Towards spectral geometry for causal sets

Yazdi, Yasaman K.; Kempf, Achim

doi:10.1088/1361-6382/aa663f

Cited by 7 publications

(12 citation statements)

References 63 publications

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“…An interesting direction that has been explored by Yazdi and Kempf (2017) is to use the spectral information of the d'Alembertian operator to obtain all the information about the causal set. This was explored for A 2 [p, q] ⊂ M 2 and it was shown that the spectrum of the d'Alembertian (or Feynman propagator) gives the link matrix (see Eq.…”

Section: The D'alembertian For a Scalar Fieldmentioning

confidence: 99%

The causal set approach to quantum gravity

2019

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The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or "causal sets". The partial order on a causal set represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity.In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.

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Section: The D'alembertian For a Scalar Fieldmentioning

confidence: 99%

The causal set approach to quantum gravity

2019

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“…And to know infinitesimal invariant distances, in this case by means of the propagator, is to know the metric. In further work, 53 , it has been shown that also within the framework of causal set theory, the propagator carries the complete information about the discretized spacetime, i.e., any causal set can be re-constructed from knowledge of a propagator. This confirms that a propagator on causal sets does not only contain the information about the light cone structure of the spacetime but that it does also contain the information about the spacetime's conformal factor, which is information that in the case of causal sets is normally encoded in the density of the sprinkled events.…”

Section: The Metric Can Be Deduced From Knowledge Of the Correlator O...mentioning

confidence: 99%

Quantum Gravity, Information Theory and the CMB

Kempf¹

2018

Found Phys

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We review connections between the metric of spacetime and the quantum fluctuations of fields. In particular, we discuss the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlators of the fluctuations of quantum fields. We also discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization would, therefore, have the benefit of not requiring the modding out of the diffeomorphism group. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background (CMB) that may become observable.

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“…This requires inverse spectral geometry and can determine the geometry down to a cut-off scale determined by the sampling density. Unfortunately, the situation with Lorentzian signature spacetimes is technically intricate and most work has focused thus far on Euclidean signature geometries (but see [47]). This could, nevertheless, be useful for probing spatial geometries through field correlations in a canonical picture of general relativity.…”

Section: Classical Spacetime From Quantum Correlationsmentioning

confidence: 99%

Reflections on the information paradigm in quantum and gravitational physics

Hoehn

2017

J. Phys.: Conf. Ser.

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Abstract. We reflect on the information paradigm in quantum and gravitational physics and on how it may assist us in approaching quantum gravity. We begin by arguing, using a reconstruction of its formalism, that quantum theory can be regarded as a universal framework governing an observer's acquisition of information from physical systems taken as information carriers. We continue by observing that the structure of spacetime is encoded in the communication relations among observers and more generally the information flow in spacetime. Combining these insights with an information-theoretic Machian view, we argue that the quantum architecture of spacetime can operationally be viewed as a locally finite network of degrees of freedom exchanging information. An advantage -and simultaneous limitation -of an informational perspective is its quasi-universality, i.e. quasi-independence of the precise physical incarnation of the underlying degrees of freedom. This suggests to exploit these informational insights to develop a largely microphysics independent top-down approach to quantum gravity to complement extant bottom-up approaches by closing the scale gap between the unknown Planck scale physics and the familiar physics of quantum (field) theory and general relativity systematically from two sides. While some ideas have been pronounced before in similar guise and others are speculative, the way they are strung together and justified is new and supports approaches attempting to derive emergent spacetime structures from correlations of quantum degrees of freedom. IntroductionThe basic discipline underlying the current information age, namely information theory, is not a physical theory (in contrast to thermodynamics ruling the age of steam engines). Nevertheless, the information paradigm is now also permeating (at least part of) physics, offering novel perspectives on old and new problems, specifically in quantum and gravitational physics, and thereby attaining direct physical relevance. After all, physics without information is not possible; a description of the world requires to gather information about it. The information paradigm in physics is by construction very operational. From an information-theoretic perspective, physical systems are information carriers which can be used to acquire, store and communicate information. This perspective is practically realised in the field of quantum information which takes quantum systems to perform all sorts of information-theoretic tasks with them.Here we are less interested in practical applications within the limits of quantum information; rather, we wish to ask how far the information paradigm, and specifically the picture of physical systems as information carriers, can possibly lead us in understanding the physical content of quantum theory and general relativity from a new angle and what it may suggest for the construction of a new physical theory incorporating both. So the questions we will ask (and partially address) are much more basic than typically investigated in...

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Towards spectral geometry for causal sets

Cited by 7 publications

References 63 publications

The causal set approach to quantum gravity

The causal set approach to quantum gravity

Quantum Gravity, Information Theory and the CMB

Reflections on the information paradigm in quantum and gravitational physics

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