It is known, there exists oracles A, B s.t.:
$P^A = NP^A; P^B \neq NP^B$, showing that any proof of P vs NP must be non-relativizing.
(1) Can we actually use Oracles to separate complexity classes? I.e. are there classes X, Y, s.t. some oracle C is instrumental in separating X & Y?
(2) If complexity classes X,Y satisfy existence of oracles A,B s.t. $X^A = Y^A ; X^B \neq Y^B$ ... then it means any proof separating X,Y can't be relativizing -- but does it mean oracles can't be used to separate the classes?