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

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

Mar 15, 2024 236 likes •355 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

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SLIDE 1

Bell’s Theorem:

  • No local theory can reproduce the statistical

predictions of quantum mechanics.

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SLIDE 2

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.

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SLIDE 3

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.
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SLIDE 4

Bell’s Theorem: step 2

  • Step 2: No deterministic local hidden variables

theory can make this same prediction.

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SLIDE 5

Step 2: No deterministic local hidden variables theory can make this same prediction.

  • Possible instruction sets.
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SLIDE 6

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.

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SLIDE 7

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

  • pposite directions in (0, 120), or in (0,240), or

in (120,240)—-is less than or equal to 3/4.

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SLIDE 8

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?

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SLIDE 9

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.

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SLIDE 10

Aspect’s experiment(s)