Posted: Oct 06, 2011 9:22 pm
mizvekov wrote:In regards to observables, Operators are used QM in the same sense that functions of the state are used in classical mechanics.
"An operator O is a mapping of a vector space onto itself."
(http://plato.stanford.edu/entries/qm/#Ope)
Mappings are functions, so you're right.
mizvekov wrote:
If you wish to think that operators exist and are not merely abstract objects, fine, you can do so consistently, but then you should also consider thinking of mathematical functions as real in the same sense too.
I'm an antirealist (fictionalist) about mathematical abstracta.
(A physicist who is also a physicalist cannot consistently be a mathematical realist.)