Angelo Bassi

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.

Models of Wave-function Collapse, Underlying Theories, and Experimental Tests

We describe the state of the art in preparing, manipulating and detecting coherent molecular matter. We focus on experimental methods for handling the quantum motion of compound systems from diatomic molecules to clusters or biomolecules. Molecular quantum optics offers many challenges and innovative prospects: already the combination of two atoms into one molecule takes several well-established methods from atomic physics, such as for instance laser cooling, to their limits. The enormous internal complexity that arises when hundreds or thousands of atoms are bound in a single organic molecule, cluster or nanocrystal provides a richness that can only be tackled by combining methods from atomic physics, chemistry, cluster physics, nanotechnology and the life sciences. We review various molecular beam sources and their suitability for matter-wave experiments. We discuss numerous molecular detection schemes and give an overview over diffraction and interference experiments that have already been performed with molecules or clusters. Applications of de Broglie studies with composite systems range from fundamental tests of physics up to quantum-enhanced metrology in physical chemistry, biophysics and the surface sciences. Nanoparticle quantum optics is a growing field, which will intrigue researchers still for many years to come. This review can, therefore, only be a snapshot of a very dynamical process.

Quantum explorations: from the waltz of the Pauli exclusion principle to the rock of the spontaneous collapse

The spin–statistics connection, in particular the Pauli exclusion principle (PEP), plays a very important role in our comprehension of matter and nature. Presently, the PEP violation, possible within some theories, generates a lively debate; it has given birth to a few experiments looking for tiny effects. The violation of the Pauli exclusion principle experiment put a very strong limit on the PEP violation probability by electrons, using the method of searching for PEP forbidden atomic transitions in a copper target. In this paper we present this experiment, the obtained results and future plans to upgrade the experimental setup with fast silicon drift detectors. We then present the idea of using an analogous experimental technique to search for x-rays as a signature of the spontaneous collapse of the wave function, predicted by the continuous spontaneous localization theories, and some very encouraging preliminary results.

Is Quantum Theory Exact

Future experiments may tell us if quantum mechanics is an approximation to a deeper-level theory. Quantum mechanics has enjoyed many successes since its formulation in the early 20th century. It has explained the structure and interactions of atoms, nuclei, and subnuclear particles, and has given rise to revolutionary technologies, such as integrated circuit chips and magnetic resonance imaging. At the same time, it has generated puzzles that persist to this day.

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.

The Schrödinger–Newton equation and its foundations

The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semi-classical theory of gravity, in the weak-field non-relativistic limit. We show that, while in the former case the Schrodinger equation stays linear, in the latter case one ends up with the so-called Schrodinger–Newton equation, which involves a nonlinear, non-local gravitational contribution. We further discuss that the Schrodinger–Newton equation does not describe the collapse of the wave-function, although it was initially proposed for exactly this purpose. Together with the standard collapse postulate, fundamentally semi-classical gravity gives rise to superluminal signalling. A consistent fundamentally semi-classical theory of gravity can therefore only be achieved together with a suitable prescription of the wave-function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schrodinger–Newton equation.

Towards quantum superpositions of a mirror: an exact open systems analysis.

We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirrors dynamics contains a nonunitary term of the Lindblad-type proportional to -[q,[q,rho]], with q the position operator for the center of mass of the mirror, and rho the statistical operator. We derive an exact formula for the fringe visibility for this system. We discuss the consequences of our result for tests of environmental decoherence and of collapse models. In particular, we find that with the conventional parameters for the continuous spontaneous localization model of state vector collapse, maintenance of coherence is expected to within an accuracy of at least 1 part in 10(8). Increasing the apparatus coupling to environmental decoherence may lead to observable modifications of the fringe visibility, with time dependence given by our exact result.

Proposal for a Noninterferometric Test of Collapse Models in Optomechanical Systems

The test of modifications to quantum mechanics aimed at identifying the fundamental reasons behind the unobservability of quantum mechanical superpositions at the macroscale is a crucial goal of modern quantum mechanics. Within the context of collapse models, current proposals based on interferometric techniques for their falsification are far from the experimental state of the art. Here we discuss an alternative approach to the testing of quantum collapse models that, by bypassing the need for the preparation of quantum superposition states might help us addressing nonlinear stochastic mechanisms such as the one at the basis of the continuous spontaneous localization model.

Decoherent histories and realism

We reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents. We put forward some assumptions which, in our opinion, are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories. We prove that such assumptions, unless one limits the set of the decoherent families which can be taken into account, lead to a logical contradiction. The line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach. The conclusion is that the decoherent histories approach, to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics, requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem.

Dynamical reduction models: present status and future developments

We review the major achievements of the dynamical reduction program, showing why and how it provides a unified, consistent description of physical phenomena, from the microscopic quantum domain to the macroscopic classical one. We discuss the difficulties in generalizing the existing models in order to comprise also relativistic quantum field theories. We point out possible future lines of research, ranging from mathematical physics to phenomenology.