Page 21 - GALIET PHYSICS BLOSSOMS IV+

(2) ENTANGLEMENT:
2.1: One of the most extraordinary features of quantum mechanics is what Einstein called its ’non-locality’, exemplified in the EPR ’thought experiment’ (now a real experiment). Suppose 2 spin-1/2 particles are emitted with their spins constrained to be opposite. One can write the state of the 2 emitted spins as
|ψ⟩ ∼ (| ↑↓⟩ + | ↓↑⟩) (0.1) This is an entangled state, with the 2 spins constrained to be opposite. One spin (”spin A”) heads for Paris, the other (”spin B”) for Tokyo; and experimental teams are waiting for them at each of these 2 places.
2.1 (a) The Tokyo measuring apparatus is set up to measure the ↑ or ↓ polarization of spin A. What is the probability that it will be ↑? Independently the Paris apparatus measures the other spin- what is the probability that it will find ↑?
1. It is equally probable (50%) that the Tokyo apparatus will find that the Paris-bound Spin A is either in an up or down state (↑ or ↓).
2. It is equally probable (50%) that the Paris apparatus will find that the Tokyo-bound Spin B is either in an up or down state (↑ or ↓).
3. Then there is a mysterious correlation, too.
a. Whatever Tokyo finds, Paris too will find to be the same.
b. Hence, both measurement results will be absolutely or necessarily correlated.
i. Each will find the same spin, whether it may be up or down.9
1. So if Tokyo finds that Spin A is up, then Paris will find that Spin B is necessarily up, too, with 100% probability or certainty;
and if Tokyo finds that Spin A is down, then Paris will find that Spin B is necessarily down, too, with 100% probability or
certainty.
2. Therefore, both states will be up or down, depending on whichever the case might be for Spin A.
4. At the beginning, it is uncertain which will be the case given that neither Spin A nor Spin B is on a definite state of up or down.
9 Dr. Stamp. From class lecture notes, and from Basic Ideas of Quantum Mechanics. II. Entangled States. 5. •21•