Let us begin by recalling the basic points of the standard argument:
Suppose that a microsystem [ltr]SS[/ltr], just before the measurement of an observable [ltr]BB[/ltr], is in the eigenstate [ltr]∣b[size=13]j⟩∣bj⟩[/ltr] of the corresponding operator. The apparatus (a macrosystem) used to gain information about [ltr]BB[/ltr] is initially assumed to be in a precise macroscopic state, its ready state, corresponding to a definite macro property—e.g., its pointer points at 0 on a scale. Since the apparatus [ltr]AA[/ltr] is made of elementary particles, atoms and so on, it must be described by quantum mechanics, which will associate to it the state vector [ltr]∣A0⟩∣A0⟩[/ltr]. One then assumes that there is an appropriate system-apparatus interaction lasting for a finite time, such that when the initial apparatus state is triggered by the state [ltr]∣bj⟩∣bj⟩[/ltr] it ends up in a final configuration [ltr]∣Aj⟩∣Aj⟩[/ltr], which is macroscopically distinguishable from the initial one and from the other configurations [ltr]∣Ak⟩∣Ak⟩[/ltr] in which it would end up if triggered by a different eigenstate [ltr]∣bk⟩∣bk⟩[/ltr]. Moreover, one assumes that the system is left in its initial state. In brief, one assumes that one can dispose things in such a way that the system-apparatus interaction can be described as:[/size]

Equation (1) and the hypothesis that the superposition principle governs all natural processes tell us that, if the initial state of the microsystem is a linear superposition of different eigenstates (for simplicity we will consider only two of them), one has:

Some remarks about this are in order:

• The scheme is highly idealized, both because it takes for granted that one can prepare the apparatus in a precise state, which is impossible since we cannot have control over all its degrees of freedom, and because it assumes that the apparatus registers the outcome without altering the state of the measured system. However, as we shall discuss below, these assumptions are by no means essential to derive the embarrassing conclusion we have to face, i.e., that the final state is a linear superposition of two states corresponding to two macroscopically different states of the apparatus. Since we know that the + representing linear superpositions cannot be replaced by the logical alternative either … or, the measurement problem arises: what meaning can one attach to a state of affairs in which two macroscopically and perceptively different states occur simultaneously?
  
  
• As already mentioned, the standard solution to this problem is given by the WPR postulate: in a measurement process reduction occurs: the final state is not the one appearing in the second line of equation (2) but, since macro-objectification takes place, it is
  
  

Nowadays, there is a general consensus that this solution is absolutely unacceptable for two basic reasons:
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[*]It corresponds to assuming that the linear nature of the theory is broken at a certain level. Thus, quantum theory is unable to explain how it can happen that the apparata behave as required by the WPR postulate (which is one of the axioms of the theory).

[*]Even if one were to accept that quantum mechanics has a limited field of applicability, so that it does not account for all natural processes and, in particular, it breaks down at the macrolevel, it is clear that the theory does not contain any precise criterion for identifying the borderline between micro and macro, linear and nonlinear, deterministic and stochastic, reversible and irreversible. To use J.S. Bell’s words, there is nothing in the theory fixing such a borderline and the split between the two above types of processes is fundamentallyshifty. As a matter of fact, if one looks at the historical debate on this problem, one can easily see that it is precisely by continuously resorting to this ambiguity about the split that adherents of the Copenhagen orthodoxy or easy solvers (Bell 1990) of the measurement problem have rejected the criticism of the heretics (Gottfried 2000). For instance, Bohr succeeded in rejecting Einstein’s criticisms at the Solvay Conferences by stressing that some macroscopic parts of the apparatus had to be treated fully quantum mechanically; von Neumann and Wigner displaced the split by locating it between the physical and the conscious (but what is a conscious being?), and so on. Also other proposed solutions to the problem, notably certain versions of many-worlds interpretations, suffer from analogous ambiguities.

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It is not our task to review here the various attempts to solve the above difficulties. One can find many exhaustive treatments of this problem in the literature. On the contrary, we would like to discuss how the macro-objectification problem is indeed a consequence of very general, in fact unavoidable, assumptions on the nature of measurements, and not specifically of the assumptions of von Neumann’s model. This was established in a series of theorems of increasing generality, notably the ones by Fine (1970), d’Espagnat (1971), Shimony (1974), Brown (1986) and Busch and Shimony (1996). Possibly the most general and direct proof is given by Bassi and Ghirardi (2000), whose results we briefly summarize. The assumptions of the theorem are:

1. that a microsystem can be prepared in two different eigenstates of an observable (such as, e.g., the spin component along the z-axis) and in a superposition of two such states;
   
   
2. that one has a sufficiently reliable way of ‘measuring’ such an observable, meaning that when the measurement is triggered by each of the two above eigenstates, the process leadsin the vast majority of cases to macroscopically and perceptually different situations of the universe. This requirement allows for cases in which the experimenter does not have perfect control of the apparatus, the apparatus is entangled with the rest of the universe, the apparatus makes mistakes, or the measured system is altered or even destroyed in the measurement process;
   
   
3. that all natural processes obey the linear laws of the theory.
   
   

From these very general assumptions one can show that, repeating the measurement on systems prepared in the superposition of the two given eigenstates, in the great majority of cases one ends up in a superposition of macroscopically and perceptually different situations of the whole universe. If one wishes to have an acceptable final situation, one mirroring the fact that we have definite perceptions, one is arguably compelled to break the linearity of the theory at an appropriate stage.

4. 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 area of 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 we were seriously concerned with quantum decay processes and in particular with the possibility of deriving, within a quantum context, the exponential decay law. For an exhaustive review of our approach see (Fonda, Ghirardi, and Rimini 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, inducing 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 an unstable system, yields, completely in general, the desired result. The ‘relative position basis’ is the preferred basis of this theory;
  
  
• Analogous ideas have been applied to measurement processes;
  
  
• The final equation for the evolution at the ensemble level is of the quantum dynamical semigroup type and has a structure extremely similar to the final one of 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-environment interactions. Accordingly, these attempts did not represent original proposals for solving the macro-objectification problem but they have paved the way for the elaboration of the GRW theory.