The theory of quantum mechanics earned its stripes by making accurate predictions concerning the behavior of atoms and the tiny particles that make them up. No one quite understands what quantum mechanics means, but it works. That's its appeal, and so it's understandable that researchers in other fields might want to borrow the insights of quantum mechanics.

Enter "quantum cognition," a new theory suggests that the mathematical principles behind quantum mechanics could be used to better understand another notoriously inexplicable area of study: human behavior.

Researchers from Ohio State University, Indiana University, and Queensland University of Technology, recently published a pair of review papers explaining this emerging theory. Quantum models are particularly useful when humans behave in ways that seem irrational under classical probability theory.

"It's interesting—when we say something is irrational in decision-making, it's because it's against what a classical probability-based decision model should predict," says Zheng Joyce Wang, an associate professor of communication at Ohio State University and a co-author on both papers. "But humans don't behave in that way."

Take, for example, the classic prisoner's dilemma. Two criminals are offered the opportunity to rat each other out. If one rats, and the other doesn't, the snitch goes free while the other serves a three year sentence. If they both rat, they each get two years. If neither rats, they each get one year. If players always behaved in their own self-interest, they'd always rat. But research has shown that people often choose to cooperate.

Classical probability can't explain this. If the first player knew for sure that the second was cooperating, it would make most sense to defect. If the first knew for sure that the second was defecting, it would also make most sense to defect. Since no matter what the other player is doing, it's best to defect, then the first player should logically defect no matter what.

A quantum explanation for why player one might cooperate anyway would be that when one player is uncertain about what the other is doing, it's like a Schrödinger's cat situation. The other player has the potential to be cooperating and the potential to be defecting, at the same time, in the first player's mind. Each of these possibilities is like a thought wave, Wang says. And as waves of all kinds (light, sound, water) are wont to do, they can interfere with each other. Depending on how they line up, the can cancel each other out to make a smaller wave, or build on each other to make a bigger one. If "the other guy's going to cooperate" thought wave gets strengthened in a player's mind, he might choose to cooperate too.

The making of a decision collapses a thought wave into a particle, according to Jerome Busemeyer and Peter Bruza's book Quantum Models of Cognition and Decision. "We argue that the wave nature of an indefinite state captures the psychological experience of conflict, ambiguity, confusion, and uncertainty; the particle nature of a definite state captures the psychological experience of conflict resolution, decision, and certainty," they write.

The act of answering a question can move people from wave to particle, from uncertainty to certainty. In quantum physics, the "observer effect" refers to how measuring the state of a particle can change the very state you're trying to measure. In a similar way, asking someone a question about the state of her mind could very well change it. For example, if I'm telling a friend about a performance review I have coming up, and I'm not sure how I feel about it, if she asks me "Are you nervous?" that might get me thinking about all the reasons I should be nervous. I might not have been nervous before she asked me, but after the question, my answer might become, "Well, I am now!"

This doesn't necessarily happen every time someone asks you a question—some answers you just know, you don't have to make them up on the spot, which means there might not be an observation effect. "For many questions you do have a stored answer that is simply retrieved on demand (e.g. Have you ever read a certain book?)," Busemeyer and Bruza write. "But other questions are new and more complex and you have to construct an answer from your current state and context (e.g. Did you like the moral theme of that book?)."

Another key concept in quantum cognition is the idea of "complementarity." Two ideas are complementary if they are incompatible, if you can't think about them both at the same time. This is similar to the uncertainty principle in quantum physics, which states that if you are certain of a particle's position in space, you must necessarily be uncertain of its speed, and vice versa. Translated to decision-making, this means that if you are certain about what you think about one thing, you can't simultaneously be certain what you think about another thing.

"We have limited capacity," Wang says. "This is nothing new. We know we cannot think about everything at the same time." We can think about some things at the same time, for example, a person can simultaneously know her name and age. Those two things are compatible. You can ask the questions "What's your name?" and "How old are you?" in whatever order and expect to get the same answers. Classical probability works here. But if the answers are incompatible, then the order you ask the questions matters. Here's an example, from the Busemeyer/Bruza book:

Suppose a teenage boy is directly asked "How happy are you?" the typical answer is "Everything is great." However if this teenager is first asked "When was the last time you had a date?" then the answer tends to be "Seems like a long time ago." Following this sobering answer, a later question about happiness tends to produce a second answer that is not so sunny and rosy.

In this scenario, asking the teen about the dates he's not having before asking if he's happy gets him thinking about happiness in terms of romantic success, which, welcome to the rest of your life, hypothetical teen boy. This explanation makes sense, but like many non-quantum explanations of the order effect, it's "vague, general, and verbal," Wang says.

"Intuitively, it makes sense, of course," she continues. "The first question changes the context to answer the second question, but the problem here is that it's not very precise. It's not really very testable."

Quantum probability can take the intuitive answer and show how it works with math. Previous work done by Wang and her colleagues showed that quantum models were able to predict order effects shown in 70 different national surveys. None of this means that the brain is necessarily a quantum machine. It may be! But we don't know. Either way, scientists can still use quantum probability to predict and model behavior.

All these behaviors that seemed irrational under classical probability models become explainable through quantum theory. (Which, incidentally, can also explain all the stuff that classical probability can, leading Wang to think that "classical probability theory is a special case of quantum probability theory.)

"Rationality itself depends on how you define it," Wang says. "It's perfectly consistent with theory, and so it's rational. Quantum rational."