Soleron on 27 September 2008
Imaginary numbers are as real as electrons. Electrons are a convenient analogy that we use to help our minds understand the world. Electrons do not exist, because there is no such thing as a 'particle' or 'wave', merely a collection of numbers that interact according to equations. Quantum theory has shown conclusively that we cannot treat electrons as real particles or the maths wouldn't work out. However, thinking of them as particles is a device that can help us to understand the world.
In the same way, imaginary or complex numbers do not exist. However, clearly some physical processes rely on these constructs to happen. Therefore, we act as if they do exist for the purposes of not having to understand what it means, just like electrons.
So, imaginary/complex numbers do not exist, but neither do electrons. Anyone is free to temporarily treat either of them as real to make it easier to understand how the world works.
