It's easy to show that a Superposition does NOT imply that a system represented by a linear sum of a pure set of basis vectors, is in all of those states simultaneusly.This follows from the fact that the WF is an element of a vector space, a Hilbert space, and in vector spaces there is no unique set of basis vectors. IOW, any set of basis vectors can represent the WF of a system, and if we claim the system is in all states of some superposition, it must also be in all states of any other superposition. And every set of basis vectors is equivalent to, and indistinguishable from any other set of basis vectors. This shows that Schrodinger could have denied the usual interpretation of the WF as a superposition where the system it represented could be interpreted as being in all pure states in its sum simultaneously, without constructing his Cat experiment. He simply had to remind his colleagues that the set of basis vectors in a vector space is not unique. AG
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