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The Wu experiment shows how parity symmetry does not hold for the weak force. However, how does this proof that parity conservation also doesn't hold?

If my understanding is correct, the absence of parity conservation would mean that particles with odd parity can change to even parity and the other way around. But what changes parity in this beta decay via the weak interaction?

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The parity mixture in the electron distribution of cesium decays, as observed by Wu, demonstrates that the ground state of the cesium nucleus is not an eigenstate of the parity operator.

Because the weak interaction can never be "turned off," our usual assumption that parity is a good quantum number for a particular state is only approximately correct. There is no such thing, in the real world, as a state with definite parity.

Particles do not change from one intrinsic parity to the other. Instead, our approximation that a particle has an intrinsic parity is incorrect. The idea of an oscillation between one parity and the other is a feature of our mathematical model, where we assume that the weak interaction is weak.

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In the Wu experiment the beta electron’s momentum is correlated with the nuclear spin, say:

$$ \vec p \cdot \vec s = c $$

Where $c$ is a scalar. The LHS is a pseudo scalar. Under a parity inversion:

$$ (-\vec p)(+\vec s)= c $$

Which violates parity for nonzero $c$.

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