Blurring Causal Lines

"Within the circle of light around the gas lamp was what at first appeared to be a heap of clothes. It was situated within a large area of reflective blackness, the edges of which were irregular—like the borders of a country on a map. The air smelled faintly of rusting iron. ’Brother Stanislav’ said Reinhardt."

Thus psychoanalyst-detective Max Liebermann is introduced to his first body in Frank Tallin’s crime novel Vienna Secrets set in Vienna, Austria, in the early years of the 20th Century. Instinctively we know that when a body turns up in suspicious circumstances, indeed any circumstances, a whole host of events must have preceded the death. In fact, it is not only detective novels that rely on such ordering; our entire lives are ruled by cause and effect.

"All events are causally ordered such that for every pair of events you can say that one event is cause or effect of the other," says quantum physicist Caslav Brukner. Causality is so ingrained in the texture of our lives, and our brains, that it is hard to imagine letting go of it. Yet this is exactly what Brukner addressed with the help of an FQXi grant of over $63,000. The implications of this idea could be enormous: we might find that space, time and causality are not the basic building blocks of nature. It would have practical consequences too—potentially helping us to build quantum computers to outperform today’s devices.

In present day Vienna at the Institute for Quantum Optics and Quantum Information at the University, Brukner heads a small group of researchers who try to understand the foundations of quantum theory, which governs the behaviour of atoms on the smallest scales. For instance, a quantum particle can be in multiple places at the same time; before it is observed, it exists in a superposition of each of these possible positions simultaneously. It’s only when the particle is measured that it settles into a well-defined position. But despite such oddities, quantum particles are still conventionally thought to show a healthy respect for causality. That’s because in quantum mechanics space and time form the pre-existing backdrop against which everything happens. This means that if event A is before B, B can never be before A.

"In all our physical theories we assume a well-defined causality," says Brukner. That’s even true for Einstein’s special and general theories of relativity, which mess with many of our everyday conceptions by stating that time is another dimension, like the three dimensions of space. Einstein taught us that, depending on how two people move relative to one another, they may disagree on the order in which they perceive two independent events to have occurred. Causality is still sanctified in relativity, however, because there’s no way any observer could perceive an effect to have taken place before its cause.

But Brukner argues that to truly understand nature and the world we live in—and perhaps to eventually combine quantum theory and general relativity into one framework—we may have to get away from this safe sense of order. "If we believe in the validity of quantum mechanical laws, and we believe in the validity of general relativity, we need to think of a situation in which the causal order is not well-defined," says Brukner.

Removing Causal Order

In research published in Nature Communications in 2012, Brukner and his colleagues developed a framework in which they suggest we might be able to free ourselves from causality by using quantum superposition of the relationship between events, such that it becomes impossible to know which comes first (O. Oreshkov, F. Costa & C. Brukner, Nature Communications 3, Article number: 1092). The researchers made events A and B into fictional characters, Alice and Bob, who both own a laboratory. In their laboratories—locally—the rules of quantum mechanics apply. (See "Cheating the Causal Game.")

The team imagined what would happen if Alice and Bob each received a particle from outside their laboratories. In this thought experiment, Alice and Bob each change their particle in some way, before sending the changed particle back out of their lab and on to the other’s lab. Each particle visits both labs only once. That means that if the labs were embedded in a causal structure, it would be possible to work out in what order a particle visits the labs.

But here was the trick. To allow the physicists to create a superposition between the order of events in Alice and Bob’s laboratories, Brukner’s team conjectured that the two laboratories were not part of a larger causal system. This causal fuzziness created an uncertainty in the order in which events between Alice and Bob had taken place.

"In absence of a global causal order the fact that the particle enters each laboratory only once would not allow us to conclude in which order the particle visits the labs," says Brukner. "We can talk about situations in which we can not see in advance whether A is before B, or B is before A and we can have something which we roughly identify with superposition of causal orders."

Superfast Computing

Removing causality is more than just an interesting conceptual shift; it may also have benefits for those attempting to build super fast computers that exploit quantum laws to outperform today’s machines. While our personal computers store information as bits that can either be 1 or 0, quantum computers—which were first proposed in the 1980s—use quantum bits, or qubits, that can represent a 1, 0, or any superposition of these states. The ability of qubits to hold multiple states at once would allow quantum computers, in theory, to solve problems more quickly than classical ones.

Here’s where causality (or a lack of it) comes in: Calculations in a quantum computer follow a fixed sequence of quantum logic gates, at the end of which one number drops out. But quantum information without causal order could, in theory, allow for an even bigger speed-up because it would no longer be necessary for the calculations to follow a sequential route. The effect would be amplified, explains Brukner, when the question is scaled up from just two ports of call—Alice and Bob in Brukner’s research—to numerous others.

It took a couple of years for the ideas of Brukner and his team to be tested, however. "Nowadays, theory is very much advanced as compared to experiment," says Stefan Wolf, an expert on quantum information at the University of Lugano in Switzerland. "The reason is that this is often a very big step, where one faces both technological difficulties and conceptual challenges."

But now, experiment is catching up. In a study published in August 2015 in Nature Communications, quantum physicist Philip Walther and his group, also at the University of Vienna, showed that the superposition of quantum logic gates can be achieved experimentally (L. M. Procopio, Nature Communications 6, Article number: 7913). They sent one photon (or particle of light) to visit two quantum gates in both orders. While it was possible to observe that both gates were indeed visited, Walther confirmed Brukner’s prediction that it was impossible to see in what order. It will take more advanced experiments to show that the predicted speed-up scales up, however.

While this work might lead to more advanced quantum computers, what makes Brukner even more excited is the idea that we can learn something fundamental about nature. He argues that the difficulties in developing a unified framework for quantum theory and Einstein’s theory of gravity might partially lie in our inability to incorporate the lack of global causality in the framework. "I hope this will help people conceptually to develop new ideas towards this goal."

"The work is very fundamental and touches on the deep questions on the global causal understanding of quantum theory and challenges the established views on space and time," adds Wolf.