Imaginary Numbers Could Be Needed To Describe Reality, New Studies Find


InfiniteZero writes: Imaginary numbers are necessary to accurately describe reality, two new studies have suggested. Imaginary numbers are what you get when you take the square root of a negative number, and they have long been used in the most important equations of quantum mechanics, the branch of physics that describes the world of the very small. When you add imaginary numbers and real numbers, the two form complex numbers, which enable physicists to write out quantum equations in simple terms. But whether quantum theory needs these mathematical chimeras or just uses them as convenient shortcuts has long been controversial. In fact, even the founders of quantum mechanics themselves thought that the implications of having complex numbers in their equations was disquieting. In a letter to his friend Hendrik Lorentz, physicist Erwin Schrodinger — the first person to introduce complex numbers into quantum theory, with his quantum wave function — wrote, “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. quantum wave function is surely fundamentally a real function.”

Schrodinger did find ways to express his equation with only real numbers alongside an additional set of rules for how to use the equation, and later physicists have done the same with other parts of quantum theory. But in the absence of hard experimental evidence to rule upon the predictions of these “all real” equations, a question has lingered: Are imaginary numbers an optional simplification, or does trying to work without them rob quantum theory of its ability to describe reality? Now, two studies, published Dec. 15 in the journals Nature and Physical Review Letters, have proved Schrodinger wrong. By a relatively simple experiment, they show that if quantum mechanics is correct, imaginary numbers are a necessary part of the mathematics of our universe. “The early founders of quantum mechanics could not find any way to interpret the complex numbers appearing in the theory,” lead author Marc-Olivier Renou, a theoretical physicist at the Institute of Photonic Sciences in Spain, told Live Science in an email. “Having them [complex numbers] worked very well, but there is no clear way to identify the complex numbers with an element of reality.” To test whether complex numbers were truly vital, the authors of the first study devised a twist on a classic quantum experiment known as the Bell test. The test was first proposed by physicist John Bell in 1964 as a way to prove that quantum entanglement — the weird connection between two far-apart particles that Albert Einstein objected to as “spooky action at a distance” — was required by quantum theory.



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