Fundamental Physics Prize Prediction: Green and Schwarz

Posted on November 5, 2013 by preskill

Michael Green

John Schwarz

The big news today is the announcement of the nominees for the 2014 Fundamental Physics Prize: (1) Michael Green and John Schwarz, for pioneering contributions to string theory, (2) Joseph Polchinski, for discovering the central role of D-branes in string theory, and (3) Andrew Strominger and Cumrun Vafa, for discovering (using D-branes) the microscopic origin of black hole entropy in string theory. As in past years, all the nominees are marvelously deserving. The winner of the $3 million prize will be announced in San Francisco on December 12; the others will receive the $300,000 Physics Frontiers Prize.

I wrote about my admiration for Joe Polchinski when he was nominated last year, and I have also greatly admired the work of Strominger and Vafa for many years. But the story of Green and Schwarz is especially compelling. String theory, which was originally proposed as a theory of the strong interaction, had been an active research area from 1968 through the early 70s. But when asymptotic freedom was discovered in 1973, and quantum chromodynamics became clearly established as the right theory of the strong interaction, interest in string theory collapsed. Even the 1974 proposal by Scherk and Schwarz that string theory is really a compelling candidate for a quantum theory of gravity failed to generate much excitement.

A faithful few continued to develop string theory through the late 70s and early 80’s, particularly Green and Schwarz, who began collaborating in 1979. Together they clarified the different variants of the theory, which they named Types I, IIA, and IIB, and which were later recognized as different solutions to a single underlying theory (sometimes called M-theory). In retrospect, Green and Schwarz were making remarkable progress, but were still largely ignored.

In 1983, Luis Alvarez-Gaume and Edward Witten analyzed the gravitational anomalies that afflict higher dimensional “chiral” theories (in which left-handed and right-handed particles behave differently), and discovered a beautiful cancellation of these anomalies in the Type IIB string theory. But anomalies, which render a theory inconsistent, seemed to be a nail in the coffin of Type I theory, at that time the best hope for uniting gravitation with the other fundamental (gauge) interactions.

Then, working together at the Aspen Center for Physics during the summer of 1984, Green and Schwarz discovered an even more miraculous cancellation of anomalies in Type I string theory, which worked for only one possible gauge group: SO(32). (Within days they and others found that anomalies cancel for E8 X E8 as well, which provided the impetus for the invention of the heterotic string theory.) The anomaly cancellation drove a surge of enthusiasm for string theory as a unified theory of fundamental physics. The transformation of string theory from a backwater to the hottest topic in physics occurred virtually overnight. It was an exciting time.

When John turned 60 in 2001, I contributed a poem to a book assembled in his honor, hoping to capture in the poem the transformation that Green and Schwarz fomented (and also to express irritation about the widespread misspelling of “Schwarz”). I have appended the poem below, along with the photo of myself I included at the time to express my appreciation for strings.

I’ll be delighted if Polchinski, or Strominger and Vafa win the prize — they deserve it. But it will be especially satisfying if Green and Schwarz win. They started it all, and refused to give up.

To John Schwarz

Thirty years ago or more
John saw what physics had in store.
He had a vision of a string
And focused on that one big thing.

But then in nineteen-seven-three
Most physicists had to agree
That hadrons blasted to debris
Were well described by QCD.

The string, it seemed, by then was dead.
But John said: “It’s space-time instead!
The string can be revived again.
Give masses twenty powers of ten!”

Then Dr. Green and Dr. Black,
Writing papers by the stack,
Made One, Two-A, and Two-B glisten.
Why is it none of us would listen?

We said, “Who cares if super tricks
Bring D to ten from twenty-six?
Your theory must have fatal flaws.
Anomalies will doom your cause.”

If you weren’t there you couldn’t know
The impact of that mightly blow:
“The Green-Schwarz theory could be true —
It works for S-O-thirty-two!”

Then strings of course became the rage
And young folks of a certain age
Could not resist their siren call:
One theory that explains it all.

Because he never would give in,
Pursued his dream with discipline,
John Schwarz has been a hero to me.
So please, don’t spell it with a “t”!

Expressing my admiration for strings in 2001.

Polarizer: Rise of the Efficiency

Posted on November 4, 2013 by Nicole Yunger Halpern

How should a visitor to Zürich spend her weekend?

