Probability in GRW Theory

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle.

[1]  A. A..  Probability, Statistics and Truth , 1940, Nature.

[2]  GianCarlo Ghirardi,et al.  Dynamical reduction models , 2003 .

[3]  J.F.A.K. van Benthem,et al.  Structures and Norms in Science , 1997 .

[4]  Peter J. Lewis.  Life in Configuration Space , 2004, The British Journal for the Philosophy of Science.

[5]  M. Suárez.  On Quantum Propensities: Two Arguments Revisited , 2004 .

[6]  GianCarlo Ghirardi,et al.  Perspectives of the Dynamical Reduction Program , 2001 .

[7]  J. Colquhoun,et al.  A matter of chance. , 1992, Australian family physician.

[8]  R. Tumulka.  A Relativistic Version of the Ghirardi–Rimini–Weber Model , 2004, quant-ph/0406094.

[9]  S. S. Wilks,et al.  Probability, statistics and truth , 1939 .

[10]  Macroscopic Reality and the Dynamical Reduction Program , 1997 .

[11]  G. Ghirardi,et al.  Quantum mechanics with spontaneous localization and experiments , 1995 .

[12]  Karl R. Popper,et al.  A World of Propensities , 1993, Popper's Views on Natural and Social Science.

[13]  David Lewis,et al.  Papers in metaphysics and epistemology: Humean Supervenience debugged , 1999 .

[14]  Pearle,et al.  Combining stochastic dynamical state-vector reduction with spontaneous localization. , 1989, Physical review. A, General physics.

[15]  Samir Okasha,et al.  Philosophical Theories of Probability , 2002 .

[16]  B. Loewer.  Determinism and Chance , 2001 .

[17]  James H. Fetzer.  Scientific Knowledge: Causation, Explanation, and Corroboration , 1981 .

[18]  Ned Hall.  Two Mistakes About Credence and Chance , 2004 .

[19]  C. Hoefer.  The Third Way on Objective Probability: A Sceptic's Guide to Objective Chance , 2007 .

[20]  Spontaneous Localization and Superconductivity , 1995 .

[21]  D. Lewis,et al.  Symposium: Chance and CredenceHumean Supervenience Debugged , 1994 .

[22]  Patrick Suppes,et al.  Logic, Methodology and Philosophy of Science , 1963 .

[23]  GianCarlo Ghirardi,et al.  Quantum dynamical reduction and reality: Replacing probability densities with densities in real space , 1996, Erkenntnis.

[24]  Paul Humphreys.  Some Considerations on Conditional Chances , 2004, The British Journal for the Philosophy of Science.

[25]  J. Hartigan.  Theories of Probability , 1983 .

[26]  David Miller,et al.  Propensities and Indeterminism , 1995, Royal Institute of Philosophy Supplement.

[27]  Weber,et al.  Unified dynamics for microscopic and macroscopic systems. , 1986, Physical review. D, Particles and fields.

[28]  R. Giere,et al.  Objective Single-Case Probabilities and the Foundations of Statistics , 1973 .

[29]  H. Dingle.  The Laws of Nature* , 1944, Nature.

[30]  Pearle,et al.  Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[31]  Nuel D. Belnap,et al.  Propensities and probabilities , 2007 .

[32]  Hans Primas,et al.  Realism and quantum mechanics , 1994 .

[33]  B. Loewer.  David Lewis’s Humean Theory of Objective Chance , 2004, Philosophy of Science.

[34]  Mauricio Suárez,et al.  Propensities in Quantum Mechanics , 2009, Compendium of Quantum Physics.

[35]  A. Zeilinger,et al.  Speakable and Unspeakable in Quantum Mechanics , 1989 .

[36]  D. H. Mellor,et al.  Probability: A Philosophical Introduction , 2004 .

[37]  Chance of Reduction as Chance of Spontaneous Localisation , 2001 .

[38]  D. Lewis.  A Subjectivist’s Guide to Objective Chance , 1980 .

[39]  Richard Von Mises,et al.  Probability, statistics and truth , 1939 .

[40]  Enrico G. Beltrametti,et al.  Advances in Quantum Phenomena , 1995 .

[41]  Peter J. Lewis.  Interpreting spontaneous collapse theories , 2005 .

[42]  On the property structure of realist collapse interpretations of quantum mechanics and the so-called "counting anomaly" , 2003 .

[43]  Losing Your Marbles in Wavefunction Collapse Theories , 1999, The British Journal for the Philosophy of Science.

[44]  Bradley Monton,et al.  The problem of ontology for spontaneous collapse theories , 2004 .

[45]  Marshall Spector,et al.  The Chances of Explanation , 1999 .

[46]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[47]  N. H. Beebe.  Studies in History and Philosophy of Modern Physics , 2009 .

[48]  J. Bell,et al.  Schrödinger: Are there quantum jumps? , 1987 .

[49]  J. Bricmont.  Chance in physics : foundations and perspectives , 2001 .

[50]  A. Elga.  Infinitesimal Chances and the Laws of Nature , 2004 .

[51]  M. Strevens.  Objective Probability as a Guide to the World , 1999 .

[52]  GianCarlo Ghirardi,et al.  Sneaking a Look at God's Cards: Unraveling the Mysteries of Quantum Mechanics , 2004 .

[53]  G. Ghirardi,et al.  Describing the macroscopic world: Closing the circle within the dynamical reduction program , 1994 .

[54]  Peter W. Milne,et al.  A NOTE ON POPPER, PROPENSITIES, AND THE TWO-SLIT EXPERIMENT , 1985, The British Journal for the Philosophy of Science.

[55]  M. Galavotti.  What Interpretation for Probability in Physics , 2001 .