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"From the Goldhaber experiment we can deduce that there are only left handed neutrinos."

I don't understand this. Can't we find an experiment that only produces overwhelmingly right handed neutrinos?

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No.

The Goldhaber experiment's purpose was to test the masslessness hypothesis of neutrinos, which was proposed in 1957 by Lev Landau and Abdus Salam. The motivation for this hypothesis was that this was the simplest possible parity-violating theory for weak interactions. In it, neutrino is strictly a left-handed particle. In a parity-conserving theory one should see an equal amount of left- and right-handed neutrinos. No right-handed were seen.

The particle theorists speculate that there are sterile neutrinos, that is, neutrinos with no weak interactions, only gravity. These would be right-handed neutrinos, but their existence is as of today not proven.

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