How to Destroy the Universe (27 page)

In 2005, US physicist Victor Yakovenko decided to work out exactly what this rule is. He based his reasoning on a rather unlikely model: the behavior of atoms in a gas. Yakovenko realized that money is rather like energy, in that it can never be destroyed—but simply flows from one place to another. He thus modeled the financial dealings of a large group of people using the same mathematical formulae used to describe atoms of gas colliding with one another and exchanging energy. The same formula from the gas theory giving the number atoms above a certain amount of energy gives the number of people with more than any given amount of wealth. When Yakovenko dug out data on the income of US citizens he found that they matched his model exactly.

These approaches use concepts from physics as analogues to the behavior of economic systems. But in the future, new physics could actually change the course of finance for real. US mathematician Steve Bleiler is one researcher who takes this view. He's been investigating a relatively new branch of science known as quantum game theory.

Ordinary game theory, as the name suggests, is the branch of math that deals with selecting the optimal strategies players should use to maximize their return
when playing a game. It works by assigning every possible strategy a numerical value known as the “pay off.” The best strategy to choose is the one that gives the highest pay off in the worst-case scenario—in other words, when your opponent is also playing optimally. This situation, where both sides play their optimal game, is known as a Nash equilibrium, after the US mathematician John Forbes Nash, who put forward the idea in the 1950s. Game theory is used by political campaigners and military planners, and by economists to help them select investment strategies.

The existing formulation of game theory relies on classical laws of information, where data is stored and processed as binary digits, or bits: a stream of 1s and 0s. But in the coming years, classical information processing looks set to give way to its quantum equivalent, using quantum computers that encode information as “qubits” (which can be both 1 and 0 at the same time), giving them capabilities that far outstrip any desktop PC of today (see
How to crack unbreakable codes
). This new information architecture will usher in a new incarnation of game theory, known as quantum game theory. Bleiler and many other researchers believe that quantum game theory will throw up radically different optimal strategies from those of the classical theory. Traders who are aware of these strategies when doing business over quantum information channels will have a distinct edge over those who don't.

If the science of how the world works can shed light on economics, then it seems reasonable to wonder whether economics can return the favor. And it seems that it can, through what have become known as prediction markets. These work rather like a stock exchange, but instead of buying and selling shares in companies, traders deal in the outcome of future events. That might be the result of a political election, for example. In this case, traders can invest in virtual shares in each political party, with each share priced between £0 and £1. As politicians hit the campaign trail, the traders can buy or sell their shares. And as they do, market forces drive the share prices to reflect each party's likelihood of getting elected. For example, if the UK Conservative party is trading at £0.42 per share, that translates into a 42 percent chance of them winning. Once all the votes in the election have been counted, those holding shares in the winner get £1 per share; everyone else gets nothing.

Since 1988, the University of Iowa has run just such a market on the result of US presidential elections. Called the Iowa Electronic Market (IEM), it's been closer to the actual outcome than the opinion polls 74 percent of the time—and correctly predicted Barack Obama's 2008 victory. With the Internet as a convenient interface for traders, there are now online markets in everything from the weather to the box office performance
of movies. The Hollywood Stock Exchange correctly forecast 32 of the 39 nominations for the 2006 Oscars.

Prediction market Intrade is even running a market on the discovery of the Higgs boson (see
How to recreate the Big Bang
), though from the prices they are offering, the odds of it turning up do not look great. Professor Robin Hanson, an economist at George Mason University, Washington DC, even believes betting on scientific issues could accelerate the pace of research—offering extra incentives to scientists and stimulating public interest in science. Hanson admits his idea still needs some development, and indeed a shift in the law—at present betting on scientific issues is illegal in some countries. But if it gets the go-ahead then, while physics could hold the future for economics, economics may well tell us the future of physics.

• Secret society

• Code breakers

• Public key encryption

• Quantum computing

• Shor's algorithm

• Quantum solace

Codes are a crucial part of military communications and for conducting secure financial transactions across the world's electronic banking networks. Modern encryption techniques are so complex it would take longer than the age of the Universe to crack them using even the fastest computers. Well, almost. Quantum physics is now making possible computers that can decipher the toughest codes in just minutes.

Every time you send your bank details over the Internet you are trusting your hard-earned savings to a system that could soon be about as secure as tissue paper. Financial dealings are encrypted, or translated into
code, before they are sent, just in case any eavesdroppers happen to be listening in. Most encryption systems rely on ciphers, which are mathematical procedures that are fiendishly hard to unpick, unless you are the intended recipient with the key that tells you how the procedure can be reversed. A simple code might involve switching the letters of the alphabet in your message for different ones. This is known as a substitution cipher. But ciphers rapidly become more complicated. For example, you could use different substitution keys for every letter—rotated in a strict cycle that only you and your recipient know.

The first example of coded text is believed to have been made in ancient Egypt in 1900
BCE
, when a scribe drafted a passage of text using a non-standard set of hieroglyphs. Some of the first cryptanalysts—code breakers—lived in 16th-century England. The English had gained a reputation for intercepting the communications of foreign diplomats, so many governments began encrypting their important messages. In response, England founded its first intelligence department, dedicated to deciphering these messages.

Perhaps the most notable triumph of England's (now Britain's) codes and cipher effort happened 350 years later, during World War II. In 1938, with war looming,
the Government Code & Cipher School (GC&CS) set up a code breaking center to decipher enemy transmissions at Bletchley Park, a Victorian mansion in Buckinghamshire. The center was assigned the codename Station X. The Bletchley code breakers were some of the greatest mathematical minds of the 20th century. By the end of the war they had broken the Nazis' most sophisticated encryption system: the Enigma.

