A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth with accurate calculations of hydrogen’s emission and absorption of light. There was, however, a snag. The central equation of quantum mechanics featured the imaginary number 𝑖, the square root of −1.
Physicists knew 𝑖 was a mathematical fiction. Real physical quantities like mass and momentum never yield a negative amount when squared. Yet this unreal number that behaves as 𝑖² = −1 seemed to sit at the heart of the quantum world.
After deriving the i-riddled equation — essentially the law of motion for quantum entities — Erwin Schrödinger expressed the hope that it would be replaced by an entirely real version. (“There is undoubtedly a certain crudeness at the moment” in the equation’s form, he wrote in 1926.) Schrödinger’s distaste notwithstanding, 𝑖 stuck around, and new generations of physicists took up his equation without much concern.
Then, in 2021, the role of imaginary numbers in quantum theory attracted newfound interest. A team of researchers proposed a way to empirically determine whether 𝑖 is essential to quantum theory or a mere mathematical convenience. Two teams quickly followed up to perform the intricate experiments and found supposedly unequivocal evidence that quantum theory needs 𝑖.
This year, however, a series of papers has overturned that conclusion.
In March, a group of theorists based in Germany rebutted the 2021 studies, putting forward a real-valued version of quantum theory that’s exactly equivalent to the standard version. Two theorists in France followed up with their own formulation of a real-valued quantum theory. And in September, another researcher approached the question from the perspective of quantum computing and arrived at the same answer: 𝑖 isn’t necessary for describing quantum reality after all.
Quanta Magazine
A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth with accurate calculations of hydrogen’s emission and absorption of light. There was, however, a snag. The central equation of quantum mechanics featured the imaginary number 𝑖, the square root of −1.
Physicists knew 𝑖 was a mathematical fiction. Real physical quantities like mass and momentum never yield a negative amount when squared. Yet this unreal number that behaves as 𝑖² = −1 seemed to sit at the heart of the quantum world.
After deriving the i-riddled equation — essentially the law of motion for quantum entities — Erwin Schrödinger expressed the hope that it would be replaced by an entirely real version. (“There is undoubtedly a certain crudeness at the moment” in the equation’s form, he wrote in 1926.) Schrödinger’s distaste notwithstanding, 𝑖 stuck around, and new generations of physicists took up his equation without much concern.
Then, in 2021, the role of imaginary numbers in quantum theory attracted newfound interest. A team of researchers proposed a way to empirically determine whether 𝑖 is essential to quantum theory or a mere mathematical convenience. Two teams quickly followed up to perform the intricate experiments and found supposedly unequivocal evidence that quantum theory needs 𝑖.
This year, however, a series of papers has overturned that conclusion.
In March, a group of theorists based in Germany rebutted the 2021 studies, putting forward a real-valued version of quantum theory that’s exactly equivalent to the standard version. Two theorists in France followed up with their own formulation of a real-valued quantum theory. And in September, another researcher approached the question from the perspective of quantum computing and arrived at the same answer: 𝑖 isn’t necessary for describing quantum reality after all.
🔗 Keep reading:
www.quantamagazine.org/physicists-take-the-imagina…
🎨 Michelle Sclafani for Quanta Magazine
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