# < JK 也能聽懂的理論物理（二）

25-10-2020

## 测量

It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong. In that simple statement is the key to science.
— Richard Feynman

$\psi = \sum_{i} c_i\psi_i$

## EPR 佯谬

It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we can say about Nature.
— Niels Bohr

$\phi =\frac{1}{\sqrt{2}}(s \otimes (-s) - (-s) \otimes s)$

## 贝尔定律

$P[A\ |\ C_{\Sigma}] = P[A\ |\ C_{\Sigma},\ B]$

$P(\hat{a}, \hat{b}) = P_{\hat{a}\hat{b}}(++) + P_{\hat{a}\hat{b}}(—) - P_{\hat{a}\hat{b}}(+-) - P_{\hat{a}\hat{b}}(-+)$

$P(\hat{a},\hat{b}) = -cos(\theta)$

$P(\hat{a}, \hat{b}) = \int\rho(\lambda)A(\hat{a}, \lambda)B(\hat{b}, \lambda)d\lambda = -\int\rho(\lambda)A(\hat{a}, \lambda)A(\hat{b}, \lambda)d\lambda$

$|P(\hat{a}, \hat{b}) - P(\hat{a}, \hat{c})|\\ = | -\int\rho(\lambda)(A(\hat{a}, \lambda)A(\hat{b}, \lambda) - A(\hat{a}, \lambda)A(\hat{c}, \lambda))d\lambda|\\ = |\int\rho(\lambda)(A(\hat{a}, \lambda)A(\hat{b}, \lambda) - A(\hat{a}, \lambda)A(\hat{b}, \lambda)A(\hat{b}, \lambda)A(\hat{c}, \lambda))d\lambda|\\ = |\int\rho(\lambda)((1 - A(\hat{b}, \lambda)A(\hat{c}, \lambda))A(\hat{a}, \lambda)A(\hat{b}, \lambda))d\lambda|$

$|P(\hat{a}, \hat{b}) - P(\hat{a}, \hat{c})|\\ \le \int\rho(\lambda)(1 - A(\hat{b}, \lambda)A(\hat{c}, \lambda))d\lambda \\ = 1 + P(\hat{b}, \hat{c})$

## 参考资料

1. Ghirardi, Giancarlo and Angelo Bassi, Collapse Theories, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.)
2. J.S. Bell, Against ‘Measurement’, reprinted in Speakable and Unspeakable in Quantum Mechanics, 2nd edn. (Cambridge University Press, Cambridge, 2004)
3. J.N. Shutt, Determinism, locality, and meta-time, 2008
4. T. Norsen, Foundations of Quantum Mechanics, (Springer, 2017)
5. Many entries on Wikipedia.