7/28/2019 Collapse Theories (4) - The Birth of Collapse Theories

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The Birth of Collapse Theories

The debate on the macro-objectification problem continued for many years after the early days of quantum mechanics. In the early 1950s an important step was taken by D. Bohm who presented (Bohm 1952) a mathematically precise deterministic completion of quantum mechanics (see the entry on Bohmian Mechanics). In the areaof Collapse Theories, one should mention the contribution by Bohm and Bub (1966), which was based on the interaction of the statevector with Wiener-Siegel hidden variables. But let us come to Collapse Theories in the sense currently attached to this expression.

Various investigations during the 1970s can be considered as preliminary steps for the subsequent developments. In the years 1970-1973 L. Fonda, A. Rimini, T. Weber and G.C. Ghirardi were seriously concerned with quantum decay processes andin particular with the possibility of deriving, within a quantum context, the exponential decay law (Fonda, Ghirardi, Rimini, and Weber 1973; Fonda, Ghirardi,and Rimini et al. 1978). Some features of this approach are extremely relevant for the DRP. Let us list them:

One deals with individual physical systems;The statevector is supposed to undergo random processes at random times, ind

ucing sudden changes driving it either within the linear manifold of the unstable state or within the one of the decay products;

To make the treatment quite general (the apparatus does not know which kind

of unstable system it is testing) one is led to identify the random processes with localization processes of the relative coordinates of the decay fragments. Such an assumption, combined with the peculiar resonant dynamics characterizing anunstable system, yields, completely in general, the desired result. The relativeposition basis is the preferred basis of this theory;

Analogous ideas have been applied to measurement processes (Fonda, Ghirardi,and Rimini 1973);

The final equation for the evolution at the ensemble level is of the quantumdynamical semigroup type and has a structure extremely similar to the final oneof the GRW theory.

Obviously, in these papers the reduction processes which are involved were not assumed to be spontaneous and fundamental natural processes, but due to system-envi

ronment interactions. Accordingly, these attempts did not represent original proposals for solving the macro-objectification problem but they have paved the wayfor the elaboration of the GRW theory.

Almost in the same years, P. Pearle (1976, 1979), and subsequently N. Gisin (1984) and others, had entertained the idea of accounting for the reduction processin terms of a stochastic differential equation. These authors were really looking for a new dynamical equation and for a solution to the macro-objectification problem. Unfortunately, they were unable to give any precise suggestion about howto identify the states to which the dynamical equation should lead. Indeed, these states were assumed to depend on the particular measurement process one was considering. Without a clear indication on this point there was no way to identify a mechanism whose effect could be negligible for microsystems but extremely re

levant for the macroscopic ones. N. Gisin gave subsequently an interesting (though not uncontroversial) argument (Gisin 1989) that nonlinear modifications of the standard equation without stochasticity are unacceptable since they imply thepossibility of sending superluminal signals. Soon afterwards, G. C. Ghirardi andR. Grassi (1991) showed that stochastic modifications without nonlinearity canat most induce ensemble and not individual reductions, i.e., they do not guarantee that the state vector of each individual physical system is driven in a manifold corresponding to definite properties.