Does measurement violate unitarity?

[hideelo]

I am taking my first semester of QM so excuse my question if it is way off mark, totally wrong, or very well known.

As I understand it, one of the postulates of QM are that states evolve unitarily, a consequence (but not THE defining feature) of unitary transformations is that they are invertible.

Consider some system in state ∑ αⁱ |Ψ_i > where |Ψ_i > are the eigenstates of some observable. Now if I measure my system, then after the measurement the state will be |Ψ_i > i.e. it will be entirely in that state in which I found it to be.

If I am correct, then we can represent this by the transformation (1/αⁱ)P_i where P_i is the projection onto the ith eigenstate and (1/αⁱ) rescales it so that <Ψ|Ψ> = 1.

The problem is that projections arent unitary. In general they arent even invertable. So am I wrong about measurements violating unitarity? Is unitary transformations not a strict requirement?

Thanks

 

[DrClaude]

Have a look at this recent thread: https://www.physicsforums.com/threads/are-the-2nd-and-3rd-axioms-of-qm-incompatible.855996

 

[bhobba]

The problem is that projections arent unitary.

Sure.

However when entangled with other systems that can break untitary evolution by turning a pure state into an effective mixed state.

Thanks
Bill