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Unless a thing can be defined by measurement, it has no place in a theory. And since an accurate value of the momentum of a localized particle cannot be defined by measurement it therefore has no place in the theory.

Richard P. Feynman, Robert B. Leighton, Matthew Sands (2013). “The Feynman Lectures on Physics, vol. 3 for tablets”, Basic Books
Unless a thing can be defined by measurement, it has no place in a theory. And since an accurate value of the momentum of a localized particle cannot be defined by measurement it therefore has no place in the theory.