Are Imaginary Numbers Not Quite So Imaginary as We Thought?
When you first study exponents and roots, you learn that there is no square root of a negative number. However, if you move beyond basic arithmetic to higher math, you learn about something called an imaginary number, which is a number that, when multiplied by itself, produces a negative number. It's generally represented with the letter i.
Although the system of imaginary numbers and complex numbers (which combine real and imaginary numbers, as in 2+5i) originally arose as a theoretical construct for dealing with calculations related to certain kinds of curves, it also has a role in quantum mechanics. Even more interesting, it appears that the imaginary numbers in quantum mechanics may not be mere simplifications of math that can be done entirely with real numbers, albeit in a more cumbersome form, but may actually be required to make the equations work properly.
And that raises some questions at the place where theoretical physics verges upon philosophy.
Although the system of imaginary numbers and complex numbers (which combine real and imaginary numbers, as in 2+5i) originally arose as a theoretical construct for dealing with calculations related to certain kinds of curves, it also has a role in quantum mechanics. Even more interesting, it appears that the imaginary numbers in quantum mechanics may not be mere simplifications of math that can be done entirely with real numbers, albeit in a more cumbersome form, but may actually be required to make the equations work properly.
And that raises some questions at the place where theoretical physics verges upon philosophy.