> Although complex numbers are essential in mathematics, they are not needed to describe physical experiments, as those are expressed in terms of probabilities, hence real numbers. Physics, however, aims to explain, rather than describe, experiments through theories. Although most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces. This has puzzled countless physicists, including the fathers of the theory, for whom a real version of quantum theory, in terms of real operators, seemed much more natural.<p>I wonder if the use of complex numbers in QM theories to describe a real world that only needed real numbers inspired Asimov's 1942 short story "The Imaginary"?<p>In that story psychology has been developed into a hard science. In some third rate college on some backwater planet some first year psychology students were doing a lab where they ran some animals through sequences of stimuli and observing the reactions and verifying they matched what the math said should happen.<p>One of the animals fell asleep, which was not what was supposed to happen. It was reproducible and very specific. You run through that exact sequence of stimuli, and as soon as you hit the last one it falls asleep. Vary the order and it doesn't sleep. Vary the timing by even a tiny amount, no sleep.<p>Word of this got back to the galactic federation's leading psychologist. Think the Einstein of psychology. He utterly could not explain it. Eventually though he came up with equations that worked, but they involved imaginary numbers. When applying these equations to the specific stimulus sequence all the imaginary quantities squared or cancelled out and you ended up with a real result, which was that the animal would sleep.<p>This was controversial and caused quite an uproar in psychological circles, and while the leading psychologist was away dealing with that a couple of his students found a case where the imaginary numbers did not get squared or cancelled out. The predicted real world reaction to the stimulus sequence involved an imaginary number, and they have no idea what the heck that even means.<p>They try it, and what it means turns out to be that some kind of slowly expanding radiation field gets created around the animal that kills other life that spends too long in the field.<p>The top psychologist is called back and is able to calculate further stimuli that will stop the expansion. That works and catastrophe is averted.<p>Asimov in 1942 would certainly have been aware of QM and the whole "complex number theory to make real number predictions" aspect of it.