ORCID Profile
0000-0001-9022-8655
Current Organisations
University of Oxford
,
Imperial College London
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Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Date: 22-08-2023
DOI: 10.22331/Q-2023-08-22-1088
Abstract: Given the importance of quantum reference frames (QRFs) to both quantum and gravitational physics, it is pertinent to develop a systematic method for switching between the descriptions of physics relative to different choices of QRFs, which is valid in both fields. Here we continue with such a unifying approach, begun in [Quantum 4, 225 (2020)], whose key ingredient is a symmetry principle, which enforces physics to be relational. Thanks to gauge related redundancies, this leads to a perspective-neutral structure which contains all frame choices at once and via which frame perspectives can be consistently switched. Formulated in the language of constrained systems, the perspective-neutral structure is the constraint surface classically and the gauge invariant Hilbert space in the Dirac quantized theory. By contrast, a perspective relative to a specific frame corresponds to a gauge choice and the associated reduced phase and Hilbert space. QRF changes thus amount to a gauge transformation. We show that they take the form of `quantum coordinate changes'. We illustrate this in a general mechanical model, namely the relational N -body problem in 3D space with rotational and translational symmetry. This model is especially interesting because it features the Gribov problem so that globally valid gauge fixing conditions, and hence relational frame perspectives, are absent. The constraint surface is topologically non-trivial and foliated by 3-, 5- and 6-dimensional gauge orbits, where the lower dimensional orbits are a set of measure zero. The N -body problem also does not admit globally valid canonically conjugate pairs of Dirac observables. These challenges notwithstanding, we exhibit how one can construct the QRF transformations for the 3-body problem. Our construction also sheds new light on the generic inequivalence of Dirac and reduced quantization through its interplay with QRF perspectives.
Publisher: IOP Publishing
Date: 12-2020
Abstract: Every clock is a physical system and thereby ultimately quantum. A naturally arising question is thus how to describe time evolution relative to quantum clocks and, specifically, how the dynamics relative to different quantum clocks are related. This is a particularly pressing issue in view of the multiple choice facet of the problem of time in quantum gravity, which posits that there is no distinguished choice of internal clock in generic general relativistic systems and that different choices lead to inequivalent quantum theories. Exploiting a recent unifying approach to switching quantum reference systems [Vanrietvelde et al 2020 Quantum 4 225 Vanrietvelde et al 2018 arXiv:1809.05093[quant-ph])], we exhibit a systematic method for switching between different clock choices in the quantum theory. We illustrate it by means of the parametrized particle, which, like gravity, features a Hamiltonian constraint. We explicitly switch between the quantum evolution relative to the non-relativistic time variable and that relative to the particle’s position, which requires carefully regularizing the zero-modes in the so-called time-of-arrival observable. While this toy model is simple, our approach is general and, in particular, directly amenable to quantum cosmology. It proceeds by systematically linking the reduced quantum theories relative to different clock choices via the clock-choice-neutral Dirac quantized theory, in analogy to coordinate changes on a manifold. This method suggests a new perspective on the multiple choice problem, indicating that it is rather a multiple choice feature of the complete relational quantum theory, taken as the conjunction of Dirac quantized and quantum deparametrized theories. Precisely this conjunction permits one to consistently switch between different temporal reference systems, which is a prerequisite for a quantum notion of general covariance. Finally, we show that quantum uncertainties generically lead to a discontinuity in the relational dynamics when switching clocks, in contrast to the classical case.
Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Date: 27-01-2020
DOI: 10.22331/Q-2020-01-27-225
Abstract: Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics relative to quantum reference systems and how the descriptions relative to different such choices are related. Here, we exploit a fruitful interplay of ideas from both fields to begin developing a unifying approach to transformations among quantum reference systems that ultimately aims at encompassing both quantum and gravitational physics. In particular, using a gravity inspired symmetry principle, which enforces physical observables to be relational and leads to an inherent redundancy in the description, we develop a perspective-neutral structure, which contains all frame perspectives at once and via which they are changed. We show that taking the perspective of a specific frame amounts to a fixing of the symmetry related redundancies in both the classical and quantum theory and that changing perspective corresponds to a symmetry transformation. We implement this using the language of constrained systems, which naturally encodes symmetries. Within a simple one-dimensional model, we recover some of the quantum frame transformations of \\cite{Giacomini:2017zju}, embedding them in a perspective-neutral framework. Using them, we illustrate how entanglement and classicality of an observed system depend on the quantum frame perspective. Our operational language also inspires a new interpretation of Dirac and reduced quantized theories within our model as perspective-neutral and perspectival quantum theories, respectively, and reveals the explicit link between them. In this light, we suggest a new take on the relation between a `quantum general covariance' and the diffeomorphism symmetry in quantum gravity.
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Augustin Vanrietvelde.