Measurement and state preparation
In the Susskind spin story, measurement is not merely looking up a pre-existing answer. It is an interaction with an apparatus that produces an outcome and prepares the system for compatible future measurements.
Spin example
A z-oriented apparatus measures σz. If it reports +1, the spin is now in the up state |u⟩. Repeating the same measurement immediately gives +1 again, assuming no intervening disturbance.
But if the apparatus is rotated and σx is measured, the result may be probabilistic. The prior σz preparation does not secretly include a sharp σx answer.
Projection idea
For an observable M, the measurement basis consists of eigenstates of M. If outcome m is obtained, the state is updated into the corresponding eigenstate or eigenspace. This is different from unitary time evolution.
Why this matters
The distinction between state and measurement is one of Susskind’s central themes. Classical mechanics often lets us blur them: a state is a list of measurable properties. Quantum mechanics does not.
Common pitfalls
- Do not treat measurement as a harmless peek in the general quantum case.
- Do not use measurement update for ordinary closed-system time evolution.
- Do not assume incompatible measurements can be repeated in arbitrary order without changing the statistics.