQ and LQC stand for?

[Jennifer Ouellette]

It should all read LQG. Loop quantum gravity. The rest are typos

[Lubos Motl]

It's actually not quite the case. LQC is used correctly in that sentence and stands for something different, namely loop quantum cosmology, which is an even less serious attempt to say something about the Universe than loop quantum gravity (LQG).

LQC is a combination of the oversimplified assumptions of the Friedmann-Robertson-Walker (FRW) cosmology combined with the manifestly wrong and silly assumptions done by LQG. Because of the additional FRW oversimplification, LQC doesn't even follow from LQG.