This paper introduces an exact correspondence between a general class of stochastic systems and quantum theory. This correspondence provides a new framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences. This paper also uses the correspondence in the other direction to reconstruct quantum theory from physical models that consist of trajectories in configuration spaces undergoing stochastic dynamics. The correspondence thereby yields a new formulation of quantum theory, alongside the Hilbert-space, (...) path-integral, and quasiprobability formulations. In addition, this reconstruction approach opens up new ways of understanding quantum phenomena like interference, decoherence, entanglement, noncommutative observables, and wave-function collapse. (shrink)

The problem of measurement is often considered an inconsistency inside the quantum formalism. Many attempts to solve it have been made since the inception of quantum mechanics. The form of these attempts depends on the philosophical position that their authors endorse. I will review some of them and analyze their relevance. The phenomenon of decoherence is often presented as a solution lying inside the pure quantum formalism and not demanding any particular philosophical assumption. Nevertheless, a widely debated question is to (...) decide between two different interpretations. The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate. For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed, so explaining the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears. In this case, explaining why only one single definite outcome is observed remains to do. In this paper, I examine the arguments that have been given for and against both interpretations and defend a new position, the “Convivial Solipsism”, according to which the outcome that is observed is relative to the observer, different but in close parallel to the Everett’s interpretation and sharing also some similarities with Rovelli’s relational interpretation and Quantum Bayesianism. I also show how “Convivial Solipsism” can help getting a new standpoint about the EPR paradox providing a way out of the seemingly unavoidable non-locality of quantum mechanics. (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.

We present an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new inter- pretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. Elementary particles are considered as extended objects and nonlocal effects are included. The role of the new concepts in the problems of measurement and of the Einstein-Podolsky-Rosen correlations is described. Experiments to distinguish the proposed interpretation from the Copenhagen one (...) are pointed out. (shrink)

This three-part paper comprises: (i) a critique by Halvorson of Bell’s (1973) paper ‘Subject and Object’; (ii) a comment by Butterfield; (iii) a reply by Halvorson. An Appendix gives the passage from Bell that is the focus of Halvorson’s critique.

The debate concerning the relations between matter and motion has the same age as philosophy itself. In modern times this problem was transformed into the one concerning the relations between mass and energy. Newton identified mass with matter. Classical thermodynamics brought this conception to its logical conclusion, establishing an ontic dichotomy between mass-matter and energy. On the basis of this pre-relativistic conception, Einstein's famous equation has been interpreted as a relation of equivalence between mass-matter and energy. Nevertheless, if we reject (...) this epistemologically illegitimate identification, it is possible to elaborate a unitary conception of matter, which at the same time is an argument for the unity between matter and motion. In particular, the classical antithesis between matter and field becomes obsolete in the frame of the proposed interpretation. (shrink)

We expound an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. The ψ function is no longer interpreted as a probability amplitude of the observed behaviour of elementary particles but as an objective physical field representing the particles themselves. The particles are thus extended objects whose extension varies in time according to (...) the variation of ψ. They are considered as fundamental regions of space with some kind of nonlocality. Special consideration is given to the Heisenberg relations, the Einstein-Podolsky- Rosen correlations, the reduction process, the problem of measurement, and the quantum-statistical distributions. (shrink)