Non-locality and quasiclassical reality in Kent’s formulation of relativistic quantum theory

Butterfield, Jeremy; Marsh, Brendan

doi:10.1088/1742-6596/1275/1/012002

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…In such an approach, the dynamics of the beables is not obtained forward in time, knowing the past, as a Cauchy problem, but depends on the future. This does not come without difficulties, as was noted by Marsh and Butterfield [57,58], but likely deserves to be explored further.…”

Section: Randomness Determinism Bell and Local Friendlinessmentioning

confidence: 71%

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: Randomness Determinism Bell and Local Friendlinessmentioning

confidence: 71%

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

Tilloy

Wiseman

2021

Quantum

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“…In such an approach, the dynamics of the beables is not obtained forward in time, knowing the past, as a Cauchy problem, but depends on the future. This does not come without difficulties, as was noted by Marsh and Butterfield [55,56], but likely deserves to be explored further.…”

Section: Is There An Alternative To Guiding Laws?mentioning

confidence: 77%

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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“…2. It allows us to attribute the emergence of classicality to decoherence -indeed, Butterfield characterises Kent's approach as a decoherence-based approach to the measurement problem which gets the role of decoherence right, since it does not 'make the error of thinking that an improper mixture is ignorance-interpretable' [75].…”

Section: Further Criteriamentioning

confidence: 99%

Do We Have Any Viable Solution to the Measurement Problem?

Adlam¹

2023

Preprint

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It has become common in foundational discussions to say that we have a variety of possible interpretations of quantum mechanics available to us and therefore we are faced with a problem of underdetermination. In ref [1] Wallace argues that this is not so, because several popular approaches to the measurement problem can't be fully extended to relativistic quantum mechanics and quantum field theory (QFT), and thus they can't reproduce many of the empirical phenomena which are correctly predicted by QFT. Wallace thus contends that as things currently stand, only the unitary-only approaches can reproduce all the predictions of quantum mechanics, so at present only the unitary-only approaches are acceptable as solutions to the measurement problem.Wallace's arguments about the difficulties of extending approaches which are not unitary-only to QFT are quite compelling, but on the other hand the Everett interpretation and the other extant unitary-only interpretations have a number of serious epistemic problems which arguably have not yet been satisfactorily resolved (see refs [2,3]), and thus we are faced with a dilemma: if neither of these obstacles can be overcome then it would seem that at present we have no viable solution to the measurement problem at all! Or at least, none of the well-studied, mainstream interpretations or modificatory strategies will suffice -and we suspect that many less well-known proposals would also be difficult to extend to non-relativistic quantum mechanics, or would face the same epistemic problems as the unitary-only interpretations. We therefore consider that it remains an urgent outstanding problem to find a viable solution to the measurement problem which can be extended to relativistic quantum mechanics and QFT.In this article we seek to understand in general terms what such a thing might look like. We argue that in order to avoid serious epistemic problems, the solution must be a single-world realist approach. We also argue that any singleworld realist solution which is able to reproduce the predictions of relativistic quantum mechanics will probably have the property that observable reality does not supervene on dynamical, precisely-defined microscopic beables. Thus we suggest three possible routes for further exploration: observable reality could be approximate and emergent, as in relational quantum mechanics (RQM) with the addition of cross-perspective links, or observable reality could supervene on beables which are not microscopically defined, as in the consistent histories approach, or observable reality could supervene on beables which are not dynamical, as in Kent's solution to the Lorentzian classical reality problem.We conclude that once all of these issues are taken into account, the options for a viable interpretation or modificatory strategy for quantum mechanics are significantly narrowed down. In light of this fact we have renewed optimism that it might eventually be possible to arrive at a definitive solution to the measurement problem, although the remaining options ...

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Non-locality and quasiclassical reality in Kent’s formulation of relativistic quantum theory

Cited by 5 publications

References 18 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

Do We Have Any Viable Solution to the Measurement Problem?

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