GianCarlo Ghirardi

Dynamical reduction models

Abstract The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schrodinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. Attention is also paid to many problems which are naturally raised by the dynamical reduction program. In particular we discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics. The review covers the work which has been done in the last 15 years by various scientists and the lively debate which has accompanied the elaboration of the new proposal.

Describing the macroscopic world: Closing the circle within the dynamical reduction program

With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe systems within a genuine Hilbert space framework, the peculiar features of the spontaneous reduction models limit drastically the states which are dynamically stable. This fact by itself allows one to work out an interpretation of the formalism which makes it possible to give a satisfactory description of the world in terms of the values taken by an appropriately defined mass density function in ordinary configuration space. A topology based on this function and which is radically different from the one characterizing the Hilbert space is introduced, and in terms of it the idea of similarity of macroscopic situations is precisely defined. Finally, the formalism and the interpretation are shown to yield a natural criterion for establishing the psychophysical parallelism. The conclusion is that, within the considered theories and at the nonrelativistic level, one can satisfy all sensible requirements for a completely satisfactory macro-objective description of reality.

General criterion for the entanglement of two indistinguishable particles

We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.

Relativistic dynamical reduction models: General framework and examples

The formulation of a relativistic theory of state-vector reduction is proposed and analyzed, and its conceptual consequences are elucidated. In particular, a detailed discussion of stochastic invariance and of local and nonlocal aspects at the level of individual systems is presented.

A general argument against the universal validity of the superposition principle

Abstract We reconsider a well-known problem of quantum theory, i.e. the so-called measurement (or macro-objectification) problem, and we rederive the fact that it gives rise to serious problems of interpretation. The novelty of our approach derives from the fact that the relevant conclusion is obtained in a completely general way, in particular, without resorting to any of the assumptions of ideality which are usually done for the measurement process. The generality and unescapability of our assumptions (we take into account possible malfunctionings of the apparatus, its unavoidable entanglement with the environmment, its high but not absolute reliability, its fundamentally uncontrollable features) allow to draw the conclusion that the very possibility of performing measurements on a microsystem combined with the assumed general validity of the linear nature of quantum evolution leads to a fundamental contradiction.

Quantum Dynamical Reduction and Reality: Replacing Probability Densities with Densities in Real Space

Consideration is given to recent attempts to solve the objectification problem of quantum mechanics by considering nonlinear and stochastic modifications of Schrodinger’s evolution equation. Such theories agree with all predictions of standard quantum mechanics concerning microsystems but forbid the occurrence of superpositions of macroscopically different states. It is shown that the appropriate interpretation for such theories is obtained by replacing the probability densities of standard quantum mechanics with mass densities in real space. Criteria allowing a precise characterization of the idea of similarity and difference of macroscopic situations are presented and it is shown how they lead to a theoretical picture which is fully compatible with a macrorealistic position about natural phenomena.

Dynamical models for state-vector reduction: do they ensure that measurements have outcomes?

Some recent criticisms of a proposed dynamical reduction theory are considered and are proved to be not cogent. By considering the visual perception process, it is made plausible that, at least at the perceptive level, the conditions required by the above-mentioned theory for dynamical reduction to occur are verified. This does not imply the attribution of a specific role to the act of conscious perception in the reduction process.

Matter Density and Relativistic Models of Wave Function Collapse

Mathematical models for the stochastic evolution of wave functions that combine the unitary evolution according to the Schrödinger equation and the collapse postulate of quantum theory are well understood for non-relativistic quantum mechanics. Recently, there has been progress in making these models relativistic. But even with a fully relativistic law for the wave function evolution, a problem with relativity remains: Different Lorentz frames may yield conflicting values for the matter density at a space-time point. We propose here a relativistic law for the matter density function. According to our proposal, the matter density function at a space-time point x is obtained from the wave function ψ on the past light cone of x by setting the i-th particle position in |ψ|2 equal to x, integrating over the other particle positions, and averaging over i. We show that the predictions that follow from this proposal agree with all known experimental facts.

Outcome predictions and property attribution: the EPR argument reconsidered

Abstract We reconsider the nonlocal aspects of quantum mechanics with special reference to the EPR argument. We first confine our considerations to the correlations between the outcomes of measurements on spatially distant constituents, without worrying about the measurement problem. We pay particular attention to the relativistic aspects of the problem. Our first conclusion is that, when developed along the lines we follow, the EPR inference that quantum correlations and locality together imply incompleteness, is appropriate. We then investigate whether the other common conclusion from the EPR argument, i.e. that standard quantum theory implies a spooky action at a distance, is correct. We emphasize the crucial role played by the locality assumption and we discuss the use of counterfactuals in the ‘relativistic’ reformulation of the EPR argument. We show that the above conclusion is false if understood as saying that standard quantum theory exhibits, at least with reference to possessed elements of physical reality, some sort of parameter dependence. Thus, in a sense, the coexistence of quantum mechanics with relativity is even more peaceful than commonly thought. We then go through a similar analysis by taking explicitly into account the measurement process. We point out the difficulties which one meets when confronting reduction mechanisms with relativistic requirements. This leads us to recognize the necessity of reconsidering the criteria for attributing objective properties to individual physical systems. Our final conclusion is that, in principle, it is perfectly possible to build up theories leading to the objectification of macroscopic properties which do not imply any spooky action at a distance.

QUANTUM MECHANICS AND FASTER THAN LIGHT COMMUNICATION: METHODOLOGICAL CONSIDERATIONS

SummaryA detailed quantum-mechanical analysis of a recent proposal of faster-than-light communication through wave packet reduction is performed. The discussion allows us to focus some methodological problems about critical investigations on physical theories.RiassuntoIn questo lavoro si fa un’accurata analisi in termini di meccanica quantistica di una recente proposta di trasmissione di segnali a velocità maggiore di quella della luce per mezzo del meccanismo di riduzione del pacchetto d’onde. La discussione permette di puntualizzare il contenuto metodologico delle analisi critiche delle teorie fisiche.РезюмеВ этой работе проводится подробный квантовомеханический анализ недавнего предложения передачи сигналов быстрее скорости света посредством преобразования волнового пакета. Обсуждение позволяет выделить методологические проблемы критических исследований физических теорий.