Quantum superpositions of Minkowski spacetime

Foo, Joshua; Senem, Arabaci, Cemile; Zych, Magdalena; Mann, Robert B.

doi:10.48550/arxiv.2208.12083

Cited by 3 publications

(4 citation statements)

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“…The fluctuations in the spacetime geometry lead to fluctuations in the gauge invariant distance between any two physical events as exemplified by the above gedanken experiment. One diagnostic that defines the resulting quantum geometry which shall be used throughout this paper, is the squared distance operator 6 between two locations, d 2 (x, y) which is well defined at least locally for x and y sufficiently close 7 . Its expectation value on each coherent state |ψ i ⟩ is just the geodesic distance between x and y on the corresponding classical geometry.…”

Section: Introductionmentioning

confidence: 99%

“…6 The Euclidean-signature version of this operator was studied in [8]. 7 The squared distance operator is (up to a factor) the same as Synge's world function σ(x, y) = d 2 (x, y)/2 which plays a central role in his remarkable treatise on General Relativity [9] and is a crucial ingredient in the Hadamard construction of Greens functions on curved spacetime [10,11].…”

Section: Introductionmentioning

confidence: 99%

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Subadditive average distances and quantum promptness

Piazza

Tolley

2023

Class. Quantum Grav.

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A central property of a classical geometry is that the geodesic distance between two events is additive. When considering quantum fluctuations in the metric or a quantum or statistical superposition of different spacetimes, additivity is generically lost at the level of expectation values. In the presence of a superposition of metrics, distances can be made diffeomorphism invariant by considering the frame of a family of free-falling observers or a pressureless fluid, provided we work at sufficiently low energies. We propose to use the average squared distance between two events 〈d^2(x,y)〉 as a proxy for understanding the effective quantum (or statistical) geometry and the emergent causal relations among such observers. At each point, the average squared distance 〈d^2(x,y)〉defines an average metric tensor. However, due to non-additivity, 〈d^2(x,y)〉 is not the (squared) geodesic distance associated with it. We show that departures from additivity can be conveniently captured by a bi-local quantity C(x, y). Violations of additivity build up with the mutual separation between x and y and can correspond to C< 0 (subadditive) or C > 0 (superadditive). We show that average Euclidean distances are always subadditive: they satisfy the triangle inequality but generally fail to saturate it. In Lorentzian signature there is no definite result about the sign of C, most physical examples give C < 0 but there exist counterexamples. The causality induced by subadditive Lorentzian distances is unorthodox but not pathological. Superadditivity violates the transitivity of causal relations. On these bases, we argue that subadditive distances are the expected outcome of dynamical evolution, if relatively generic physical initial conditions are considered.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Subadditive average distances and quantum promptness

Piazza

Tolley

2023

Class. Quantum Grav.

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“…They proved that any system (for example, a field), mediating entanglement between two quantum systems ought to be quantum. Foo et al [4] investigated the quantum superposition of different spacetimes not related by a global coordinate transformation -the so-called "spacetime superpositions". Their purpose was to study the effects induced on quantum matter residing within such spacetimes.…”

Section: Introductionmentioning

confidence: 99%

Gravity and the Superposition Principle

Culetu

2023

Int J Theor Phys

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The relation between gravity and quantum mechanics is investigated in this work. The link is given by the wave packet expansion process, rooted from the Uncertainty Principle. The basic idea is to express the de Broglie wavelength used by Schrodinger for a massive particle in terms of the associated Compton wavelength which is replaced by the Michell-Laplace radius Gm/c 2 of the spherical object of mass m ≥ mP , where mP is the Planck mass.The wave packet spreading is studying in spherical coordinates, having the width σ(t), expressed in terms of G and c instead of . Therefore, for masses larger than the Planck mass, a faster dispersion rate of σ(t) is obtained, compared to the standard case. The dispersion of the wave packet is observed only by a free falling observer and the process breaks down once the observer hits the surface of the object. Different freely falling observers notice different rates of expansion of the wave packet and the source of gravity is in a quantum superposition. We further confront the Mita formula for the mean energy of the wave packet with the de Broglie-Bohm quantum potential energy when the Schrodinger equation is expressed in the Madelung form.

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“…Recently, the phenomenon of black hole mass superposition has been studied in the context of spacetime superpositions [20,21]. Examples include quantum superpositions of Minkowski spacetime [22] and the signatures of rotating black holes in quantum superpositions [23]. Researchers are also attempting to apply these concepts to analog black holes [24,25], building on earlier work [26][27][28][29], and testing quantum effects in gravity through tabletop experiments [30][31][32].…”

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confidence: 99%

Core Content Selection and Textbook Design for High School Mathematics

Zhang¹,

Zhou²,

Wang³

et al. 2021

School Mathematics Textbooks in China

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This paper is devoted to studying the following fractional L 2 -critical nonlinear Schrödinger equation≥ 0 is an external potential. We obtain normalized L 2 -norm solutions of the above equation by solving the associated constraint minimization problem (1.4). It shows that there is a threshold a * > 0 such that (1.4) has minimizers for 0 < a < a * , and minimizers do not exist for any a > a * . For the case of a = a * , it gives a fact that the existence and non-existence of minimizers depend strongly on the value of V (0). Especially for V (0) = 0, we prove that minimizers occur blow-up behavior and the mass of minimizers concentrates at the origin as a ր a * . Applying implicit function theorem, the uniqueness of minimizers is also proved for a > 0 small enough.

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Quantum superpositions of Minkowski spacetime

Cited by 3 publications

References 0 publications

Subadditive average distances and quantum promptness

Subadditive average distances and quantum promptness

Gravity and the Superposition Principle

Core Content Selection and Textbook Design for High School Mathematics

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