"if Quantum Mechanics (QM) is complete (and there are no "hidden variables"), then there cannot be simultaneous reality to non-commuting operators" - Taken from http://drchinese.com/David/Bell_Theo...babilities.htm
I am trying to understand this sentence but I do not fully comprehend 'non-commuting operators'. Wikipedia uses an example of
"physical variables are represented by linear operators such as x (meaning multiply by x), and d/dx. These two operators do not commute as may be seen by considering the effect of their products x (d/dx) and (d/dx) x on a one-dimensional wave function ψ(x):"
is it the 'ψ(x)' that makes this non-commuting? Also, based on reading this, am I to assume that this means that the answer I arrive at is based on solely on the variable I measure first? I thought the idea was no matter what I measure, the other will reflect my observation. For example, I measure 'up' spin on variable A, therefore variable B must be 'down'. Regardless of the variable I measure first, the end result is the same: A is up and B is down.
Also, so I can try to nail down a clear definition, when EPR says 'simultaneous reality' are they referring to identical simultaneous instance of a variable?