G. C. Ghirardi

Decay Theory of Unstable Quantum Systems

The present review article is aimed at a clear formulation of the basic problematics of the decay and at a description of the various recent attempts to solve this delicate problem, illustrating both their successes and limitations. The organisation of the article is as follows. After a short summary of the classical description of the decay, a detailed study of the quantum non-decay probability is given. Then the peculiar dynamical situation leading to the formation of an unstable system is identified and the formal and physical aspects of the process are discussed. A detailed analysis is then made of the preparation procedure of an unstable system which is shown to amount to a localisation of the decay fragments within a distance of the order of the range of the forces acting between them. After this the discussion of the general properties of the non-decay probability at all times is completed.

Entanglement and Properties of Composite Quantum Systems: A Conceptual and Mathematical Analysis

Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of the paper deals with composite systems in pure states. After a detailed discussion and a precise formal analysis of the case of systems of distinguishable particles, the problems of entanglement and the one of the properties of subsystems of systems of identical particles are thoroughly discussed. This part is the most interesting and new and it focuses in all details various subtle questions which have never been adequately discussed in the literature. Some inappropriate assertions which appeared in recent papers are analyzed. The relations of the main subject of the paper with the nonlocal aspects of quantum mechanics, as well as with the possibility of deriving Bells inequality are also considered.

On the quantum foundations of the exponential decay law

SummaryBy assuming that in every actual decay process the unstable system is subject to repeated processes of measurement which ascertain whether the system is decayed or not, we prove that the decay law is exponential, obtaining a consistent reconciliation of the quantum and the classical statistical descriptions of decay experiments. We also show that the measurement process is a localization of the decay products and that, consequently, the unstable system is reduced to a unique quantum state. We are able to give, within the framework of ordinary quantum mechanics, a natural definition of the wave function of the unstable system.RiassuntoNell’ipotesi che in ogni effettivo processo di decadimento il sistema instabile sia soggetto a ripetuti processi di misura che accertano se il sistema è decaduto o no, si dimostra che la legge di decadimento è esponenziale, giungendo ad una coerente riconciliazione delle descrizioni statistica e quantistica degli esperimenti di decadimento. Si mostra inoltre che il processo di misura è una localizzazione dei prodotti di decadimento e che, conseguentemente, il sistema instabile viene ridotto ad un unico stato quantistico. Nel quadro della meccanica quantistica ordinaria si dà una definizione naturale della funzione d’onda del sistema instabile.РеэюмеПредполагая, что в каждом реальном процессе распада нестабильная система подвергается повторным процессам иэмерения, которые устанавливают распалась ли система или нет, мы докаэываем, что эакон распада является зкспоненциальным, что приводит непротиворечивому примирению квантового и классического статистического описаний зкспериментов по распаду. Мы также покаэываем, что процесс иэмерения представляет локалиэацию продуктов распада и, следовательно, нестабильная система приводится к единственной квантовой системе. В рамках обычной квантовой механики мы можем дать естественное определение волновой функции нестабильной частицы.

The interpretation of quantum mechanics: where do we stand?

We reconsider some important foundational problems of quantum mechanics. After reviewing the measurement problem and discussing its unavoidability, we analyze some proposals to overcome it. This analysis leads us to reconsider the current debate on our best theory, i.e. quantum mechanics itself. We stress that, after the remarkable interest and the many efforts which have lead, in the last years of the past century, to a revival of the subject, and, more important, to new interesting results, we are now witnessing a re-emergence of the vague and unprofessional positions which have characterized the debate in the second quarter of the XXth century. In particular we consider as extremely serious the fact that a completely mistaken position concerning the real meaning of Bells theorem seems to have been taken by many scientists in the field.

Contribution to the decay theory of unstable quantum systems. — II

SummaryIn the context of a theory of decay proposed by the authors, two theorems, which are necessary in order to guarantee the physical consistency of the formalism, are proved.RiassuntoNel contesto di una teoria del decadimento proposta dagli autori, si stabiliscono due teoremi che sono essenziali per garantire la coerenza fisica del formalismo.

On the Fermi golden rule

SummaryThe derivation of the Fermi golden rule for the transition rates of an unstable system is reconsidered within a recently proposed theoretical framework to describe decay processes. It is shown that the obtained transition rates contain a dominant term which coincides with the standard result, plus correction terms whose features are discussed.RiassuntoSi riconsidera il problema di derivare la «golden rule» di Fermi per i tassi di decadimento di un sistema instabile, utilizzando lo schema teorico recentemente proposto per descrivere i processi di decadimento. Si mostra che i tassi di decadimento così ottenuti contengono un termine dominante che coincide col risultato usuale, più termini correttivi di cui si discutono le caratteristiche.РеэюмеВ рамках недавно предложенного теоретического подхода к описанию процессов распада эаново рассматривается вывод эолотого правила Ферми для интенсивностей переходов нестабильной системы. Покаэывается, что полученные интенсивности переходов содержат основной член, который совпадает с обшепринятым реэультатом, плюс поправочные члены, свойства которых обсуждаются.

Fermi golden rule

SummaryThe derivation of the Fermi golden rule for the transition rates of an unstable system is reconsidered within a recently proposed theoretical framework to describe decay processes. It is shown that the obtained transition rates contain a dominant term which coincides with the standard result, plus correction terms whose features are discussed.RiassuntoSi riconsidera il problema di derivare la «golden rule» di Fermi per i tassi di decadimento di un sistema instabile, utilizzando lo schema teorico recentemente proposto per descrivere i processi di decadimento. Si mostra che i tassi di decadimento così ottenuti contengono un termine dominante che coincide col risultato usuale, più termini correttivi di cui si discutono le caratteristiche.РеэюмеВ рамках недавно предложенного теоретического подхода к описанию процессов распада эаново рассматривается вывод эолотого правила Ферми для интенсивностей переходов нестабильной системы. Покаэывается, что полученные интенсивности переходов содержат основной член, который совпадает с обшепринятым реэультатом, плюс поправочные члены, свойства которых обсуждаются.

Threshold effects and unstable particles

The anomalous behaviour of cross sections at the threshold for a reaction involving unstable particles is derived by making use of the unitarity of the S-matrix and of analyticity arguments. Both the case of metastable particle production and that of virtual particle (antibound state) production are discussed.

Entanglement, Nonlocality, Superluminal Signaling and Cloning

The paper is a Chapter of a book. In it an exhaustive review of the proposals to send faster than light signals resorting to quantum nonlocality and the reduction process is presented, together with a critical analysis and rebuttal of all proposals. The most interesting part of the Chapter is the one in which the problem of quantum cloning is discussed. Actually, a proposal of superluminal signaling based on an hypothetical cloning machine has been presented by N. Herbert. The proposal does not work just because of the assumption that one can clone nonorthogonal states. The fact that such a machine is incompatible with quantum theory (i.e., the so-called No-Cloning Theorem) has been proved, for the first time, by the author of the present chapter in his referees report to Herberts paper. In the final part of the paper some recent (different but similarly not correct) proposals are analyzed and the reasons for which they are basically wrong are presented.

Energy dependent complex potentials and bound states

Abstract The Levinson theorem is derived for a class of rotationally invariant, energy-dependent, complex local potentials. Proper conditions are imposed on the potentials in order to make them reasonable. The obtained relation connects the real part of the scattering phase shift to the number of bound states.