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arXiv:1711.02928 · Physical Review A

Comment on “Spontaneous collapse: A solution to the measurement problem and a source of the decay in mesonic systems”

Antoine Tilloy

Published Nov 7, 2017• 1 citation
arXivHTMLPDF

Abstract

In a recent article [Phys. Rev. A 94, 052128 (2016)], the authors compute the predictions of two collapse models on the transition probabilities of neutral mesons. Notably, they claim to find an influence on the decay rates and attempt to prove that a new parameter $\ensuremath{\theta}(0)$ is required to fully characterize the noise of standard collapse models. These two claims are incorrect and motivated by flawed computations. This Comment derives the correct transition probabilities exactly from the master equation, explains how they could be computed perturbatively in a safe way, and finally shows where the main mistake of the authors of the original article was made.

DOI
10.1103/physreva.96.056101

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In a recent article [Phys. Rev. A 94, 052128 (2016)], the authors compute the predictions of two collapse models on the transition probabilities of neutral mesons. Notably, they claim to find an influence on the decay rates and attempt to prove that a new parameter \ensuremathθ(0)\ensuremath{\theta}(0)\ensuremathθ(0) is required to fully characterize the noise of standard collapse models. These two claims are incorrect and motivated by flawed computations. This Comment derives the correct transition probabilities exactly from the master equation, explains how they could be computed perturbatively in a safe way, and finally shows where the main mistake of the authors of the original article was made.
Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor-oscillating neutral mesons for the two most promising collapse models, the QMUPL (quantum mechanics with universal position localization) model and the mass-proportional CSL (continuous spontaneous localization) model. Our results are showing (i) a strong sensitivity to the very assumptions of the noise field underlying those two collapse models and (ii) under particular assumptions the CSL case allows one even to recover the decay dynamics. This in turn allows one to predict the effective collapse rates solely based on the measured values for the oscillation (mass differences) and the measured values of the decay constants. The four types of neutral mesons (KKK meson, DDD meson, Bd{B}_{d}Bd​ meson, and Bs{B}_{s}Bs​ meson) lead surprisingly to ranges comparable to those put forward by Adler [J. Phys. A: Math. Theor. 40, 2935 (2007)] and Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)]. Our results show that these systems at high energies are very sensitive to possible modifications of the standard quantum theory, making them a very powerful laboratory to rule out certain collapse scenarios and study the detailed physical processes solving the measurement problem.
Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is governed by a phenomenological non-Hermitian Hamiltonian. In turn, we apply two popular collapse models, the Quantum Mechanics with Universal Position Localization and the Continuous Spontaneous Localization models, to a neutral meson system. By using the equivalence between the approaches to the time evolution of decaying systems with a non-Hermitian Hamiltonian and a dissipator of the Lindblad form in an enlarged Hilbert space, we show that spontaneous collapse can induce the decay dynamics in both quantum state and master equations. Moreover, we show that the decay property of a flavor-oscillating system is intimately connected to the time (a)symmetry of the noise field underlying the collapse mechanism. This (a)symmetry, in turn, is related to the definition of the stochastic integral and can provide a physical intuition behind the It\ifmmode \bar{o}\else \={o}\fi{}-Stratonovich dilemma in stochastic calculus.
Why do we never see a table in a superposition of here and there? This problem gets a solution by so called collapse models assuming the collapse as a genuinely physical process. Here we consider two specific collapse models and apply them to systems at high energies, i.e. flavour oscillating neutral meson systems. We find on one hand a potentially new interpretation of the decay rates introduced by hand in the standard formalism and on the other hand that these systems at high energies constrain by experimental data the possible collapse scenarios.
In [Phys. Rev. A 82, 042103 (2010)], the authors showed that "for a class of the non-Markovian master equations in time-local forms", the quantum Fisher information (QFI) flow can be decomposed into additive subflows corresponding to different dissipative channels. However, the paper does not specify the class of non-Markovian time-local master equations for which their analytic decomposition of the QFI flow is valid. Here we show that several suppositions have to be made in order to reach the central result of Ref. \cite{luwsun10}, which appears to be valid for a narrow class of density operators ρ(θ;t)ρ(θ;t)ρ(θ;t) and quantum Fisher information F(θ;t)\mathcal{F}(θ;t)F(θ;t), and under strict conditions on the time-local master equation. More precisely, the decomposition of the QFI flow obtained in Ref. \cite{luwsun10} is valid under two conditions not mentioned in the paper: (i) ddt(∂ρ∂θ)=\frac{d}{dt} \left( \frac{\partial ρ}{\partial θ} \right)=dtd​(∂θ∂ρ​)= ∂∂θ(dρdt)\frac{\partial}{\partial θ} \left( \frac{d ρ}{dt} \right)∂θ∂​(dtdρ​); (ii) ∂H∂θ=0\frac{\partial H}{\partial θ}=0∂θ∂H​=0, ∂γi∂θ=0\frac{\partial γ_i}{\partial θ}=0∂θ∂γi​​=0, ∂Ai∂θ=0\frac{\partial A_i}{\partial θ}=0∂θ∂Ai​​=0, meaning that the Hamiltonian H(t)H(t)H(t), the decay rates γi(t)γ_i(t)γi​(t), and the Lindblad operators Ai(t)A_i(t)Ai​(t) appearing in the non-Markovian time-local master equation have to not depend on the parameter θθθ about which the quantum Fisher information is defined.
Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function ( e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.
Spontaneous collapse models have been proposed as a possible realist solution of the quantum measurement problem. They assume that the standard unitary evolution is valid only in the microscopic limit, with stochastic corrections leading to a dynamical reduction of the wave function at macroscopic level. A remarkable feature of collapse models is that, unlike interpretations of quantum mechanics, they predict departures from standard theory that can be experimentally tested. A common prediction is a violation of energy conservation, which manifests as an universal force noise acting on mechanical systems. Here, we will discuss recent bounds on collapse models set by mechanical experiments, focusing on ultracold cantilevers and gravitational wave detectors. First notable results are a partial exclusion of the CSL parameters proposed by Adler and a full exclusion of an early model based on quantum gravity arguments.