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I understand that if we have a quantum mechanical system, then its state at some given time ##t## is fully described by a state vector ##\lvert\psi(t)\rangle## in a corresponding Hilbert space. This state vector containing all possible information about the distributions (of all possible values) of the observables of the system. When we talk of quantum superposition this arises by projecting the state onto an eigenbasis of one of its observables, and hence it is in a

*superposition*of all possible eigenstates of this given observable. I get that superposition follows mathematically from the linearity of the Schrödinger equation, but what is the physical interpretation of it? Is it simply that before making any measurement the system is not in a well-defined eigenstate of the given observable that we are measuring and it is only by making an observation that the quantum state of the system collapses into a particular eigenstate of the observable measured in the experiment? (Clearly the quantum system itself is in some well-defined state ##\lvert\psi\rangle## before measurement, but is the point that unless the state is prepared to be in a given eigenstate at the start of the experiment then there is no way, even in principle, a priori to predict with certainty that it is in a given eigenstate and in general it will be in a superposition of all possible eigenstates available to it, "pointing" in some definite "direction" in Hilbert space.)
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