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

Dürr, Detlef; Zanghı̀, Nino

doi:10.1007/s10955-019-02362-9

Cited by 19 publications

(35 citation statements)

References 21 publications

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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

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“…22 Where metaphysical anti-realists are critical of metaphysical questions -for instance describing them as "devoid of cognitive content" (Carnap, 1950, 28) -naturalized 20 Notice that this does not entail that the non-spatial theories of quantum gravity considered by Lam and Wüthrich take priority over other theories of quantum gravity that are more hospitable to fundamental spatial relations (e.g. Goldstein & Teufel 2001;Dürr et al, 2018). Thus, while metaphysicians, on their view, should end their criticism of the non-spatial theories, metaphysicians are of course welcome to spend their time on the metaphysical implications of other theories of quantum gravity.…”

Section: Naturalized Metaphysics and Metaphysical Questionsmentioning

confidence: 99%

An apology for conflicts between metaphysics and science in naturalized metaphysics

Jaksland

2021

Euro Jnl Phil Sci

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According to naturalized metaphysics, metaphysics should be informed by our current best science and not rely on a priori reasoning. Consequently, naturalized metaphysics tends to dismiss metaphysicians’ attempts to quarrel with science. This paper argues that naturalized metaphysics should instead welcome such conflicts between metaphysics and science. Naturalized metaphysics is not (and should not be) eliminative of metaphysics. So, if such conflicts are driven by the immediate absence in science of an answer to a metaphysical question, then the conflict should not be dismissed, but instead be received as an occasion to do (more) naturalized metaphysics. That conflicts between metaphysics and science might be beneficial for naturalized metaphysics is exemplified by the case of non-spatial theories of quantum gravity. These theories are criticized by metaphysicians who, often following David Lewis, argue that spatial distance is an indispensable fundamental element in any coherent metaphysics due to its role as the world-making relation. The resulting conflict, however, is found to be well-motivated since the non-spatial theories of quantum gravity offer no alternative world-making relation to spatial distance. Rather than dismissing this conflict, naturalized metaphysics should therefore receive the Lewisians’ resistance as a call to search for one. How this plays out as a negotiation between the scientific theory and the metaphysical question is exemplified in the last part of the paper where entanglement is proposed as an alternative world-making relation in loop quantum gravity.

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“…It corresponds to a particular choice of absolute spatio-temporal reference frame ("gauge") in the shape space theory; cf. Dürr et al (2018). L = 0 is then the only canonical choice, and the only one suggested by Machian principles.…”

Section: Gravity and Typicality From A Relational Point Of Viewmentioning

confidence: 99%

“…Dürr, Goldstein, and Zanghì (2018) provide an insightful discussion of typicality measures on shape space, though focussing on the quantum case.…”

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confidence: 99%

Arrow(s) of Time without a Past Hypothesis

Lazarovici¹,

Reichert

2020

Statistical Mechanics and Scientific Explanation

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The paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a Past Hypothesis, i.e. the assumption of a special (low-entropy) initial state of the universe. After discussing the role of the Past Hypothesis and the controversy about its status, we explain why Carroll's model -which establishes an arrow of time as typical -can ground sensible predictions and retrodictions without assuming something akin to a Past Hypothesis. We then propose a definition of a Boltzmann entropy for a classical N -particle system with gravity, suggesting that a Newtonian gravitating universe might provide a relevant example of Carroll's entropy model. This invites comparison with the work of Barbour, Koslowski, and Mercati that identifies typical arrows of time in a relational formulation of classical gravity on shape space. We clarify the difference between this gravitational arrow in terms of shape complexity and the entropic arrow in absolute spacetime, and work out the key advantages of the relationalist theory. We end by pointing out why the entropy concept relies on absolute scales and is thus not relational.

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

Cited by 19 publications

References 21 publications

Pure shape dynamics: General framework

Pure shape dynamics: General framework

An apology for conflicts between metaphysics and science in naturalized metaphysics

Arrow(s) of Time without a Past Hypothesis

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