Physical content of Heisenberg's uncertainty relation: Limitation and   reformulation
  Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of Heisenberg's relation proven valid for arbitrary measurements is proposed and reveals two distinct types of possible violations of Heisenberg's relation. 
Masanao Ozawa (Tohoku University)