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By Peskin M.

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Again, the quantum measurement problem is not that quantum mechanics is counter-intuitive-it is that the theory is at least ambiguous and perhaps logically inconsistent. In the context of the standard theory, the measurement problem results from the fact that the two dynamical laws are mutually incompatible. Since the first is deterministic and continuous and the second is stochastic and discontinuous, no physical system can be governed by both laws simultaneously-indeed, as we shall see, the two laws would typically lead to very different physical states.

In these cases, the time-evolution of the state is no longer correctly described by the deterministic dynamics. The introduction of indeterminacy into the results of observations, which we had to make in our discussion of the photon, must now be extended to the general case. When an observation is made on an atomic system that has been prepared in a given way and is thus in a given state, the result will not in general be determinate; that is, if the experiment is repeated several times under identical conditions, several different results may be obtained.

Each physical quantity that one might observe corresponds to a Hermitian operator on an appropriate Hilbert space (von Neumann 1955: 200). If a system S is in the state 1ft and if 1ft is an eigenstate of the observable o with eigenvalue A (that is, if 01ft = A1ft), then if one measures 0 of S, then one is guaranteed to get the result A. This tells us how to predict the result of a measurement whenever a system is in an eigenstate of the observable being measured. In general, however, a system will not be in an eigenstate of the observable being measured, so we need to know what happens when a measurement is made in these situations.

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