In this volume in honor of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. 10 problems are introduced, 9 of which were seen following my initial work. 4 of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's Spontaneous Localization (SL) model (which added 1 more problem). This stimulated a (somewhat different) resolution of these 5 problems in the Continuous Spontaneous Localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in honor of Abner Shimony I shall discuss the status of the 5 remaining post-CSL problems.
In this volume in honor of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. 10 problems are introduced, 9 of which were seen following my initial work. 4 of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's Spontaneous Localization (SL) model (which added 1 more problem). This stimulated a (somewhat different) resolution of these 5 problems in the Continuous Spontaneous Localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in honor of Abner Shimony I shall discuss the status of the 5 remaining post-CSL problems.
In this volume i.h. of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. 10 problems are introduced, 9 of which were seen following my initial work. 4 of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's Spontaneous Localization (SL) model (which added 1 more problem). This stimulated a (somewhat different) resolution of these 5 problems in the Continuous Spontaneous Localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in h. of Abner Shimony I shall discuss the status of the 5 remaining post-CSL problems.
In this volume in honour of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. Ten problems are introduced, nine of which were seen following my initial work. Four of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's spontaneous localization (SL) model (which added one more problem). This stimulated a (somewhat different) resolution of these five problems in the continuous spontaneous localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in honour of Abner Shimony, I shall discuss the status of the remaining five post-CSL problems.
Different attempts to solve the measurement problem of the quantum me-chanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions. To the difference, Ghirardi, Rimini and Weber took the collapse as a real phenomenon, and proposed a calculus by which the wave-function should undergo a sudden localization. Later on, Ghirardi, Pearle and Rimini came with a change of this calculus into the CSL (continuous spontaneous localization) model of collapse. Both these proposals rely on the experimental fact that the reduction of the wave-function occurs when the microscopic system encounters a macroscopic object and involves a big amount of its particles. Both these proposals also change the quantum formalism by introducing in the Schr?dinger equation additional terms with noisy behavior. However, these terms have practically no influence as long as the studied system contains only one or a few components. Only when the amount of components is very big, these terms become significant and lead to the reduction of the wave-function to one of its components. The present work has two purposes: 1) proving that the collapse postulate is unavoidable; 2) ap-plying the CSL model to the process in a detector and showing step by step the modification of the wave-function, until reduction. As a side detail, it is argued here that the noise cannot originate in some classical field, contrary to the thought/hope of some physicists, because no classical field is tailored by the wave-functions of entanglements.
Models of dynamical wave function collapse consistently describe the breakdown of the quantum superposition with the growing mass of the system by introducing non-linear and stochastic modifications to the standard Schrödinger dynamics. Among them, Continuous Spontaneous Localization (CSL) was extensively investigated both theoretically and experimentally. Measurable consequences of the collapse phenomenon depend on different combinations of the phenomenological parameters of the model-the strength λ and the correlation length rC-and have led, so far, to the exclusion of regions of the admissible (λ-rC) parameters space. We developed a novel approach to disentangle the λ and rC probability density functions, which discloses a more profound statistical insight.
John Bell was a staunch supporter of the dynamical wave function collapse approach to making a well-defined quantum theory. Through letters from him, I reminisce on my handful of interactions with him, all of which were memorable tome. Then I discuss nonlocality, violation of Bell's inequality and some further implications within the framework of the CSL (continuous spontaneous localization) model of dynamical collapse. Interactions I was an instructor at Harvard with a newly minted Ph.D. from MIT, earned with an indifferent thesis on particle theory. It took me two years to come to terms with, dare I say it, the fact that I did not care about the S-matrix. I was going to be out of a job anyway in 1966 so, in the fall of 1965, I put my full energy into writing my very first paper, about what I did care: that, to my eyes there was something deeply wrong with the quantum theory I had been taught; that the rules of how to use it were inadequate. The title of the paper [1] was “Elimination of the reduction postulate from quantum theory and a framework for hidden variable theories.” It was a long title, because it was really two rather separate papers. The first was based upon the perceived inadequacy that the collapse (reduction) postulate of the theory is ill-defined. The second stated some postulates I thought a good hidden variable theory ought to obey, and gave a model for their satisfaction in a two-dimensional (i.e., spin-1/2) Hilbert space. Try as I might, I was not able to generalize my model to a higher-dimensional (i.e., spin-1) Hilbert space, but I put it out there for someone more clever than I to achieve. I sent the paper to a very few people who I thought might be interested. One was John Bell, and he replied (see Figure 23.1)! So someone more clever than I pointed out that generalizing my model could not be achieved. I therefore excised the model and, after rewriting and retitling, published my very first paper [2]! After a three-year stint at Case Institute of Technology, which graduated to become Case Western Reserve University while I was there, in 1969 I became ensconced at Hamilton College.
Abstract Before examining experimental consequences of CSL, this chapter discusses the spontaneous localization (SL) theory of Ghirardi, Rimini and Weber (GRW). As for CSL, the chapter presents the structure of the theory, and then specializes it to a non-relativistic theory. SL does not add a term to Schrodinger’s equation. Instead, the state vector is suddenly altered by a “hit” (GRW’s ‘spontaneous localization’), that is, multiplication by an operator, followed by renormalization. The hits occur at random times. The chapter shows the specific choice of operator made by GRW for their non-relativistic theory. Emphasized are two aspects of SL that helped the journey to CSL. One is that the collapse is always acting (one need not “turn it on.” The other is the “smeared” character of the GRW operator. The chapter then shows how the density matrix is calculated. Finally, it discusses the numerical values, chosen by GRW, of the two parameters of SL theory, λ and a, that are provisionally adopted for CSL.