# Weekly Papers on Quantum Foundations (6)

Approaches to causality and multi-agent paradoxes in non-classical theories. (arXiv:2102.02393v1 [quant-ph])

This thesis reports progress in the analysis of causality and multi-agent logical paradoxes in quantum and post-quantum theories. These research areas are highly relevant for the foundations of physics as well as the development of quantum technologies. In the first part, focussing on causality, we develop techniques for using generalised entropies to analyse distinctions between classical and non-classical causal structures. We derive new properties of Tsallis entropies of systems that follow from the relevant causal structure, and apply these to obtain new necessary constraints for classicality in the Triangle causal structure. Supplementing the method with the post-selection technique, we provide evidence that Shannon and Tsallis entropic constraints are insufficient for detecting non-classicality in Bell scenarios with non-binary outcomes. This points to the need for better methods of characterising correlations in non-classical causal structures. Further, we investigate the relationships between causality and space-time by developing a framework for modelling cyclic and fine-tuned influences in non-classical theories. We derive necessary and sufficient conditions for such causal models to be compatible with a space-time structure and for ruling out operationally detectable causal loops. In particular, this provides an operational framework for analysing post-quantum theories admitting jamming non-local correlations. In the second part, we investigate multi-agent logical paradoxes such as the Frauchiger-Renner paradox and develop a framework for analysing such paradoxes in arbitrary physical theories. Applying this to box world, a post-quantum theory, we derive a stronger paradox that does not rely on post-selection. Our results reveal that reversible evolution of agents’ memories is not necessary for deriving multi-agent paradoxes, and that certain forms of contextuality might be.

The outcomes of measurements in the de Broglie-Bohm theory. (arXiv:2102.02519v1 [quant-ph])

Within the de Broglie-Bohm (dBB) theory, the measurement process is usually discussed only in terms of the effect of the Bohmian positions of the measured system S, while the effects of the Bohmian positions associated with the measurements apparatus M are ignored. This article shows that the latter variables actually play an essential role in the determination of the result. Indeed, in many cases, the result of measurement is practically independent of the initial value of a Bohmian position associated with S, and determined only by those of M. The measurement then does not reveal the value of any pre-existing variable attached to S, but just the initial state of the measurement apparatus. Quantum contextuality then appears with particular clarity as a consequence of the dBB dynamics for entangled systems.

Times of Arrival and Gauge Invariance. (arXiv:2102.02661v1 [quant-ph])

We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz., the Aharonov-Bohm and Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski’s result is pointed out, along with an inescapable consequence of the “negative arrival times” inherent to this proposal (and generalizations thereof). The ABK free-particle restriction is lifted in a discussion of an explicit arrival-time setup featuring a charged particle moving in a constant magnetic field. A natural generalization of the ABK distribution is in this case shown to be critically gauge-dependent. A direct comparison to the QF distribution, which does not exhibit this flaw, is drawn (its acknowledged drawback concerning the quantum backflow effect notwithstanding).

The equivalence of local-realistic and no-signalling theories. (arXiv:1710.01380v2 [quant-ph] UPDATED)

We provide a framework that describe all local-realistic theories and all no-signalling theories. We show that every local-realistic theory is a no-signalling theory. We also show that every no-signalling theory with invertible dynamics has a local-realistic model. This applies in particular to unitary quantum theory.

Local description of the Aharonov-Bohm effect with a quantum electromagnetic field. (arXiv:1910.10650v4 [quant-ph] UPDATED)

In the seminal works from Santos and Gozalo [Europhys. Lett. $\mathbf{45}$, 418 (1999)] and Marletto and Vedral [Phys. Rev. Lett. $\mathbf{125}$, 040401 (2020)], it is shown how the Aharonov-Bohm effect can be described as the result of an exchange of virtual photons between the solenoid and the quantum charged particle along its propagation through the interferometer, where both the particle and the solenoid interact locally with the quantum electromagnetic field. This interaction results in a local and gauge-independent phase generation for the particle propagation in each path of the interferometer. Here we improve the cited treatments by using the quantum electrodynamics formalism in the Lorentz gauge, with a manifestly gauge-independent Hamiltonian for the interaction and the presence of virtual longitudinal photons. Only with this more complete and gauge-independent treatment it is possible to justify the acquired phases for interferometers with arbitrary geometries, and this is an advantage of our treatment. We also extend the results to the electric version of the Aharonov-Bohm effect. Finally, we propose an experiment that could test the locality of the Aharonov-Bohm phase generation.