Deciphering the Enigma was facilitated in part by the capture of actual Enigma machines and codebooks. Indeed, the danger that a third party may get hold of the key is the weakness of all codes. Or at least it was prior to a discovery in the early 1970s by a team of researchers working at Britain's Government Communications Headquarters (GCHQ). James Ellis, Clifford Cocks and Malcolm Williamson devised an encryption system in which you can tell the key to whomever you like, confident that only the message's intended recipient will be able to read it. Called “public-key cryptography,” the system works using some smart yet simple math. The intended recipient of the message picks two very large prime numbers, that is numbers which can only be divided by themselves and the number one. These form the secret key, needed to read the message, and aren't revealed to anybody. Multiplying these two numbers together produces what is called
the public key, which the recipient broadcasts to all and sundry. Encrypting a message using the code only requires knowledge of the public key, but to decode that message requires the two factors, which are only known to the recipient. It is easy to multiply two big numbers together, but splitting one large number into its factors is phenomenally hard, so the secret key remains secret.

GCHQ's secrecy policy means this system is often credited to a team from MIT, who discovered it several years later. Today, it's best known as RSA, after the three initials of the MIT group's surnames, Rivest, Shamir and Adleman. RSA is one of the most secure encryption systems in use today and is employed widely in electronic commerce. It is very secure. As of April 2010, the largest number factorized is 232 decimal digits long. It took researchers two years using hundreds of computers to get the answer. It is estimated that to factorize a 2,000-digit number would take longer than the estimated time for the Sun to burn itself out. But now RSA looks set to be undermined by a radical new breed of computer—one that runs in parallel universes.

Quantum computers were first conceived by the British physicist David Deutsch in 1982. Ordinary, or
“classical,” computers work by storing data in the form of binary digits, or “bits,” represented by a stream of 1s and 0s. These are stored inside the computer's circuits using electronic switches called transistors—switching the transistor to the “off” position corresponds to 0, while switching it “on” records a 1. The data is then manipulated using electronic logic gates, which operate according to the laws of classical electromagnetism. However, on the smallest scales, matter doesn't obey classical electromagnetism. It is dominated instead by the laws of quantum theory. Deutsch realized that if you could build logic gates which were small enough that they operated according to quantum laws, they could permit a new kind of computing machine with unusual and powerful capabilities.

Quantum computation is based not on bits but on qubits, short for “quantum bit.” Whereas a classical bit can take the value either 0 or 1, a qubit is both 0 and 1 at the same time. This is thanks to a weird property of quantum systems that enables them to exist in all possible states at the same time until the system is actually measured. A number of qubits together make a “qubyte.” A classical byte, made from 8 bits, can store any one number between 0 and 255. An 8-qubit qubyte, however, stores every number between 0 and 255 at the same time.

Passing a qubyte through a quantum processor allows all 256 different numbers stored in the qubyte to be
processed in one go instead of one-by-one. Deutsch calls this “quantum parallelism.” If he is right, quantum computers run their parallel processes in parallel universes. The technical name for this is the “many worlds interpretation” of quantum theory. It says that there is an infinite number of universes in which every conceivable eventuality happens (see
How to live forever
). Deutsch has calculated that a quantum processor could easily be 10
⁵⁰⁰
times more effective than its classical counterpart—that's a staggeringly large factor of 1 followed by 500 zeroes. But all the data for these parallel calculations must be stored somewhere. The number of atoms in the Universe is only 10
⁸⁰
. As each atom can at most store one bit of useful information, there simply aren't enough atoms in our Universe alone to do the calculation. And that's where parallel worlds come in. Deutsch says the computer draws upon the computing power and data storage of its counterparts in these other universes to get tasks done super quick.

The discovery of quantum computers alone wasn't enough to make cryptographers sweat. Just like ordinary PCs, quantum processors need to be programmed. That means coming up with an algorithm—a sequence of steps that the computer can follow in order to get the calculation done. Since the rules of quantum programming were so new, no one quite knew where to start.
That changed in 1994 when a computer scientist called Peter Shor, based in New Jersey, worked out the algorithm that would allow a quantum computer to split a number of any size into its two prime factors. Whereas this calculation can take conventional computers tens of billions of years, a quantum computer may be able to do it in just a few minutes. This means that anyone intercepting a public encryption key could now have the means not only to send messages using that key but also to eavesdrop on the conversations of others.

It all looks great on paper, but actually building a quantum computer is no easy matter. Very basic designs have been constructed in labs. These work by storing data on the quantum states of subatomic particles, such as the nuclei of atoms. Each atomic nucleus has a property called quantum spin, with just two values: “spin up” and “spin down.” Crucially, a particle can exist in a superposition of both spin states at the same time, and this makes it ideal for storing the value of a qubit. The system is manipulated by bombarding the atoms with radio pulses. The final states of the qubits are then read out by measuring electromagnetic signals from the nuclei, called resonances. The problem that's holding the researchers up is a phenomenon known as decoherence. This is where a quantum system interacts with its surrounding environment, destroying the delicate balance of purely quantum interactions on which a quantum computer relies.
However, researchers are making progress. In 2009, scientists in Bristol in the UK built a rudimentary quantum processor from silicon. Whereas the silicon chips in your computer work electronically by manipulating electric charges, the Bristol chip is an optical device that acts on individual photons of light. The device was not only free from the effects of decoherence, but the team were able to run Shor's algorithm on it. It may still be some time until we have quantum processors buzzing under our desks, but most researchers believe it will happen one day in the coming decades. When we do, RSA and all other forms of public-key encryption will be rendered obsolete.