I keep coming across the opinion that physics containing imaginary numbers is somehow a crazy and weird phenomenon, such as this article.
Complex numbers are an excellent tool for modelling rotations. When we multiply a vector by i, we effectively rotate it anticlockwise by 90 degrees around the origin. Rotations are everywhere in reality, and it’s thus unsurprising that a tool that’s good at modelling rotations shows up in things like the Schrödinger Equation.
The article was weird because it implied you couldn’t do without them, before backing off. ‘Physicist says math with imaginary numbers is more beautiful than alternatives.’
I keep coming across the opinion that physics containing imaginary numbers is somehow a crazy and weird phenomenon, such as this article.
Complex numbers are an excellent tool for modelling rotations. When we multiply a vector by i, we effectively rotate it anticlockwise by 90 degrees around the origin. Rotations are everywhere in reality, and it’s thus unsurprising that a tool that’s good at modelling rotations shows up in things like the Schrödinger Equation.
The article was weird because it implied you couldn’t do without them, before backing off. ‘Physicist says math with imaginary numbers is more beautiful than alternatives.’
Exactly. We can replace the use of imaginary numbers with matrix operations.
Schrödinger himself was annoyed by the imaginary part in his equation. In a letter to Lorentz on 6 June, 1926, Schrödinger wrote:
Surely he knew that he could have done without imaginary numbers.