Classical and Quantum Measurement Theory

Abstract: Classical and quantum measurement theories are usually held to be different because the algebra of classical measurements is commutative, however the Poisson bracket allows noncommutativity to be added naturally. After we introduce noncommutativity into classical measurement theory, we can also add quantum noise, differentiated from thermal noise by Poincar\'e invariance. With these two changes, the extended classical and quantum measurement theories are equally capable, so we may speak of a single "measurement theory". The reconciliation of general relativity and quantum theory has been long delayed because classical and quantum systems have been thought to be very different, however this unification allows us to discuss a unified measurement theory for geometry in physics.