A brief review of the conceptual difficulties met by the quantum formalism is presented. The main attempts to overcome these difficulties are considered and their limitations are pointed out. A recent proposal based on the assumption of the occurrence of a specific type of wave function collapse is discussed and its consequences for the above-mentioned problems are analyzed.

The property of fundamental mechanical theories which allows to treat compound objects as particles under suitable conditions is considered. It is argued that such a property, called compoundation invariance, is a nonreleasable property of any mechanical theory not declaring to which elementary constituents it applies. Compoundation invariance is discussed in the framework of Bohmian mechanics. It is found that standard Bohmian mechanics satisfies the requirement of compoundation invariance, with some reservation in the case of compound objects with spin. On the (...) contrary that requirement is violated when additional terms are added to the standard velocity. (shrink)

Two different kinds of stochastic processes in Hilbert space used to introduce spontaneous localization into the quantum evolution are investigated. In the processes of the first type, finite changes of the wave function take place instantaneously with a given mean frequency. The processes of the second type are continuous. It is shown that under a suitable infinite frequency limit the discontinuous process transforms itself into the continuous one.

In the framework of the history approach to quantum mechanics and, in particular, of the formulation of Gell-Mann and Hartle, the question of the existence of inequivalent decoherent sets of histories is reconsidered. A simple but acceptably realistic model of the dynamics of the universe is proposed and a particular set of histories is shown to be decoherent. By suitable tranformations of this set, a family of sets of histories is then generated, such that the sets, first, are decoherent on (...) the basis of the assumed dynamics of the universe and, secondly, arc certainly inequivalent, apart from trivial special cases. Finally, the original set of histories is refined to get a model of the usual quasiclassical domain and it is shown that, applying to it the previously considered transformations, a family of sets of histories is obtained which share typical properties of the usual quasiclassical domain. (shrink)

The property of fundamental mechanical theories which allows one to treat compound objects as particles under suitable conditions is considered. It is argued that such a property, called composition invariance, is a nonreleasable property of any fundamental mechanical theory. The proof that standard quantum mechanics enjoys composition invariance is reviewed. Finally, it is shown that the requirement of composition invariance allows one to choose between two alternative forms of quantum mechanics with spontaneous localization.

A new proposal for a Lorentz-invariant spontaneous localization process in the framework of relativistic quantum field theory is presented. As in all dynamical reduction models, a stochastic process is introduced, which drives the state vector towards the eigenspaces of a set of operators representing suitably chosen physical quantities. Such operators constitute a Lorentz scalar field and are built as time averages and space integrals of a local field-theoretic operator in such a way that the quantities they represent acquire a macroscopic (...) character. As always in dynamical reduction theories, the action of the process on microscopic systems takes place via the micro-macro correlations which arise, e.g., as a consequence of measurements. (shrink)