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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Reply to ‘‘Comment on ‘Repeated measurements in stochastic mechanics’ ’’

Philippe Blanchard, Maurizio Serva

Published Mar 15, 1995• 2 citations
Publisher

Abstract

In a previous paper we showed that predictions about the results of repeated measurements coincide in quantum and stochastic mechanics when wave-packet collapse is taken into acocunt. Our result removed some apparent paradoxes pointed out by Grabert, H\"anggi, Talkner, and Nelson. Recently Wang and Liang argued that our analysis was incorrect and they produced an explicit counterexample in order to confute our results. We think that their comment is due to a misunderstanding of our paper. For this reason we discuss here, in more detail, the controversial point of our work, concerning the regularization of the quantum-mechanical propagator. After stating more clearly our point, we show that the criticism of Wang and Liang is supported by an improper treatment of the divergences in their counterexample.

DOI
10.1103/physrevd.51.3132

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In a previous paper we showed that predictions about the results of repeated measurements coincide in quantum and stochastic mechanics when wave-packet collapse is taken into acocunt. Our result removed some apparent paradoxes pointed out by Grabert, H"anggi, Talkner, and Nelson. Recently Wang and Liang argued that our analysis was incorrect and they produced an explicit counterexample in order to confute our results. We think that their comment is due to a misunderstanding of our paper. For this reason we discuss here, in more detail, the controversial point of our work, concerning the regularization of the quantum-mechanical propagator. After stating more clearly our point, we show that the criticism of Wang and Liang is supported by an improper treatment of the divergences in their counterexample.
Stochastic mechanics provides a probabilistic scheme for the description of quantum systems. Grabert, Haaumlnggi, and Talkner, and Nelson have pointed out that its multitime correlations seem to be in disagreement with quantum-mechanical predictions. We show that these difficulties are removed upon a careful analysis of repeated measurements in stochastic mechanics. The wave-packet reduction is naturally described in the stochastic framework, and the predictions for repeated measurements consequently agree in both theories.
Seoane et al. [preceding Comment, Phys. Rev. A 111, 066201 (2025)] criticized our work [Phys. Rev. A 109, 022238 (2024)], saying that our argument that realistic interpretations of weak values lead to inconsistencies is not valid for all weak values and quantum theories. This is true. We never intended that the arguments we presented would be valid for all weak values. We believe it is clearly stated in our work that we were dealing only with the weak values related to the quantum paradoxes cited in our paper. Seoane et al. also said in their Comment that the ``general argument'' we present in our paper is formally incorrect. However, this criticism is related to the interpretation they give to the expression ``equivalent,'' which is different from the one we use. In this sense, the presented criticisms are a matter of semantics, not of physics.