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Equation 1 · God Plays Dice, and Evolution Loads Them

What does this equation mean?

S=∣E(a,b)−E(a,b′)+E(a′,b)+E(a′,b′)∣≤2S = \left| E(a,b) - E(a,b') + E(a',b) + E(a',b') \right| \le 2

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Inputs and operations| E(a,b) - E(a,b') + E(a',b) + E(a',b') | ≤ 2
Result or conditionS
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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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SS

Symbol S

S is part of the quantity the equation computes from the expression on the right.

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EE

Symbol E

E is one of the signed contributions combined to compute the quantity on the left.

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aa

Symbol a

a is one of the signed contributions combined to compute the quantity on the left.

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bb

Symbol b

b is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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addition

addition

Add the term after the plus sign to the term or group before it.

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subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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How to interpret it

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What the article says around this equation

EPR’s paper stayed a philosophical argument until 1964, when John Bell showed it could be turned into an experiment [ 3 ] . Bell proved that any theory obeying both locality — no faster-than-light influence — and realism, in the sense of outcomes fixed by pre-existing local properties, must satisfy a statistical bound. For a simple two-setting test, S=∣E(a,b)−E(a,b′)+E(a′,b)+E(a′,b′)∣≤2S = \left| E(a,b) - E(a,b') + E(a',b) + E(a',b') \right| \le 2. holds for any local realist theory, while quantum mechanics allows S up to 22\sqrt{2} ≈\approx 2.83 . Early experimental violations left the detection loophole (too many unmeasured particles to rule out a biased subsample) and the locality loophole (stations not separated fast and far enough to exclude a hidden signal) open to…
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EPR’s paper stayed a philosophical argument until 1964, when John Bell showed it could be turned into an experiment [ 3 ] . Bell proved that any theory obeying both locality — no faster-than-light influence — and realism, in the sense of outcomes fixed by pre-existing local properties, must satisfy a statistical bound. For a simple two-setting test, S=∣E(a,b)−E(a,b′)+E(a′,b)+E(a′,b′)∣≤2S = \left| E(a,b) - E(a,b') + E(a',b) + E(a',b') \right| \le 2. holds for any local realist theory, while quantum mechanics allows S up to 22\sqrt{2} ≈\approx 2.83 . Early experimental violations left the detection loophole (too many unmeasured particles to rule out a biased subsample) and the locality loophole (stations not separated fast and far enough to exclude a hidden signal) open to a committed skeptic.

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