Quantum Counterpart of Classical Equipartition of Energy. (arXiv:1911.06570v3 [quant-ph] UPDATED)

It is shown that the recently proposed quantum analogue of classical energy equipartition theorem for two paradigmatic, exactly solved models (i.e., a free Brownian particle and a dissipative harmonic oscillator) also holds true for all quantum systems which are composed of an arbitrary number of non-interacting or interacting particles, subjected to any confining potentials and coupled to thermostat with arbitrary coupling strength.

A time-symmetric formulation of quantum entanglement. (arXiv:2003.07183v3 [quant-ph] UPDATED)

I numerically simulate and compare the entanglement of two quanta using the conventional formulation of quantum mechanics and a time-symmetric formulation that has no collapse postulate. The experimental predictions of the two formulations are identical, but the entanglement predictions are significantly different. The time-symmetric formulation reveals an experimentally testable discrepancy in the original quantum analysis of the Hanbury Brown-Twiss experiment, suggests solutions to some parts of the nonlocality and measurement problems, fixes known time asymmetries in the conventional formulation, and answers Bell’s question “How do you convert an ‘and’ into an ‘or’?'”

Time-travelling billiard ball clocks: a quantum model. (arXiv:2007.12677v2 [quant-ph] UPDATED)

General relativity predicts the existence of closed timelike curves (CTCs), along which an object could travel to its own past. A consequence of CTCs is the failure of determinism, even for classical systems: one initial condition can result in multiple evolutions. Here we introduce a new quantum formulation of a classic example, where a billiard ball can travel along two possible trajectories: one unperturbed and one, along a CTC, where it collides with its past self. Our model includes a vacuum state, allowing the ball to be present or absent on each trajectory, and a clock, which provides an operational way to distinguish the trajectories. We apply the two foremost quantum theories of CTCs to our model: Deutsch’s model (D-CTCs) and post-selected teleportation (P-CTCs). We find that D-CTCs reproduce the classical solution multiplicity in the form of a mixed state, while P-CTCs predict an equal superposition of the two trajectories, supporting a conjecture by Friedman et al. [Phys. Rev. D 42, 1915 (1990)].

Schr\”odinger’s Cat. (arXiv:2102.01808v2 [quant-ph] UPDATED)

The basic idea here is that observation (or one’s experience) is fundamental and the `atomic world’ is postulated as the source of such observation. Once this source has been inferred to exist one may attempt to explicitly derive its structure in such a way that the observation itself can be reproduced. And so here is a purely quantum mechanical model of observation coupled to its supposed source, and the observation itself is realised as a projection of this quantum system.

Lapsing Quickly into Fatalism: Bell on Backward Causation. (arXiv:2102.02392v1 [quant-ph])

Authors: Travis NorsenHuw Price

This is a dialogue between Huw Price and Travis Norsen, loosely inspired by a letter that Price received from J. S. Bell in 1988. The main topic of discussion is Bell’s views about retrocausal approaches to quantum theory, and their relevance to contemporary issues.

Why Do You Think It is a Black Hole?. (arXiv:2102.02592v1 [physics.hist-ph])

Authors: Galina Weinstein

This paper analyzes the experiment presented in 2019 by the Event Horizon Telescope (EHT) Collaboration that revealed the first image of the supermassive black hole at the center of galaxy M87. The very first question asked by the EHT Collaboration is: What is the compact object at the center of galaxy M87? Does it have a horizon? Is it a Kerr black hole? In order to answer these questions, the EHT Collaboration first endorses the working hypothesis that the central object is a black hole described by the Kerr metric, i.e. a spinning Kerr black hole as predicted by classical general relativity. They choose this hypothesis based on previous research and observations of the galaxy M87. After having adopted the Kerr black hole hypothesis, the EHT Collaboration proceeds to test it. They confront this hypothesis with the data collected in the 2017 EHT experiment. They then compare the Kerr rotating black hole hypothesis with alternative explanations and finally find that their hypothesis is consistent with the data. In this paper I describe the complex methods used to test the spinning Kerr black hole hypothesis. I conclude this paper with a discussion of the implications of the findings presented here with respect to Hawking radiation.

Reconstructing the graviton. (arXiv:2102.02217v1 [hep-th])

We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity of asymptotically safe quantum gravity.

