What the quantum mechanical commutation relation says is that if you do “position and then momentum” versus “momentum and then position,” the two answers will be different by exactly the amount iℏ, where i is the square root of (-1), and ℏ is the reduced Planck’s constant
See, this is part of what makes my liberal arts major head hurt. The reduced Planck’s constant is a number I can plug in, at least approximately (since it is Planck’s constant divided by 2pi. But if I want to calculate what this difference will be just what the Hell do I use for square root of -1?
My wife, the science fiction novelist, refers to “imaginary” numbers as “fictional numbers.” Just what do I plug into that “i” part of the formula to figure out what the difference is? I mean to me it almost doesn’t matter what the constant is when it is multiplied by a number that is . . . fictional.