Objective probabilities, quantum counterfactuals, and the ABL rule—A response to R. E. Kastner

The ABL rule is derived as a tool of standard quantum mechanics. The ontological significance of the existence of objective probabilities is discussed. Objections by Kastner [Am. J. Phys. 69, 860–863 (2001)] and others to counterfactual uses of the ABL rule are refuted. Metaphysical presumptions leading to such views as Kastner is defending in her Comment are examined and shown to be unwarranted.

[1]  L. Vaidman.  Weak-measurement elements of reality , 1996 .

[2]  T. Nagel.  The view from nowhere , 1987 .

[3]  B. Englert,et al.  Quantum optical tests of complementarity , 1991, Nature.

[4]  N. Goodman.  The Problem of Counterfactual Conditionals , 1947 .

[5]  Quantum Mechanics and the Cookie Cutter Paradigm , 2000, quant-ph/0009001.

[6]  D. Lewis.  Philosophical Papers: Volume II , 1987 .

[7]  A. Gleason.  Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[8]  Brown,et al.  Curious properties of quantum ensembles which have been both preselected and post-selected. , 1986, Physical review letters.

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

[10]  J. Sánchez-Gómez,et al.  On the probabilistic postulate of quantum mechanics , 1996 .

[11]  R. E. Kastner,et al.  The Three-Box “Paradox” and Other Reasons to Reject the Counterfactual Usage of the ABL Rule , 1998 .

[12]  M. Redhead.  Incompleteness, nonlocality, and realism , 1987 .

[13]  U. Mohrhoff.  The One, the Many, and the Quantum , 2000, quant-ph/0005110.

[14]  Cohen.  Pre- and postselected quantum systems, counterfactual measurements, and consistent histories. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[15]  J. Lebowitz,et al.  TIME SYMMETRY IN THE QUANTUM PROCESS OF MEASUREMENT , 1964 .

[16]  Huw Price,et al.  Time's Arrow & Archimedes' Point , 1997 .

[17]  Albert,et al.  Curious new statistical prediction of quantum mechanics. , 1985, Physical review letters.

[18]  R. E. Kastner.  Time-Symmetrised Quantum Theory, Counterfactuals and ‘Advanced Action’ , 1998 .

[19]  N. Shanks,et al.  The curious quantum statistics in the interval between measurements , 1989 .

[20]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[21]  Realism and time symmetry in quantum mechanics , 1995, quant-ph/9505017.

[22]  R. Audi.  The Cambridge Dictionary of Philosophy , 1995 .

[23]  U. Mohrhoff.  What quantum mechanics is trying to tell us , 2000 .

[24]  Berthold-Georg Englert,et al.  The Duality in Matter and Light , 1994 .

[25]  N. David Mermin,et al.  What is quantum mechanics trying to tell us , 1998, quant-ph/9801057.

[26]  The Pondicherry interpretation of quantum mechanics , 1999, quant-ph/9903051.

[27]  J. Wheeler.  ‘‘On recognizing ‘law without law,’ ’’ Oersted Medal Response at the joint APS–AAPT Meeting, New York, 25 January 1983 , 1983 .

[28]  Niall Shanks,et al.  The Rise and Fall of Time-Symmetrized Quantum Mechanics , 1993, Philosophy of Science.