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State vector reduction. Part 2: Elements of physical reality, nonlocality and stochasticity in relativistic dynamical reduction models

G. C. Ghirardi, Philip Pearle

Published Feb 1, 1991• 0 citations
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II. Elements of Physical Reality, Nonlocality and Stochasticity in Relativistic Dynamical Reduction Models

G. C. Ghirardi, Philip Pearle

In this part we will consider recent attempts to get a relativistic CSL theory. The problem of getting such a generalization, or at least of making plausible that it exists, is of great interest. J. Bell (1990), after having expressed his dissatisfaction with the fundamental lack of precision of the standard formulation of quantum mechanics and the opinion that the only available acceptable alternatives are the Pilot Wave and the Spontaneous Localization schemes has stated: The big question, in my opinion, is which, if either, of these two precise pictures can be redeveloped in a Lorentz invariant way. The point of view of this paper is that what is most interesting is not a detailed exposition of the formal aspects of the generalization, but some crucial conceptual points which have come into focus in this attempt.

PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association•Jan 1, 1990•10 citations

State vector reduction in relativistic quantum mechanics: An introduction

Heinz‐Peter Breuer, Francesco Petruccione

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Stochastic dynamical reduction theories and superluminal communication

Philip Pearle

In theories which describe the reduction of the state vector as a physical process, the possibility exists, for certain experiments, of predictions which differ from those of quantum theory. These are ``interrupted reduction interference'' experiments, characterized by an interaction which triggers the reduction, followed rapidly (before the reduction is completed) by a measurement of interference between the superposed states that make up the state vector (possible examples: double Stern-Gerlach experiment, two-slit neutron interference). We consider the general class of stochastic reduction theories, and ask whether they allow superluminal communication by means of such experiments. We show that, if the state vector that precedes reduction is precisely reproducible, then superluminal communication can occur in certain circumstances, unless the off-diagonal elements of the density matrix decay exponentially, with a universal time constant. We also show, in that case, that no state vector ever reduces in a finite time, so such a theory is not satisfactory. However, superluminal communication can be avoided if reduction is triggered only in irreproducible state vectors, of such complexity that prior to reduction the ``effective'' density matrix, constructed from the ensemble of such state vectors and traced over the variables outside the experimenter's control, is diagonal. Then predictions are identical to those of quantum theory for ``interrupted reduction interference'' experiments and thus apparently for all experiments. The lesson of this paper is that the ``effective'' density matrix must always be used to make physical predictions in dynamical reduction theories. This supplies a resolution of the problem of reconciling state-vector reduction with relativity: even if the reduction dynamics is not relativistically invariant, its experimental predictions are. It also implies that the ``effective'' entropy increases during a measurement, but remains constant during reduction, which is the reverse of a common dictum.

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Relativistic dynamical reduction models: General framework and examples

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Foundations of Physics•Nov 1, 1990•263 citations

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Ways to describe dynamical state-vector reduction

Philip Pearle

The continuous-spontaneous-localization (CSL) description of state-vector reduction allows one to describe reality by the state vector. The mathematical structure of the theory, based upon a c-number white-noise source interacting with the quantum system, is reviewed. Then this description is generalized in two ways. First, a generalization is made to a wide class of c-number stochastic processes: using the square root of the probability density functional of the process, it is shown how to construct an evolution equation for the state vector which results in state-vector reduction. Second, within this wider framework the c-number source is completely eliminated and replaced by quantum operators, dubbed ``index'' operators, representing new physical variables which interact with the quantum system. In this case the state vector cannot represent reality as in the previous case, but it is shown how to write it unambiguously as a sum of ``preferred basis'' states, any one of which can represent reality. Therefore this quantum theory is open to the ensemble interpretation, where ``ensemble'' refers to the collection of possible real states. Three requirements sufficient for a viable ensemble interpretation are specified. It is shown how to satisfy these requirements, obtaining a purely quantum model that is equivalent to CSL and capable of describing reality.

Physical Review A•Aug 1, 1993•57 citations
In this part we will consider recent attempts to get a relativistic CSL theory. The problem of getting such a generalization, or at least of making plausible that it exists, is of great interest. J. Bell (1990), after having expressed his dissatisfaction with the fundamental lack of precision of the standard formulation of quantum mechanics and the opinion that the only available acceptable alternatives are the Pilot Wave and the Spontaneous Localization schemes has stated: The big question, in my opinion, is which, if either, of these two precise pictures can be redeveloped in a Lorentz invariant way. The point of view of this paper is that what is most interesting is not a detailed exposition of the formal aspects of the generalization, but some crucial conceptual points which have come into focus in this attempt.
In theories which describe the reduction of the state vector as a physical process, the possibility exists, for certain experiments, of predictions which differ from those of quantum theory. These are ``interrupted reduction interference'' experiments, characterized by an interaction which triggers the reduction, followed rapidly (before the reduction is completed) by a measurement of interference between the superposed states that make up the state vector (possible examples: double Stern-Gerlach experiment, two-slit neutron interference). We consider the general class of stochastic reduction theories, and ask whether they allow superluminal communication by means of such experiments. We show that, if the state vector that precedes reduction is precisely reproducible, then superluminal communication can occur in certain circumstances, unless the off-diagonal elements of the density matrix decay exponentially, with a universal time constant. We also show, in that case, that no state vector ever reduces in a finite time, so such a theory is not satisfactory. However, superluminal communication can be avoided if reduction is triggered only in irreproducible state vectors, of such complexity that prior to reduction the ``effective'' density matrix, constructed from the ensemble of such state vectors and traced over the variables outside the experimenter's control, is diagonal. Then predictions are identical to those of quantum theory for ``interrupted reduction interference'' experiments and thus apparently for all experiments. The lesson of this paper is that the ``effective'' density matrix must always be used to make physical predictions in dynamical reduction theories. This supplies a resolution of the problem of reconciling state-vector reduction with relativity: even if the reduction dynamics is not relativistically invariant, its experimental predictions are. It also implies that the ``effective'' entropy increases during a measurement, but remains constant during reduction, which is the reverse of a common dictum.
The continuous-spontaneous-localization (CSL) description of state-vector reduction allows one to describe reality by the state vector. The mathematical structure of the theory, based upon a c-number white-noise source interacting with the quantum system, is reviewed. Then this description is generalized in two ways. First, a generalization is made to a wide class of c-number stochastic processes: using the square root of the probability density functional of the process, it is shown how to construct an evolution equation for the state vector which results in state-vector reduction. Second, within this wider framework the c-number source is completely eliminated and replaced by quantum operators, dubbed ``index'' operators, representing new physical variables which interact with the quantum system. In this case the state vector cannot represent reality as in the previous case, but it is shown how to write it unambiguously as a sum of ``preferred basis'' states, any one of which can represent reality. Therefore this quantum theory is open to the ensemble interpretation, where ``ensemble'' refers to the collection of possible real states. Three requirements sufficient for a viable ensemble interpretation are specified. It is shown how to satisfy these requirements, obtaining a purely quantum model that is equivalent to CSL and capable of describing reality.