According to new research, if we try to leave them out of quantum mechanics, our description of nature becomes faulty:
“Without imaginary numbers, the device on which you are reading this article probably wouldn’t even work. As science writer Padavic-Callaghan points out, When you set out to try and capture a quantum state in the language of mathematics, these seemingly impossible square roots of negative numbers are an integral part of your vocabulary. Eliminating imaginary numbers would highly limit how accurate of a statement you could make. The discovery and development of quantum mechanics upgraded imaginary numbers from a problem seeking a solution to a solution that had just been matched with its problem. As the physicist and Nobel laureate Roger Penrose noted in the documentary series Why Are We Here? (2017): ‘[Imaginary numbers] were there all the time. They’ve been there since the beginning of time. These numbers are embedded in the way the world works at the smallest and, if you like, most basic level.’ – Karmela Padavic-Callaghan, “Imaginary Numbers Are Real” at Aeon (July 14, 2022)”News, “Recent research: Imaginary numbers are part of the real world” at Mind Matters News (July 17, 2022)
Takehome: Perhaps the universe is bound to seem mysterious, in part because it is not wholly material. It keeps the rules but the rules are not always what we expect.
You may also wish to read: You may also wish to read: Yes, you can manipulate infinity in math. The hyperreals are bigger (and smaller) than your average number — and better! (Jonathan Bartlett)