Launch this question at a Swiss lunchtable, and you split diners into two camps. To take advantage of Zürich, some say, visit Geneva, Lucerne, or another spot outside Zürich. Other locals suggest museums, the lake, and the 19^th-century ETH building.

The 19th-century ETH building

ETH, short for a German name I’ve never pronounced, is the polytechnic from which Einstein graduated. The polytechnic houses a quantum-information (QI) theory group that’s pioneering ideas I’ve blogged about: single-shot information, epsilonification, and small-scale thermodynamics. While visiting the group this August, I triggered an avalanche of tourism advice. Caught between two camps, I chose Option Three: Contemplate polar codes.

Polar codes compress information into the smallest space possible. Imagine you write a message (say, a Zürich travel guide) and want to encode it in the fewest possible symbols (so it fits in my camera bag). The longer the message, the fewer encoding symbols you need per encoded symbol: The more punch each code letter can pack. As the message grows, the encoding-to-encoded ratio decreases. The lowest possible ratio is a number, represented by H, called the Shannon entropy.

So established Claude E. Shannon in 1948. But Shannon didn’t know how to code at efficiency H. Not for 51 years did we know.

I learned how, just before that weekend. ETH student David Sutter walked me through polar codes as though down Zürich’s Banhofstrasse.

The Banhofstrasse, one of Zürich’s trendiest streets, early on a Sunday.

Say you’re encoding n copies of a random variable. When I say, “random variable,” think, “character in the travel guide.” Just as each character is one of 26 letters, each variable has one of many possible values.

Suppose the variables are independent and identically distributed. Even if you know some variables’ values, you can’t guess others’. Cryptoquote players might object that we can infer unknown from known letters. For example, a three-letter word that begins with “th” likely ends with “e.” But our message lacks patterns.

Think of the variables as diners at my lunchtable. Asking how to fill a weekend in Zürich—splitting the diners—I resembled the polarizer.

The polarizer is a mathematical object that sounds like an Arnold Schwarzenegger film and acts on the variables. Just as some diners pointed me outside Zürich, the polarizer gives some variables one property. Just some diners pointed me to within Zürich, the polarizer gives some variables another property. Just as I pointed myself at polar codes, the polarizer gives some variables a third property.

These properties involve entropy. Entropy quantifies uncertainty about a variable’s value—about which of the 26 letters a character represents. Even if you know the early variables’ values, you can’t guess the later variables’. But we can guess some polarized variables’ values. Call the first polarized variable u₁, the second u₂, etc. If we can guess the value of some u_i, that u_i has low entropy. If we can’t guess the value, u_i has high entropy. The Nicole-esque variables have entropies like the earnings of Terminator Salvation: noteworthy but not chart-topping.

To recap: We want to squeeze a message into the tiniest space possible. Even if we know early variables’ values, we can’t infer later variables’. Applying the polarizer, we split the variables into low-, high-, and middling-entropy flocks. We can guess the value of each low-entropy u_i, if we know the foregoing u_h’s.

Almost finished!

In your camera-size travel guide, transcribe the high-entropy u_i’s. These u_i’s suggest the values of the low-entropy u_i’s. When you want to decode the guide, guess the low-entropy u_i’s. Then reverse the polarizer to reconstruct much of the original text.

The longer the original travel guide, the fewer errors you make while decoding, and the smaller the ratio of the encoded guide’s length to the original guide’s length. That ratio shrinks–as the guide’s length grows–to H. You’ve compressed a message maximally efficiently. As the Swiss say: Glückwünsche.

How does compression relate to QI? Quantum states form messages. Polar codes, ETH scientists have shown, compress quantum messages maximally efficiently. Researchers are exploring decoding strategies and relationships among (quantum) polar codes. With their help, Shannon-coded travel guides might fit not only in my camera bag, but also on the tip of my water bottle.

Should you need a Zürich travel guide, I recommend Grossmünster Church. Not only does the name fulfill your daily dose of umlauts. Not only did Ulrich Zwingli channel the Protestant Reformation into Switzerland there. Climbing a church tower affords a panorama of Zürich. After oohing over the hills and ahhing over the lake, you can shift your gaze toward ETH. The worldview being built there bewitches as much as the vista from any tower.

A tower with a view.

With gratitude to ETH’s QI-theory group (particularly to Renato Renner) for its hospitality. And for its travel advice. With gratitude to David Sutter for his explanations and patience.