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Making Waves with GravityXiao-Gang Wen thinks it’s time physicists look outside of 

Schrödinger’s Box for ways to unify gravity and quantum mechanics.

by JEFF KANIPE

The realms of the very small and the

very large are indisputably bound. Scien-tists know that both realities exist be-cause galaxies, stars, and people can bereduced to molecules, atoms, and quarks.

LINKING GRAVITY ANDQUANTUM MECHANICS Xiao-Gang-Wen 

The problem is that somewhere at theextreme end of the microscopic level,the two realms not only go their sepa-rate ways, but also act as if the otherdoesn’t exist. In the sub-microscopicdomain — smaller than atoms — quan-tum theory is very successful at describ-ing the behaviors and properties of at-oms and elementary particles, but onlywhen the law of gravity is ignored. Atthe very largest, or macroscopic, scales,gravity is very successful at describing themotions of planets, stars, and galaxies, butonly if the principles governing the quan-tum world are assumed not to exist.

A unified framework is needed to in-clude these two disparate realms, saysXiao-Gang Wen, a physicist at MIT. Thatis what he hopes to discover with hisresearch project, “Microscopic Origin of 

Gravity and Light,” sponsored by a grantworth $94,924 from The FoundationalQuestions Institute.

 Wave Machine In simple terms, light – a sub-microscopic form of radiation – helps usvisualize our world, while gravity – amacroscopic attractive force – keeps

our world spinning around the Sun. Butphysicists note that light and gravityshare an important quality: both can berepresented as wave phenomena (atleast theoretically for gravity). But whatmedia gives rise to light and gravitationalwaves? In other words, muses Wen,what is waving?

In earlier work with Michael Levin, nowa postdoctoral researcher in condensedmatter theory at Harvard, Wen proposedthat space might be formed by microdegrees of freedoms, like a magnetformed by quantum spins. With this pic-

ture of space, Levin and Wen described aunified understanding of light and elec-trons as the collective motions of prop-erly organized “spins” forming the space.Wen now plans to do something similarfor gravity, despite a formidable challenge:Einstein’s General Theory of Relativity.

General Relativity reveals a definitelink between gravity and light, indicatingthat, like light, gravity can also be in awave form. In particular, both lightwaves and gravitational waves belong toa particular class of waves described byso-called “gauge theories.” However,

“despite our success in understandinglight as collective motions of properlyorganized spins,” says Wen, “we still donot know which organization of spinsgives rise to gravitational waves. I hopeto find a quantum spin model, similar tothat of a magnet, where the wave-likecollective modes satisfy the EinsteinEquation and give rise to gravitons.”

If such a spin system can be found, itwould allow physicists to gain a deeperunderstanding of both gravity and light.

Surfer Dude 

Wen has long been noted for his re-search accomplishments and ability toquestion everything that everyone elseaccepts as fundamental. "He is a re-

markably creative physicist whose ideasare so innovative that it typically takes 10years before they are appreciated andunderstood by his colleagues," says Levin.

For instance, in 1989, Wen pointedout that spins in a spin liquid have a newkind of organization dubbed topologicalorder, which opened a new field in con-densed matter physics, Wen’s specialty.In 2002, Wen introduced a mathematicalnotion, called projective symmetrygroup, to describe a novel class of evenmore general spin organizations knownas quantum orders. And in 2005, Wen

and Levin developed “string-net” theoryfor the new spin organizations, whichunifies light and electrons. This theorycan also be applied to his new projectfor FQXi.

Despite our success inunderstanding light as

collective motions of properly organizedspins, we still do notknow which organiza-tion of spins gives riseto gravitational waves.

- Xiao-Gang-Wen

One of the most basic and long-standing assumptions physicists make isthat matter is best understood by subdi-viding it into smaller bits. However,

News 

August 2, 2007FQXi Awardee: Xiao-Gang Wen, MIT

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A PICTURE OF OUR VACUUM A string - net theory of Light and electrons. 

Wen says this approach may be funda-mentally flawed because it assumes thatthe vacuum of space is empty, and thatparticles placed in the vacuum are alwaysdivisible. Instead, matter and empty spacemay be two aspects of the same thing.Elementary particles may in fact arisefrom the collective behavior of somedeeper structure that forms the space.

For example, according to quantumtheory, sound waves propagating inside acrystal behave like particles called pho-nons. These particles cannot be under-stood by dividing them into smaller partsbecause phonons, as sound waves, arisefrom the collective motions of the atomsthat form the entire crystal. In otherwords, phonons have no smaller parts.

Similarly, says Wen, photons and elec-trons may not be elementary at all butrather arise from the collective motionsof degrees of freedom that form thespace. Looked at this way, the vacuum is

not a void but a dynamical medium formedby “spins” (or “qbits”). The collective mo-tions of “spins” can give rise to both force-carrying elementary particles (such as pho-tons, gluons, and the W and Z particles)and matter-forming elementary particles(such as electrons and quarks).

String Nets 

Supporting this notion is Wen andLevin’s work, conducted in 2004, whichdescribed how spins should organize sothat their collective motions behave likeelectromagnetic waves (light). Theproper organization is called a “string-net liquid,” where spin orientations forma pattern that looks like networks of 

strings that fill the entire space.Such string-nets can fluctuate ran-

domly to form a string-net liquid. (Seehttp://dao.mit.edu/~wen/stringnet.htmlfor a picture of a string-net.) This specialorganization satisfies the Maxwell Equa-tions and behaves like a light wave.

Normally, as the temperature de-creases in a ferromagnetic material, spinorientations will eventually stop fluctuat-ing, and point to a fixed direction. Thewaves in such organized spins satisfy adifferent equation, the Euler Equation,and do not correspond to light waves.

However, if spins interact with eachother in a certain way, even at tempera-tures approaching absolute zero, spinorientations can still fluctuate in a well-coordinated manner to form a string-netliquid. Materials with such spin interac-tions will contain waves that satisfy the

Maxwell Equations and behave exactlylike light.

Furthermore, string-net theory notonly provides an origin of light, it alsoprovides an origin of electrons. It turnsout that in a string-net liquid, a singleend of an open string moves aroundfreely and behaves like an independentparticle: that is, an electron. It interacts

with light like an electron and even car-ries the Fermi statistics of electrons.Other fermions (i.e., matter particles

such as quarks) and other force-carryingparticles (such as gluons) can arise in asimilar fashion from different string-netsformed by different spins. So, string-nettheory unifies light with electrons, ormore generally, interactions with matter.

Still, gravity is not in this picture. Withhis new research project, says Wen, “wewant to find a new organization of spins,something similar to but beyond thestring-net organizations, that produces

gravitational waves. If successful, the spinsystem will correspond to a quantum the-ory of gravity, thus solving the problem of linking gravity and quantum mechanics.”

Wave on, string nets.