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P(a)=∣⟨a∣ψ⟩∣2P(a) = |\langle a \mid \psi \rangle|^2

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Start with the settled part, because it is smaller than most accounts suggest and it is worth stating precisely. Quantum mechanics gives the Born rule: the probability of a measurement outcome is the squared modulus of a probability amplitude, P(a)=∣⟨a∣ψ⟩∣2P(a) = |\langle a \mid \psi \rangle|^2. for a system in state |ψ\psi⟩\rangle measured in a basis containing |a⟩\rangle . Every interpretation discussed here reproduces this rule for every experiment that has actually been performed. That includes Bell tests. John Bell showed in 1964 that any theory obeying two assumptions — that a measurement’s outcome depends only on a hidden variable carried by the particle and on the local setting of its own detector, not on the distant…

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P(a)=∣⟨a∣ψ⟩∣2P(a) = |\langle a \mid \psi \rangle|^2

Equation 1 · Physics

Comparing the Main Approaches to Quantum Foundations and Measurement

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Start with the settled part, because it is smaller than most accounts suggest and it is worth stating precisely. Quantum mechanics gives the Born rule: the probability of a measurement outcome is the squared modulus of a probability amplitude, P(a)=∣⟨a∣ψ⟩∣2P(a) = |\langle a \mid \psi \rangle|^2. for a system in state |ψ\psi⟩\rangle measured in a basis containing |a⟩\rangle . Every interpretation discussed here reproduces this rule for every experiment that has actually been performed. That includes Bell tests. John Bell showed in 1964 that any theory obeying two assumptions — that a measurement’s outcome depends only on a hidden variable carried by the particle and on the local setting of its own detector, not on the distant…

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