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Image: Gravity and quantum physics
Researchers are trying to bridge the gap between general relativity, which explains the gravitational properties of galaxies and black holes; and quantum mechanics, which explains the behavior of subatomic particles. The efforts could lead to a "theory of everything."
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Science

Scientists generally believe that everything happening in nature, from the birth of galaxies, to the hiccups of subatomic particles, obeys the same fundamental laws. An ultimate “theory of everything” that ties these laws together into one elegant package has eluded its pursuers for decades. A study in Friday’s issue of Science may provide a new route toward solving this tantalizing puzzle.

To find out how most anything works, you’ll eventually get to physics if you probe deep enough. (In this spirit, Ernest Rutherford supposedly pronounced, “All science is either physics or stamp collecting.”)

At the heart of modern physics are three basic principles, each of which has its own logic and distinct set of rules. Quantum mechanics describes the behavior of extremely small objects. Albert Einstein’s theory of special relativity deals with very fast objects, and his theory of general relativity typically involves very large ones.

Scientists have managed to blend the first two principles, quantum mechanics and special relativity, in ways that account for some of the most fundamental forces in the universe, such as electromagnetism.

General relativity, however, the only one to explain the gravitational force, has steadfastly resisted efforts at unification. When scientists have tried to tie together quantum mechanics and general relativity, their efforts just produced mathematical nonsense.

Thus, we can’t answer key questions about the universe, such as what ultimately happens to matter inside a black hole, and a theory of everything (also called a “grand unified theory,” or GUT) continues to elude us.

One promising approach to this problem is called superstring theory, in which the universe consists of tiny loops, or strings, vibrating in 10 dimensions. The new Science study proposes an alternative scenario, however, in which the universe is more like the surface of a water droplet — albeit one with some very unusual properties.

Co-authors Shou-Cheng Zhang and Jiangping Hu of Stanford University suggest thinking of the universe as the surface of a so-called “quantum liquid,” whose interior has four spatial dimensions instead of the usual three. Gravity and electromagnetism then reveal themselves in the form of tiny quivers at the edge of the liquid.

In search of symmetry
Zhang and Hu took their inspiration from solid-state physics, the relatively tangible world of semiconductors and other solids. These systems involve the behavior of many objects, usually electrons, whizzing around in a confined space.

In these systems, which obey the rules of quantum mechanics, “symmetries” can appear under certain conditions — meaning that seemingly different things turn out to be essentially the same, and thus interchangeable.

For example, after a system is changed from one energy state to another through a quantum phase transition, differences among individual electrons lose their significance in light of the greater similarities they turn out to share. Each electron starts acting like a member of a cohesive group, in which one electron can influence another even if the two are far apart.

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In their Science study, Zhang and Hu noted that special and general relativity are both statements of symmetry.

The main idea in special relativity is that any event will appear differently to various observers, depending on their locations and the speeds at which they are moving. Using this logic, Einstein showed mathematically that energy and mass are fundamentally the same thing. (In the famous equation, E=mc2, “E” stands for energy, and “m” stands for mass.)

According to general relativity, space and time form a four-dimensional surface that is distorted by the presence of mass. This distortion goes by the name of gravity. In yet another example of symmetry, the force of gravity is the same as the force caused by some other acceleration. For example, the earthward tug an astronaut feels during liftoff could be attributed to either gravity or the acceleration of the spacecraft.

Could the symmetries within special and general relativity have come about as a result of some type of quantum phase transition? If so, it would mean that you could start by studying a system in which the laws of quantum mechanics prevailed, and then logically arrive at relativity theory. The tension between quantum mechanics and general relativity would ease.

Jiggles in a liquid universe
Zhang and Hu started with a phenomenon called the Quantum Hall Effect, which concerns some peculiar behavior of electrons confined to a two-dimensional interface between semiconductors. This type of system has offered up many important insights into quantum mechanics, so the scientists expanded it to a theoretical four-dimensional space. The result was an “incompressible quantum liquid,” whose fourth spatial dimension functions like a vacuum.

In this fluid, nothing can happen, energywise, except at the boundaries. There, tiny excitations occur, which are similar, in a sense, to tugging on one end of a spring. The excitations distort the shape of the liquid without changing its volume.

According to Zhang and Hu, we see these excitations as photons and gravitons, massless bundles of energy that travel at the speed of light. Physicists have determined that streams of photons make up a light wave, while streams of gravitons make up a gravitational wave.

In Zhang and Hu’s calculations, the math that describes the photons in this system satisfies Maxwell’s equation, the classic equation for electromagnetism.

And, in an important step toward a possible grand unified theory, the math describing the gravitons turned out to satisfy an equation called the “linearized Einstein equation” — which is the starting point for relativity.

These findings suggest that, for a grand unified theory that unites quantum mechanics, and special and general relativity, “maybe you don’t put everyone on equal footing together,” Zhang said.

Instead, it may be possible to nudge forth the preliminary elements of relativity out of quantum mechanics.

Zhang stressed that their work is still quite preliminary, and has some important problems yet to resolve. For example, their model also includes other massless particles, in addition to the photons and gravitons, which the authors don’t understand yet. “We have an embarrassment of riches,” Zhang said.

Another challenge will be to find a way to test the concepts in this model with real-life experiments.

Zhang doesn’t necessarily think that his work will ultimately rule out superstring theory. In spite of the differences in the number of dimensions involved, the two approaches do share some concepts that are deeply related.

“Our theory is at a much more primitive stage (than superstring theory). My feeling is that they could still be somehow related to each other,” Zhang said.

© 2013 American Association for the Advancement of Science

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