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By J. C. Polkinghorne

[Polkinghorne] bargains a lot perception during this completely pleasant little ebook into the character of the conceptual difficulties on the center of the 20th century's such a lot profitable idea. . . . I wholeheartedly suggest The Quantum global. . . .

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This makes an orthonormal set of ¯uctuations. Normalization is no problem, because ¯uctuations are always used with coef®cients, and unwanted constant factors can be absorbed into the coef®cients. Orthogonality is the problem. H H can be diagonalized by an orthogonal transforThe symmetric matrix Xkk mation: Xjj H ˆ ˆ kkH H tr H OkH j H Y Ojk Xkk …2X36† giving a new set of ¯uctuations that are linear combinations of the old ones: dw0j ˆ ˆ k Ojk dwHk X …2X37† For the new ¯uctuations, the off-diagonal covariances are zero and, if some of the old ¯uctuations dwHk are linearly dependent, some of the new variances dw0j are zero too.

Although the ®nal density operator qH for the system is diagonal in g, its unravelling into pure states is not unique, and need not consist of eigenstates of G. 2. 5 Measurement and preparation 39 the ensemble are all eigenstates of G. 2 is not into eigenstates. The correct unravelling is not given by the density operator alone, but needs further conditions. Thus in a measurement, the ®nal density operator does not give full information about individual states of the ensemble. Quantum state diffusion for pure states and the master equation for density operators have similar properties, but their evolution is continuous and takes a ®nite time.

The theory of wide open systems is relatively simple and has many applications. The same theory can often be applied to systems in which the Hamiltonian is important, by using a form of interaction representation to remove the Hamiltonian from the equations. The simplest type of wide open system is the elementary open system with only one Lindblad and with master equation • ˆ Lq…t†Ly À 12 Ly Lq…t† À 12 q…t†Ly LX q…t† …4X2† There are many types of interaction with the environment. We illustrate the properties of master equations and QSD equations using elementary open systems with simple Lindblads representing measurement and dissipation.

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