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The paper focuses on the fact that quantum projective measurements do notnecessarily conserve energy. On the other hand the Wigner-Araki-Yanase (WAY)theorem states that assuming a "standard" von Neumann measurement model and"additivity" of the total energy operator, projective measurements of a systemmust conserve energy as defined by the system's energy operator. This paperexplores the ideas behind the WAY theorem in hopes of uncovering the origin ofthe contradiction.  After Araki and Yanase published their proof of the WAY theorem, Yanaseappended a new condition now known as the Yanase condition. Under thesimplifying assumption that the observable being measured has discrete andnon-degenerate eigenvalues, we prove that the Yanase condition actually followsfrom the hypotheses of the original WAY theorem.  The paper also proves that the hypotheses of the WAY theorem, together withthe simplifying assumption, imply that the energy operator for the measuringapparatus must be a multiple of the identity, which seems physically unlikely.It seems probable that this surprising conclusion, along with the Yanasecondition, also holds without the simplifying assumption.

Quantum measurements need not conserve energy: relation to the Wigner-Araki-Yanase theorem