Page 27 - GALIET PHYSICS BLOSSOMS IV+

5) A two particle quantum-mechanical state is the sum of all possible pair states, consistent with any constraints placed on it. a) All two-particle possible pair states can be put in a correlated state.
i) In any superposition, each and every state can correlate particle 1 with particle 2, where both have to be the same. (1) Forexample,2particlesareputinthesamestateinallthesuperposition’spossiblestates:
(a) the EPR state |Ψ⟩ = (↑↑⟩ + | ↓↓⟩)/√2.
(b) Orthestate|Ψ⟩=[|→→⟩+|←←⟩]/√2
(c) In fact, any superposition of 2 equally weighted opposite states yields the same EPR state.
2-STATE SUPERPOSITION
6) Because quantum mechanics’ different EPR states are the same, they affirm a 2-State superposition.
a) In each state, we do not know the direction of the spins, but only that the spins are parallel: up-up, down- down, left-left, right-right; and that each state
differs from the other.
b) As a result, only the pair’s state, not the spin’s state, is meaningful.
7) When measuring the state of Spin 1 in the up or down direction, a definite state results: either up or down. a) Consequently:
i) ifSpin1isup,soisSpin2.
ii) if Spin 1 is down, so is Spin 2.
8) Likewise, when measuring the state of Spin 1 in the left or right direction, a definite state results: either left or right. a) Consequently:
i) ifSpin1isleft,soisSpin2. ii) if Spin 1 is right, so is Spin 2.
EPR THOUGHT EXPERIMENT
9) EPR places two measuring systems really far away from each other to measure whether spins are up or down.
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BOTH ARE IDENTICAL