Six Degrees to the Emergence of Reality

"I know a guy who knows a guy who knows a guy who knows a guy who knows a guy who knows Kevin Bacon." — "Weird Al" Yankovich

One evening in 1994, a heavy snowstorm in Pennsylvania kept four college students indoors, watching one film with actor Kevin Bacon after another and then another. Given the numerous films in which he had acted, they reasoned, Kevin Bacon must himself know a lot of celebrities. This idea turned into the now famous parlour game "Six degrees of Kevin Bacon," in which any actor—dead or alive—can be connected with Kevin Bacon in six or fewer steps. Take Sherlock’s famous Benedict Cumberbatch, for instance: He played alongside Toby Jones in Tinker Taylor Soldier Spy, who played alongside Kevin Bacon in Frost/Nixon, so he is only two degrees removed from Kevin Bacon.

But this game highlights what turns out to be an interesting and quite common phenomenon: complex networks—whether social networks, web pages, genes, or ecosystems—may contain much more order than it might at first appear.

About 15 years ago, physicist Albert-László Barabási, now at Northeastern University while studying the complexity of the World Wide Web, created a network model to illustrate how a relatively small number of websites receives the majority of browsing hits, while the majority of sites on the internet share the remaining amount of traffic. This and related realizations led to the development of a whole new branch within the field of network science and is based on the idea that social and biological networks follow non-random patterns. (See "Embracing Complexity.") But can aspects of quantum physics be expressed in terms of a quantum theory of complex networks? Theoretical physicist Jacob Biamonte is now grappling with that question. If successful, this new line of thinking could help explain how familiar everyday physics—and even time’s arrow—emerge from the fuzzy quantum realm.

In network theory, networks are often depicted as graphs in which the nodes represent the objects we are interested in, and we can hop from node to node along the connections to perform a so-called random walk. For instance, in biology, we can try to understand genetic disorders with a graph in which the nodes form specific genes and the edges—the connections between the nodes—represent the information we can gather by studying how often specific genes in a disorder work together and actually lead to the disorder.

Biamonte, an FQXi awardee who leads a theory group currently hosted at the Institute for Scientific Interchange in Torino in Italy, describes the importance of network theory with a simple example that explains why the rich find it easy to get richer: "If you have a million dollars, you are a million times more likely to get an extra dollar than someone who only has one dollar, according to this model." That is because when you have a network in which one node has many connections, if another node enters the network, it is highly likely that this new node will also connect to a highly connected node.

The challenge is to now think about quantum physics in such a framework. "It’s already enlightening to think-up quantum generalizations of even this simplistic idea," Biamonte says.

Quantum Networks

One of the benefits of thinking about quantum networks is that it could help understand how the weird quantum realm transitions to the very different visible "classical" reality around us. When I put my coffee cup down on the table to write the next sentence, I know my cup will stay there. Yet, according to quantum mechanics, my cup could fall through the solid surface, and it could even be in more than one place at the same time. Only when I look at the cup, at which point, in quantum mechanical terms, I am making a measurement of its properties, I find it in one particular place and state. "When you are suddenly exposed to quantum theory for the first time, you face these unfamiliar concepts paired with seemingly strange mathematical questions, and it does not look a darn thing like what you have learned before," says Biamonte. This incongruence is frustrating, because quantum mechanics works so well at describing the behavior of atoms on the smallest scales, despite being so counterintuitive. "One of the oldest examples of emergence, and arguably the most important, is the question of why the world around us seems too often well described using classical physics, while the world we live in is, in actual fact quantum," says Biamonte.

This emergence of the classical reality might come about as a result of the idea that the whole is more than the sum of its parts, which, as Barabási and others already showed, also is the case in complex networks that are found to follow an organizing principle rather than being a completely random pattern. "Complex network theory studies various types of networks with some particular focus on emergence—seeing the forest through the trees," says Biamonte. With the aid of an FQXi grant of over $85,000, Biamonte and others are pioneering a new field of research that combines complex network theory and quantum information theory, and Biamonte is optimistic that this will start to shed light on emergence. "Having a better theory of networks and really understanding the differences between theories of networks that are not quantum and those that are will become increasingly important for the foundations of physics," explains Biamonte.

Time’s Arrow

One of the discrepancies between the classical world and the quantum world is how our world is governed by the passage of time, which only flows in one direction, from the past to the future. When watching videos in the olden days, if you accidentally hit rewind instead of fast forward, it would only take a second to realize your mistake. A barista walking backwards only to see the coffee flowing up from a cup into his pot; or an animal being unborn in a wildlife documentary; these things look inherently odd and impossible to us because they suggest that time is in fact reversed. However, microscopic processes are time symmetric—collisions between atoms or chemical reactions—can occur backwards or forwards. So any quest to understand emergence must also include trying to understand how these seemingly contradictory processes can be matched.

Biamonte and colleagues have revisited the foundations of quantum physics dealing with time symmetry laid out by Hungarian-American theoretical physicist Eugene Wigner as early as the late 1920s and reformed into a network theory in terms of "quantum walks"—the equivalent of random walks in the quantum world. In this picture, particles are located on the network’s nodes. The connections between the particles represent the interaction between the particles and "walks" are generally thought of as time-symmetric, jumping backwards and forwards with the same probability. But with clever mathematical insight it is possible to find certain walks that do not follow time-symmetry, giving rise to a host of new quantum behaviors that can potentially be used for technological applications in quantum computing (arXiv:1405.6209).

"To verify this effect, we’ve written several papers and in the process we ended up putting this theory of time reversal symmetry into the language of quantum information science," explains Biamonte. His collaborator, Seth Lloyd, an FQXi member and professor of mechanical engineering at MIT, explains that they have shown that things work differently in a universe that is perfectly time symmetric, compared with a universe that has only approximate time symmetry.

"Time and reality are large concepts and hard to grapple with," says Lloyd. "Our work shows that there are counterintuitive subtleties in the physical nature of time and is an example of how small quantum information processes can be used to explore big questions about nature."