IMAGINE that someone asks you how to distinguish consciousness from unconsciousness – a difficult task indeed. If consciousness has a physical basis, can the same be said about unconsciousness?

You might have expected psychologists to have tackled this question, but perhaps not physicists. After all, physics is concerned with the study of matter and radiation. But you would be wrong. Wolfgang Pauli, winner of the 1945 Nobel prize in physics for his work on quantum mechanics, did just that. He proposed that the interaction between consciousness and unconsciousness is analogous to one of the central ideas in quantum physics, called complementarity – that it is impossible to distinguish between the behaviour of an atomic object and its interaction with the instrument observing it.

Pauli’s analogy deals with two totally different scales of enquiry: the quantum scale, which is the realm of atoms, electrons and photons, and the macroscopic scale (in this case, the brain). Is it really possible to equate these two worlds? After all, since the 1920s, when quantum mechanics was being formulated, the mainstream position has been that the theory does not really apply to a scale beyond the quantum.

The rules that apply at the quantum scale do not obey the logic of the macroscopic world. Electrons exhibit different behaviours depending on whether they have been detected or not – as shown by the seminal double-slit experiment – and appear to be in two places at the same time. Then there’s entanglement, in which particles behave as a unit even if some distance apart.

However, over the past 15 years there has been growing evidence that quantum mechanical processes can occur on a macroscopic level, too. Anton Zeilinger of the University of Vienna, Austria, and colleagues showed that one of the key features of quantum mechanics, the interference of an electron with itself, exists even in very large molecules called buckyballs. And in a recent study of our sense of smell, it was proposed that a quantum mechanism is involved when odour molecules activate receptors in the nose.

These examples show that certain physical processes on scales larger than the very small can be explained by the rules of the quantum world. But can we use these rules even in situations where no quantum behaviour exists? We think there is great potential in this idea, and it is one of the central premises in our recent book *Quantum Social Science*. In it, we propose the use of models that are “quantum-like” (in the sense of their not having an immediate connection with quantum physics) to areas outside the natural remit of quantum physics. Specifically, we are interested in their application to the behaviour of complex social systems.

**Economic insight**

The idea of using quantum mechanics outside physics started more than a decade ago when we were trying to find new ways to model information in the social sciences – for example, information driving asset prices. We found that concepts from the quantum world can have insightful economic meaning. For instance, quantum potentials – a central concept in a particular interpretation of quantum mechanics – can play a role in the construction of pricing formulae.

Although the idea of applying quantum mechanics to social science is still quite new,there are an increasing number of examples that provide convincing evidence it will offer a new way of understanding complex situations. The area where this approach has seen the most progress is that of decision-making.

Models that describe decision-making behaviour are widely used in psychology and economics,

【For the past decade Andrei Khrennikov of Linnaeus University in Kalmar, Sweden, and Emmanuel Haven of the University of Leicester, UK, have worked together on applying the formalism of quantum mechanics to areas outside of physics. Their new book is Quantum Social Science (Cambridge University Press)】

but finding accurate ones is a challenge. Many of the traditional models are based on the assumption that we are rational beings who act to ensure an optimal outcome. But in reality this doesn’t happen because our reasoning is swayed by many biases. A classic demonstration of this is the Ellsberg paradox, a version of which was used by psychologists Amos Tversky of Stanford University in California and Eldar Shafir of Princeton University to test how people make decisions in a two-stage gamble. They showed that even though the outcome of the second stage does not depend on the first stage, a participant’s decision to enter the second gamble is influenced by whether or not they are told how they did in the first gamble.

This behaviour highlights our aversion to ambiguity and our preference for the known over the unknown, but it still puzzles economists and psychologists because it violates the basic law of total probability – a classical model to calculate the probability of an outcome.

Where does quantum physics fit into all this? Well, it turns out that this same law of total probability is also violated in the doubleslit experiment, which shows that an electron interferes with itself. To explain this mathematically, a special factor called an interference term is needed. This interference term can also be used to explain the weird probability values at play in the Ellsberg paradox, according to work led by Jerome Busemeyer from the University of Indiana in Bloomington and Diederik Aerts from the Free University of Brussels, Belgium. In Quantum Social Science we show how other decisionmaking paradoxes can also be understood using the probability laws of quantum mechanics.

Why does the mathematics of quantum mechanics offer a better way of understanding these paradoxes? Real-life decisions often depend on context – a complex blend of physical, social and financial factors. Classical probability laws cannot really accommodate context, whereas it can easily be factored into the rules of quantum probability.

Brain science is another area that could benefit from a quantum-like approach. Applying the laws of quantum information theory to modelling the brain has kick-started the field of quantum-like artificial intelligence, in which machine learning exploits algorithms sourced from quantum mechanics. Reflecting the level of interest in this new field, in May this year Google and NASA announced the launch of their Quantum Artificial Intelligence Lab.

We are also working on understanding how voters are influenced by a stream of mass media information. It turns out that the socalled quantum master equation allows us to describe interactions between a social system and its environment (we call it a “social bath”), and thus the dynamics of voters’ preferences.

Quantum social science is still a young field, but it offers an important new way of modelling information in complex situations. But we need to be clear that this is not about reformulating social science on a quantum scale, and we are not suggesting that quantum physics is happening in the complex and large-scale processes we have described.

What would Pauli have made of this new field of quantum social science? Who knows. But judging from the reception this new avenue is receiving at conferences, and the increasing number of research grants being awarded, the future bodes well.

**为您推荐**

"the natural remit of quantum physics"是什么玩意……

结尾怎么回事？“the future bodes well. n” n是干啥的？