Consistent treatments of quantum mechanics Reply

Alexander Meehan

Ishwar S Singh, M. A. B. Whitaker

Masanao Ozawa, Yuichiro Kitajima

Halvorson and Clifton have given a mathematical reconstruction of Bohr's reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr's reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr's requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.

L. E. Ballentine

Yakir Aharonov, Sandu Popescu, Jeff Tollaksen

Aharonov, Popescu, and Tollaksen reply: We are grateful to David Mermin for stating loud and clear, in his unmistakable style, that “the authors are correct.” As for the rest of his letter, a lesson on clear writing from a great master of the subject is always welcome. We did strive for clarity in our article, but there is always space for improvement, and Freudian slips of Newspeak often creep in—that’s their very nature.However, as Mermin certainly knows, analyzing sentences in isolation without the many clues found in context doesn’t do them justice. The initial setup is indeed elementary, and we put in all the details, so it is hard to see how it could be misinterpreted. The situation becomes far more interesting and surprising, though, when weak measurements are taken into account; to ignore them, as Michael Nauenberg and Art Hobson did, is to completely miss the point. We believe that no true understanding of quantum mechanics can be obtained without taking weak measurements seriously.The letter by Robert Griffiths is mainly concerned with the merits of the consistent histories approach to quantum mechanics. It is an interesting subject but one that has very little to do with our article. We presented a number of quantum effects that arise in the context of pre- and postselection, first and foremost the effects that appear when weak measurements are involved. And no, there is no error in reasoning when we claim that in a situation like that described in our article, spin measurements may, in a consistent way, indicate that spin-1⁄2 particles have value 100; that is a statement of fact about results of measurements, which incidentally have been confirmed experimentally. One is free to disagree with the meaning we attach to those facts but cannot deny the facts themselves. Of course, since our effects are purely quantum mechanical, they can be analyzed using any interpretation of quantum mechanics, including consistent histories. However, before having such a discussion, it helps if the effects are first discovered! Their existence is our main message.© 2011 American Institute of Physics.

Edward M. MacKinnon

The consistent histories reformulation of quantum mechanics was developed by Robert Griffiths, given a formal logical systematization by Roland Omn\`{e}s, and under the label `decoherent histories', was independently developed by Murray Gell-Mann and James Hartle and extended to quantum cosmology. Criticisms of CH involve issues of meaning, truth, objectivity, and coherence, a mixture of philosophy and physics. We will briefly consider the original formulation of CH and some basic objections. The reply to these objections, like the objections themselves, involves a mixture of physics and philosophy. These replies support an evaluation of the CH formulation as a replacement for the measurement, or orthodox, interpretation.