Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...

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 ...

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

Now, on to the subject of complex numbers. We have stayed away from this subject until now simply because we did not want to confuse things. Initially, it is easy to think of signals as “real valued.” ...

In a previous post, I argued that concepts and concerns, such as free will and determinism, can be complex in the same sense in which numbers can be: in other words, in combining a real with an ...