It should be impossible to measure an imaginary number in the lab, but a group of researchers have found a way to do so. They produced the equivalent of a magnetic field of imaginary strength, meaning the imaginary quantities in their experiment were measurable.
Imaginary numbers are defined as the square root of a negative number, which is a value that shouldn’t be able to show up on the dials of a measuring instrument. This may make imaginary numbers seem like an impractical quirk of mathematics, but they are important ingredients of many physics theories where, for instance, they are useful for balancing equations.
at the Beijing Computational Science Research Center and her collaborators have now constructed an experiment in which these important imaginary numbers can actually be measured.
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They set out to study a system comprising a row of tiny magnets. These can either all be aligned to make a single large magnet, or they can each be orientated so that their individual magnetic fields cancel out, and the whole system is non-magnetic. At high temperatures, this system is typically non-magnetic, but cooling it down makes it undergo a phase transition: there is a temperature at which all the individual magnets align and the whole system suddenly becomes magnetic, just as water undergoes a phase transition to become ice at 0°C (32°F).
What interested Gao and her colleagues is that the equations which capture this magnetic phase transition contain imaginary numbers, most notably a magnetic field of imaginary strength.
Since all existing magnets produce real magnetic fields, the researchers found a different way to convert the equations into reality. They used a mathematical trick to translate the system of magnets into a system of photons, or particles of light. These photons were sent through a special maze that changed the photons’ quantum properties. The researchers then measured these properties when the photons exited the maze, which led them to one of two detectors. In this photonic version of the magnetic system, creating an imaginary magnetic field was equivalent to forcing some photons to get lost in the maze in a specific way, stopping them from ever reaching its end.
Gao says that it was challenging to fine-tune every element of the experiment to make this happen, but her team ultimately succeeded. This allowed them to physically measure several quantities that are typically considered to be purely mathematical. For instance, something called the “partition function” – which is a theorist’s starting point for examining what the magnets do during the phase transition – was now something that the team could measure instead of deriving mathematically with a pen and paper.
“The line between experiment and theory becomes very blurry here,” says at University of Nebraska–Lincoln. He studied a similar problem in 1998, but he says that back then the line was more like a “brick wall”.
at Aalto University in Finland says that very few experiments have so far managed to access mathematical quantities in this way, and the new experiment surpasses them in how many of them became experimentally accessible.
Binek and Flindt both say that the new method could be a powerful way to study exotic phase transitions that are not theoretically well-understood yet – for instance, those in more complicated models of magnets – or to test aspects of theories that previously seemed untestable.
Reference: Physical Review Letters,
