People often say that quantum physics is weird because it doesn’t seem rational. But of course, if you think about it, quantum physics is actually perfectly rational, if you understand the math. It’s people who typically seem irrational.

In fact, some psychologists have spent their careers making fun of people for irrational choices when presented with artificial situations amenable to statistical analysis. Making allowances for sometimes shaky methodology, there really are cases where people make choices that don’t seem to make much sense. One well-known example involved asking students whether they would buy a ticket for a Hawaii vacation in three different situations: They had passed a big test, they had failed the test, or they didn’t yet know whether they had passed or failed. More than half said they would buy the ticket if they had passed. Even more said they would buy the ticket if they failed. But 30 percent said they wouldn’t buy a ticket until they found out whether they had passed or failed.

It seems odd that people would decide to buy right away if they knew the outcome of the test, no matter what it was, but hesitated when the outcome was unknown. Such behavior violated a statistical maxim known as the “sure thing principle.” Basically, it says that if you prefer X if A is true, and you prefer X if A isn’t true, then you should prefer X whether A is true or not. So it shouldn’t matter whether you know if A is true. That seems logical, but it’s not always how people behave.

So are people just incapable of thinking logically? Maybe. But in recent years a number of investigators have developed the view that those supposedly irrational choices merely reflect the fact that people’s brains are guided by the mathematical principles of quantum physics.

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These researchers are not saying that the brain is a quantum computer, exploiting actual quantum weirdness for thinking and reasoning. They’re just saying that the quantum mathematics describing physical processes operating in the natural world is the same as the math describing the cognitive processes operating in the brain.

“Twenty years ago, a group of physicists and psychologists introduced the bold idea of applying the abstract principles from quantum theory outside of physics to the field of human judgment and decision making,” Jerome Busemeyer of Indiana University and collaborators write in a recent paper on arXiv.org. “This new field, called quantum cognition, has proved to be able to account for puzzling behavioral phenomena that are found in studies of a variety of human judgments and decisions.”

Violation of the sure thing principle, for instance, can be explained using quantum math, as Jose Acacio de Barros of San Francisco State University and Gary Oas of Stanford show in another recent paper on arXiv.org. Whether to buy the ticket to Hawaii or not can be viewed as a double-slit quantum interference experiment, where an electron passes through a screen with two slits in it and lands on a detector surface. If one of the slits is closed (corresponding to pass or fail on the test), the electron behaves like a particle and lands at a precise spot on the screen. If the two slits are open (you don’t know the test outcome) the electron behaves like a wave, making it impossible to say which slit the electron actually passed through (corresponding to not knowing the test outcome). The electron wave interferes with itself, changing the probabilities of where it will land on the screen. A quantum mechanical analysis shows that those quantum probabilities violate the sure thing principle predictions, just as the psychology students did.

Various other supposedly irrational decision making practices and poor probability judgments have been analyzed using aspects of quantum math. “Quantum models of judgment and decision have made impressive progress organizing and accounting for a wide range of puzzling findings using a common set of principles,” Busemeyer and colleagues write.

Most recently, a quantum analysis was invoked to explain the puzzle of why public opinion polls get different results when the same questions are asked in a different order. Suppose, for instance, you ask whether Shoeless Joe Jackson should be in the Baseball Hall of Fame. And then you ask the same for Pete Rose. If you switch the order, asking about Rose first and then Jackson, you get different yes/no proportions. (Jackson gets more “yes” votes if you ask about him first.) Psychologists refer to this phenomenon as a “context effect.”

Quantum probabilities can explain this paradox, as Zheng Wang and Tyler Solloway of Ohio State University, collaborating with Busemeyer and Richard Shiffrin of Indiana, reported online June 16 in the Proceedings of the National Academy of Sciences.

To oversimplify, in quantum mechanics A x B does not necessarily equal B x A (because the math uses matrices, which do not commute). So doing an operation in a different order can produce a different result. But even more striking is another quantum requirement. Not only will switching order change the answers, but the number of people who change from answering “yes” to both questions to answering “no” both times must be offset by the number who switch from “no-no” to “yes-yes.” “Likewise, the number of people who switch from ‘yes–no’ to ‘no–yes’ must be offset by the number who switch in the opposite direction,” Wang and colleagues write.

Analyzing data from dozens of opinion polls shows that this equal offset requirement is actually met when question order is switched to test the context effect, the Ohio State and Indiana investigators found. Such a result is predicted by quantum math even though there is no obvious psychological reason for it.

“To our knowledge, no traditional psychology theories impose this precise kind of symmetry constraint on context effects,” Wang and collaborators write. Since quantum physics does demand this sort of constraint, maybe it’s time to apply subatomic math to subconscious reasoning. “Even if the brain’s neural processes operate by classical rules, quantum probability may provide a better description than classical probability for the way humans reason under uncertainty,” Wang’s group asserts.

It would no doubt to be wise to withhold judgment for a while on whether quantum math really holds the secrets to quantifying cognition. But it’s at least curiosity-worthy that so many examples of quantum-brain analogies seem to describe psychological phenomena. And in a way, these experiments support some of the insights articulated by Niels Bohr, one of quantum physics’s founding fathers, many decades ago.

In 1929, Bohr noted that quantum physics refuted the view that analyzing brain processes could “reveal a causal chain that formed a unique representation of the emotional mental experience.” But in quantum physics, Bohr emphasized, an observer inevitably interacted with whatever was being observed, so “any attempt to acquire a knowledge of such [mental] processes involves a fundamentally uncontrollable interference with their course.”

Bohr foresaw that grasping the similarities shared by quantum and mental processes could lead to a deeper understanding of human thought.

“Although, in the present case, we can be concerned only with more or less fitting analogies, yet we can hardly escape the conviction that in the facts which are revealed to us by the quantum theory … we have acquired a means of elucidating general philosophical problems.”

So it might still be wrong, but it’s not entirely crazy, to think that human thought is susceptible to quantum quantification. Quantum reality underlies the ordinary (or “classical”) reality that we perceive. That reality emerges from quantum systems operating in the context of environmental influences, ranging from specific experimental observations to air molecules bouncing off of other atoms.

In a similar way, as Wang and colleagues assert, human judgments “are often not simply read out from memory, but rather, they are constructed from the cognitive state for the question at hand.” Consequently drawing a conclusion about one question alters the context, disturbing the cognitive system just as a quantum measurement disturbs an electron. Such disturbances will influence the answer to the next question, so that “human judgments do not always obey the commutative rule of Boolean logic.”

“If we replace ‘human judgments’ with ‘physical measurements,’” Wang and colleagues write, “and replace ‘cognitive system’ with ‘physical system,’ then these are exactly the same reasons that led physicists to develop quantum theory in the first place.”

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