Decoherent Histories and Realism

We reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents. We put forward some assumptions which, in our opinion, are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories. We prove that such assumptions, unless one limits the set of the decoherent families which can be taken into account, lead to a logical contradiction. The line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach. The conclusion is that the decoherent histories approach, to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics, requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem.

[1]  R. Omnes,et al.  Logical reformulation of quantum mechanics. I. Foundations , 1988 .

[2]  Kent,et al.  Properties of consistent histories. , 1995, Physical review letters.

[3]  A. Kent.  CONSISTENT SETS YIELD CONTRARY INFERENCES IN QUANTUM THEORY , 1996, gr-qc/9604012.

[4]  Arthur I. Miller.  Sixty-Two Years of Uncertainty , 1990 .

[5]  C. Ross.  Found , 1869, The Dental register.

[6]  Max Born,et al.  THE INTERPRETATION OF QUANTUM MECHANICS* , 1953, The British Journal for the Philosophy of Science.

[7]  R. Omnes.  Consistent interpretations of quantum mechanics , 1992 .

[8]  Gell-Mann,et al.  Classical equations for quantum systems. , 1992, Physical review. D, Particles and fields.

[9]  Y. Aharonov,et al.  Complete description of a quantum system at a given time , 1991 .

[10]  R. Griffiths.  Correlations in separated quantum systems: A consistent history analysis of the EPR problem , 1987 .

[11]  B. D'espagnat.  Consistent histories and the measurement problem , 1987 .

[12]  J. Bell.  On the impossible pilot wave , 1982 .

[13]  James T. Cushing,et al.  Bohmian mechanics and quantum theory: an appraisal , 1996 .

[14]  I. Giardina,et al.  On the existence of inequivalent quasideterministic domains , 1996 .

[15]  R. Leighton,et al.  Feynman Lectures on Physics , 1971 .

[16]  M. Gell-Mann,et al.  Physics Today. , 1966, Applied optics.

[17]  G. Ghirardi,et al.  Can the decoherent histories description of reality be considered satisfactory , 1998, gr-qc/9811050.

[18]  Robert B. Griffiths,et al.  Consistent histories and the interpretation of quantum mechanics , 1984 .

[19]  Robert B. Griffiths.  Choice of Consistent Family, and Quantum Incompatibility , 1998 .

[20]  Griffiths.  Consistent histories and quantum reasoning. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[21]  Linearly positive histories: Probabilities for a robust family of sequences of quantum events. , 1994, Physical review letters.