Bohmian mechanics, collapse models and the emergence of classicality

Toroš, Marko; Donadi, Sandro; Bassi, Angelo

doi:10.1088/1751-8113/49/35/355302

Cited by 9 publications

(16 citation statements)

References 33 publications

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“…The first is that both approaches are realist in the most trivial sense: they ultimately describe the dynamics of local beables (or 'stuff') from which all predictions can in principle be extracted [11,12]. The second is that the evolution for the wave-function in the Ghirardi-Rimini-Weber (GRW) model, the simplest collapse model, approximates, in an appropriate limit, the dynamics of a Bohmian conditional wave function in a setup where a bath is added [13].…”

Section: Introductionmentioning

confidence: 99%

Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Tilloy

Wiseman

2021

Quantum

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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.

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Section: Introductionmentioning

confidence: 99%

Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Tilloy

Wiseman

2021

Quantum

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“…Hence for every dt, one needs to compute a new complete noise trajectory w [t] (s) using ( 12), and construct the associated state |ψ w [t] (t) using ( 2) [31]. In the end, a non-linear stochastic trajectory t → |ψ w [t] (t) can be computed using the linear stochastic Schrödinger equation ( 2), the normalization (7) and the continuous change of noise field (12): this fully specifies the non-linear dynamics. However, one should remember that the relationship between what one would naturally see as the noise field w [t] (t) and the state |ψ w [t] (t) is non trivial.…”

Section: Non-linear Non-markovian Dynamicsmentioning

confidence: 99%

“…Our starting point is a generic collapse model with colored noise, whose dynamics are fully determined by equations ( 2) and (12). As advertised, our objective is to construct a bath such that the dynamics of the system + bath setup, where the bath is given Bohmian particle positions, is exactly that of the collapse model.…”

Section: Setupmentioning

confidence: 99%

“…Our objective is to compute the explicit expression of the transformed noise trajectory w [t] , given in equation (12), starting from the implicit prescription (10):…”

Section: Appendix: Change Of Noise Variablesmentioning

confidence: 99%

“…The first is that both approaches are realist in the most trivial sense: they ultimately describe the dynamics of local beables (or "stuff") from which all predictions can in principle be extracted [10,11]. The second is that the evolution for the wave-function in the Ghirardi-Rimini-Weber (GRW) model, the simplest collapse model, approximates, in an approriate limit, the dynamics of a Bohmian conditional wave function in a setup where a bath is added [12].…”

Section: Introductionmentioning

confidence: 99%

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Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Tilloy,

Wiseman

2021

Preprint

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Spontaneous collapse models 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 particle positions of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian positions. 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.

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Collapse Models: Main Properties and the State of Art of the Experimental Tests

Carlesso

Donadi

2019

Springer Proceedings in Physics

Self Cite

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Collapse models represent one of the possible solutions to the measurement problem. These models modify the Schrödinger dynamics with non-linear and stochastic terms, which guarantee the localization in space of the wave function avoiding macroscopic superpositions, like that described in the Schrödinger's cat paradox. The Ghirardi-Rimini-Weber (GRW) and the Continuous Spontaneous Localization (CSL) models are the most studied among the collapse models. Here, we briefly summarize the main features of these models and the advances in their experimental investigation.

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Bohmian mechanics, collapse models and the emergence of classicality

Cited by 9 publications

References 33 publications

Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Collapse Models: Main Properties and the State of Art of the Experimental Tests

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