Information content and minimum-length metric: A drop of light

Pesci, A.

doi:10.1007/s10714-022-02960-1

Gen Relativ Gravit

2022

DOI: 10.1007/s10714-022-02960-1

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Information content and minimum-length metric: A drop of light

A. Pesci

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Cited by 3 publications

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“…In his later years, Paddy was studying various attempts to incorporate a zero point length in the spacetime metric, making geometrical quantities non-local and then studying its consequences on various aspects of gravity. The review article by Alessandro Pesci [22] summarizes the recent developments in this direction and also adds new ingredients into this field of research. It turns out that such a non-local description of the gravitational interaction at the large scale yields, not the Ricci scalar, but the Ricci tensor contracted with appropriate null vectors-related to the heat content of the null surfaces foliating the spacetime-as the action for gravity.…”

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confidence: 99%

Topical collection: In memory of Professor T Padmanabhan

et al. 2022

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Professor Thanu Padmanabhan contributed significantly to a broad spectrum of topics in astrophysics, cosmology, and classical and quantum aspects of gravitation. In his memory, the Editorial Board of General Relativity and Gravitation invited us to edit a Topical Collection "In Memory of Professor T Padmanabhan". This collection gives a snapshot of ongoing research in the subjects he worked on.Professor Thanu Padmanabhan (affectionately known as Paddy) was an internationally acclaimed Indian Theoretical Physicist and Cosmologist, who passed away on 17 September 2021. He was a guiding light for all his students and younger colleagues who interacted with him [1]. We had the good fortune of discussing various aspects of physics with Paddy on several occasions. The Editors of General Relativity and Gravitation (GRG) invited us to organise a Topical Collection "In Memory of Professor T Padmanabhan". We have put together this volume in his fond memory and invited contributions in subjects Paddy had worked on.

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Topical collection: In memory of Professor T Padmanabhan

et al. 2022

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Relics of the quantum spacetime: from Synge’s world function as the fundamental probe of spacetime architecture to the emergent description of gravity

Kothawala

2023

J. Phys.: Conf. Ser.

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All our observations that characterise space and time are expressed in terms of non-local, bi-tensorial objects such as geodesic intervals between events and two-point (Green) functions. In this contribution, I highlight the importance of characterising spacetime geome-try in terms of such non-local objects, focusing particularly on two important bi-tensors that play a particular fundamental role – Synge’s World function and the van Vleck determinant. I will first discuss how these bi-tensors help capture information about spacetime geometry, and then describe their role in characterising quantum spacetime endowed with a lower bound, say ℓ 0, on spacetime intervals. Incorporating such a length scale in a Lorentz covariant manner necessitates a description of spacetime geometry in terms of above bi-tensors, and naturally replaces the conventional description based on the metric tensor gab (x) with a description in terms of a non-local bi-tensor qab (x, y). The non-analytic structure of qab (x, y) which renders a perturbative expansion in ℓ 0 meaningless, also generically leaves a non-trivial “relic” in the limit ℓ 0 → 0. I present some results where such a relic term is manifest; specifically, I will discuss how this: (i) suggests a description of gravitational dynamics different from the one based on Einstein-Hilbert lagrangian, (ii) implies dimensional reduction to 2 at small scales, (iii) connects with the notion of cosmological constant itself being a non-local vestige of the small scale structure of spacetime, (iv) helps address the issues of spacetime singularities. I will conclude by discussing the ramifications of these ideas for quantum gravity.

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Limits of a non-local quantum spacetime

Kothawala

2023

Int. J. Mod. Phys. D

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A generic implication of incorporating gravitational effects in the analysis of quantum measurements is the existence of a zero-point length of spacetime. This requires an inherently non-local description of spacetime, beyond the usual one based on metric [Formula: see text] etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form [Formula: see text]. A deeper look then reveals a subtle interplay between non-locality and the limit [Formula: see text]. In particular, the so-called emergent gravity paradigm — in which gravitational dynamics/action/spacetime are emergent and characterized by an entropy functional — arises as the Cheshire grin of a fundamentally non-local quantum spacetime. This paper describes the flow of metric with respect to Planck length, and proposes a novel action for the same.

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Information content and minimum-length metric: A drop of light

Cited by 3 publications

References 105 publications

Topical collection: In memory of Professor T Padmanabhan

Topical collection: In memory of Professor T Padmanabhan

Relics of the quantum spacetime: from Synge’s world function as the fundamental probe of spacetime architecture to the emergent description of gravity

Limits of a non-local quantum spacetime

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