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In quantum mechanics, measurement of observables exhibits some seemingly mysterious phenomena. This often leads to many misconceptions about the nature of quantum mechanics itself. The facts of the matter, however, are far more prosaic. Specifically, if a system is in a state described by a wave function, the measurement process affects the state in a non-deterministic, but statistically predictable way. In particular, after a measurement is applied, the state description by a single wave function may be destroyed, being replaced by a Statistical Ensemble of wave functions. The Irreversible nature of measurement operations in quantum physics is sometimes referred to as the Measurement Problem and is described mathematically by Quantum Operation s. By the structure of quantum operations, this description is mathematically equivalent to that offered by Relative State Interpretation where the original system is regarded as a subsystem of a larger system and the state of the original system is given by the Partial Trace of the state of the larger system. Physically meaningful observables must also satisfy Transformation Law s which relate observations performed by different Observer s in different Frames Of Reference . These transformation laws are Automorphism s of the state space, that is Bijective Transformation s which preserve some mathematical property. In the case of quantum mechanics, the requisite automorphisms are Unitary (or Anti-unitary ) linear transformations of the Hilbert space ''V''. Under Galilean Relativity or Special Relativity , the mathematics of frames of reference is particularly simple, and in fact restricts considerably the set of physically meaningful observables. REFERENCES
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