On the Conceptual Issues Surrounding the Notion of Relational Bohmian Dynamics

Vassallo, Antonio; Ip, Pui Him

doi:10.1007/s10701-016-9992-z

Cited by 12 publications

(6 citation statements)

References 55 publications

(44 reference statements)

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“…In this regard, it may be useful to focus on a particular quantum theory that shares with PSD the fundamental role accorded to instantaneous spatial configurations. The most promising candidate to this role is the de Broglie-Bohm theory, which has been recently shown to be amenable to the quotienting out procedure discussed in §1 (Vassallo and Ip, 2016;Dürr et al, 2020). Nonetheless, the details of this construction still require much work-as does the extension to quantum field theory-and will be the subject of our future investigations.…”

Section: Discussionmentioning

confidence: 99%

Pure shape dynamics: General framework

Koslowski¹,

Naranjo²,

Vassallo³

2021

Preprint

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We put forward a general framework for describing relational physical theories. This framework-which we call Pure Shape Dynamics (PSD)-represents a conceptual evolution of the original insights brought about by the Shape Dynamics programme. PSD's novel take on relationalism is its insistence on describing any dynamical system by means of the intrinsic geometry of its associated curve on the suitable relational configuration space of the theory, namely shape space, whereby the corresponding equation of state of the curve expresses the ratio of change of its geometric degrees of freedom. The mathematical structure underlying the equation of state is the suitable action of a local section in some unit tangent bundle over a natural generalisation of yet another unit tangent bundle, which we call shape phase space.

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Section: Discussionmentioning

confidence: 99%

Pure shape dynamics: General framework

Koslowski¹,

Naranjo²,

Vassallo³

2021

Preprint

Self Cite

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“…where ∆ B and ∇ B are, respectively, the Laplace-Beltrami operator and the gradient on the configuration space equipped with respect to the Riemannian metric (4). This is all there is to say about the formulation of Bohmian mechanics on shape space (this should perhaps be contrasted with more involved approaches as in, e.g., [21]).…”

Section: Bohmian Motion On Shape Spacementioning

confidence: 99%

Quantum Motion on Shape Space and the Gauge Dependent Emergence of Dynamics and Probability in Absolute Space and Time

Dürr

Zanghı̀

2019

J Stat Phys

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Relational formulations of classical mechanics and gravity have been developed by Julian Barbour and collaborators. Crucial to these formulations is the notion of shape space. We indicate here that the metric structure of shape space allows one to straightforwardly define a quantum motion, a Bohmian mechanics, on shape space. We show how this motion gives rise to the more or less familiar theory in absolute space and time. We find that free motion on shape space, when lifted to configuration space, becomes an interacting theory. Many different lifts are possible corresponding in fact to different choices of gauges. Taking the laws of Bohmian mechanics on shape space as physically fundamental, we show how the theory can be statistically analyzed by using conditional wave functions, for subsystems of the universe, represented in terms of absolute space and time. CONTENTS

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“…The geometry and the time with its metric can be conceived as a mere means to represent the particle configuration and its change, that is, the change in the relative distances of the particles (see Esfeld and Deckert (2017, ch. 3.2) for the philosophical argument and Vassallo and Ip (2016) for a relationalist formulation of BM). Consequently, the particles are individuals that are absolutely discernible by their position in a configuration.…”

Section: Typicality Measurementioning

confidence: 99%

Individuality and the Account of Nonlocality: The Case for the Particle Ontology in Quantum Physics

Esfeld¹

2019

Quantum Worlds

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For Olimpia Lombardi (ed.), Quantum worlds: identity, indistinguishability and non-locality in quantum physics, Cambridge University Press, forthcomingThe paper explains why an ontology of permanent point particles that are individuated by their relative positions and that move on continuous trajectories as given by a deterministic law of motion constitutes the best solution to the measurement problem in both quantum mechanics and quantum field theory. This case is made by comparing the Bohmian theory to collapse theories such as the GRW matter density and the GRW flash theory. It is argued that the Bohmian theory makes the minimal changes, concerning only the dynamics and neither the ontology nor the account of probabilities, that are necessary to get from classical mechanics to quantum physics. There is no cogent reason to go beyond these minimal changes. 1 1 The measurement problem 2 2 The collapse solution and its ontology 6 3 The particle solution and its dynamics 11 4 Permanent particles in quantum field theory 20

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On the Conceptual Issues Surrounding the Notion of Relational Bohmian Dynamics

Cited by 12 publications

References 55 publications

Pure shape dynamics: General framework

Pure shape dynamics: General framework

Quantum Motion on Shape Space and the Gauge Dependent Emergence of Dynamics and Probability in Absolute Space and Time

Individuality and the Account of Nonlocality: The Case for the Particle Ontology in Quantum Physics

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