-- In quantum theory observables can be represented by Hermitian matrices.

-- If an observable of a system can be represented by a particular matrix at a particular instant, then all matrices of the same dimension represent observables of that system.

-- In a state specified by the vector |psi>, an observable X is sharp if and only if X|psi> = x|psi> for some real number x. In which case x is an eigenvalue of X and |psi> is an eigenvector of X.

Now let Y be any matrix that

*does not*have |psi> among its eigenvectors. (For any vector, there exists an infinity of such matrices.)

If the actual state is |psi>, the observable Y cannot be sharp. (Because of the 'if and only if' above.)

## Messages (2)

In other words, not all observables of a system are sharp at any given point in time. (Sharp means the same in all universes.)

curiat 5:58 PM on September 4, 2017 | #8982 | reply | quote> (Sharp means the same in all universes.)

Clarification: Sharp is the same in all

*relevant*universes. Like for an experiment, it only includes the universes in which the experiment is done. We're basically just looking at the universes which could be the same, ignoring the ones that are permanently different.curiat 11:35 PM on May 2, 2019 | #12268 | reply | quote