Bells Theorem: No local theory can reproduce the statistical - PowerPoint PPT Presentation

Mar 15, 2024 •236 likes •353 views

Bells Theorem: No local theory can reproduce the statistical predictions of quantum mechanics. Bells Theorem: step 1 Step 1: The only kind of local theory that can make the fact 1 prediction is a DETERMINISTIC HIDDEN

Bell’s Theorem: • No local theory can reproduce the statistical predictions of quantum mechanics.
Bell’s Theorem: step 1 • Step 1: The only kind of local theory that can make the “fact 1” prediction is a DETERMINISTIC HIDDEN VARIABLES THEORY.
Bell’s Theorem: step 2 • Fact 2: According to the statistical predictions of QM, the probability that the electrons in the singlet state are deflected in opposite directions when any of the experiments • (0, 120), (120,0), (120,240), (240,120), (0, 240), (240,0) • is performed is 1/4.
Bell’s Theorem: step 2 • Step 2: No deterministic local hidden variables theory can make this same prediction.
Step 2: No deterministic local hidden variables theory can make this same prediction. • Possible instruction sets.
Step 2: No deterministic local hidden variables theory can make this same prediction. • A DLHVT makes the “fact 2” prediction only if: • The proportion of pairs that will go in opposite directions when the experiment (0, 120) is conducted is 1/4. • The proportion of pairs that will go in opposite directions when the experiment (0, 240) is conducted is 1/4. • The proportion of pairs that will go in opposite directions when the experiment (120, 240) is conducted is 1/4.
Step 2: No deterministic local hidden variables theory can make this same prediction. • Intermediate conclusion: A DLHVT makes the “fact 2” prediction only if: • The proportion of pairs with this property (call it “property X”): EITHER they will go in opposite directions in (0, 120), or in (0,240), or in (120,240)—-is less than or equal to 3/4.
Step 2: No deterministic local hidden variables theory can make this same prediction. • The proportion of pairs with this property (call it “property X”): EITHER they will go in opposite directions in (0,120), or in (0,240), or in (120,240)—-is less than or equal to 3/4. • Which instruction sets give a pair that carries it property X?
Bell’s Theorem • Step 1: The only kind of local theory that can make the fact 1 prediction is a DETERMINISTIC HIDDEN VARIABLES THEORY. • Step 2: No deterministic local hidden variables theory can make the fact 2 prediction. • QM makes both the fact 1 and fact 2 predictions. • Therefore, no local theory can make the statistical predictions of QM.
Aspect’s experiment(s)

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