Susskind QM Lecture 1 - Systems and Experiments
One-line takeaway
Quantum mechanics starts by separating three things that classical intuition tends to merge: the system, the apparatus, and the state prepared by a measurement.
Plain-language map
Susskind uses a single spin as the simplest real quantum system. Classically, a two-state system would be like a coin: either +1 or -1, with nothing in between. Quantum spin refuses to behave like that because the answer depends on the direction in which the apparatus is oriented.
A z-oriented apparatus measures σz. If it gives +1, the spin has been prepared in the up state |u⟩. If the same measurement is immediately repeated without disturbance, it gives the same result. That looks classical.
The nonclassical part appears when the apparatus is rotated. A state prepared to be definite for σz is not generally definite for σx or σy. The theory must therefore describe preparations and measurement probabilities, not just a hidden list of pre-existing components.
Core objects
- Qubit and spin: the isolated spin is the minimal quantum system.
- Measurement and state preparation: measurement both reports an outcome and prepares a state for compatible future measurements.
- Quantum state: the state is not a classical property-list.
- Bra-ket notation: spin states are eventually written as kets such as |u⟩ and |d⟩.
Equations / labels
σz = +1 -> up state |u⟩
σz = -1 -> down state |d⟩The important point is not the symbol σ by itself; it is the pairing of a component, an apparatus orientation, and a prepared state.
Common pitfalls
- Do not picture spin as a tiny classical arrow that merely points somewhere before measurement.
- Do not assume that a state definite for σz also has definite hidden values for σx and σy.
- Do not forget the apparatus orientation; changing it changes the observable.