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State vector reduction. Part 1: Dynamical reduction theories; changing quantum theory so the statevector represents reality

G. C. Ghirardi, Philip Pearle

Published Feb 1, 1991• 0 citations
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Related papers

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

G. C. Ghirardi, Philip Pearle

Unknow•Feb 1, 1991•0 citations

Toward a Relativistic Theory of Statevector Reduction

Philip Pearle

NATO ASI series. Series B : Physics•Jan 1, 1990•103 citations

I. Dynamical Reduction Theories: Changing Quantum Theory so the Statevector Represents Reality

G. C. Ghirardi, Philip Pearle

We dedicate these papers to the memory of John Bell, whose contributions to, support for, and encouragement of the research program described here has meant more than words can say to those involved in it. In Schrödinger’s “cat paradox” example, a nucleus which has a 50% probability of decaying within an hour is coupled to a cat by a “hellish contraption” which, if it detects the decay, will kill the cat. If we take the point of view that what we see around us is real, what occurs in reality is one of the two following evolutions : (—> means “evolves in an hour into“). According to Schrödinger’s equation, the evolution of the statevector describing this situation is The right hand side of Eq. (1.2) does not correspond to either the reality on the right hand side of (1.1a) nor to the reality on the right hand side of (1.1b).

PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association•Jan 1, 1990•34 citations

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

Suppose the State Vector Is Real: The Description and Consequences of Dynamical Reduction

Philip Pearle

Annals of the New York Academy of Sciences•Dec 1, 1986•46 citations

The Quantum State Vector and Physical Reality

Peter G. Bergmann

Studies in the foundations methodology and philosophy of science•Jan 1, 1967•3 citations
We dedicate these papers to the memory of John Bell, whose contributions to, support for, and encouragement of the research program described here has meant more than words can say to those involved in it. In Schrödinger’s “cat paradox” example, a nucleus which has a 50% probability of decaying within an hour is coupled to a cat by a “hellish contraption” which, if it detects the decay, will kill the cat. If we take the point of view that what we see around us is real, what occurs in reality is one of the two following evolutions : (—> means “evolves in an hour into“). According to Schrödinger’s equation, the evolution of the statevector describing this situation is The right hand side of Eq. (1.2) does not correspond to either the reality on the right hand side of (1.1a) nor to the reality on the right hand side of (1.1b).
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.