Testing No-Hair Theorem by Quasi-Periodic Oscillations: the quadrupole of GRO J1655$-$40. (arXiv:2102.02232v1 [gr-qc])

Authors: Alireza AllahyariLijing Shao

We perform an observational test of no-hair theorem using quasi-periodic oscillations within the relativistic precession model. Two well motivated metrics we apply are Kerr-Q and Hartle-Thorne metrics in which the quadrupole is the parameter that possibly encodes deviations from the Kerr black hole. The expressions for the quasi-periodic frequencies are derived before comparing the models with the observation. We encounter a degeneracy in constraining spin and quadrupole parameters that makes it difficult to measure their values. In particular, we here propose a novel test of no-hair theorem by adapting the Hartle-Thorne metric. It turns out that a Kerr black hole is a good description of the central object in GRO J1655$-$40 given the present observational precisions.

Probing Hawking radiation through capacity of entanglement. (arXiv:2102.02425v1 [hep-th])

We consider the capacity of entanglement in models related with the gravitational phase transitions. The capacity is labeled by the replica parameter which plays a similar role to the inverse temperature in thermodynamics. In the end of the world brane model of a radiating black hole the capacity has a peak around the Page time indicating the phase transition between replica wormhole geometries of different types of topology. Similarly, in a moving mirror model describing Hawking radiation the capacity typically shows a discontinuity when the dominant saddle switches between two phases, which can be seen as a formation of island regions. In either case we find the capacity can be an invaluable diagnostic for a black hole evaporation process.

Analogue Hawking temperature of a laser-driven plasma. (arXiv:2102.02556v1 [gr-qc])

Authors: C. FiedlerD.A. Burton

We present a method for exploring analogue Hawking radiation using a laser pulse propagating through an underdense plasma. The propagating fields in the Hawking effect are local perturbations of the plasma density and laser amplitude. We derive the dependence of the resulting Hawking temperature on the dimensionless amplitude of the laser and the behaviour of the spot area of the laser at the analogue event horizon. We demonstrate one possible way of obtaining the analogue Hawking temperature in terms of the plasma wavelength, and our analysis shows that for a high intensity near-IR laser the analogue Hawking temperature is less than approximately 25K for a reasonable choice of parameters.

Diving inside a hairy black hole. (arXiv:2102.02707v1 [gr-qc])

Authors: Nicolás GrandiIgnacio Salazar Landea

We investigate the interior of the Einstein-Gauss-Bonnet charged black-hole with scalar hair. We find a variety of dynamical epochs, with the particular important feature that the Cauchy horizon is not present. This makes the violation of the no-hair theorem a possible tool to understand how might the strong cosmic censorship conjecture work.

Possible alterations of local gravitational field inside a superconductor. (arXiv:2102.01489v2 [gr-qc] UPDATED)

Authors: G. A. UmmarinoA. Gallerati

We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg-Landau theory. We try to estimate which are the most favourable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behaviour of high-$T_\text{c}$ and classical low-$T_\text{c}$ superconductors with respect to the gravity/superfluid interplay.

Knowledge is closed under analytic content

Abstract

I am concerned with epistemic closure—the phenomenon in which some knowledge requires other knowledge. In particular, I defend a version of the closure principle in terms of analyticity; if an agent S knows that p is true and that q is an analytic part of p, then S knows that q. After targeting the relevant notion of analyticity, I argue that this principle accommodates intuitive cases and possesses the theoretical resources to avoid the preface paradox.

A Principle Explanation of Bell State Entanglement

Stuckey, W. M. and Silberstein, Michael and McDevitt, Timothy (2021) A Principle Explanation of Bell State Entanglement. In: UNSPECIFIED.

No-go Theorems: What are they good for?

Dardashti, Radin (2021) No-go Theorems: What are they good for? [Preprint]

Spacetime singularities and a novel formulation of indeterminism

Azhar, Feraz and Namjoo, Mohammad Hossein (2021) Spacetime singularities and a novel formulation of indeterminism. [Preprint]

The Concept of Time: A Grand Unified Reaction Platform

Hamidreza, Simchi (2019) The Concept of Time: A Grand Unified Reaction Platform. [Preprint]

Demystifying mysteries. How metaphors and analogies extend the reach of the human mind

Boudry, Maarten and Vlerick, Michael and Edis, Taner (2021) Demystifying mysteries. How metaphors and analogies extend the reach of the human mind. [Preprint]

The Local versus the Global in the History of Relativity: The Case of Belgium

ten Hagen, Sjang L. (2020) The Local versus the Global in the History of Relativity: The Case of Belgium. [Preprint]

Clarifying the New Problem for Quantum Mechanics: Reply to Vaidman

Meehan, Alexander (2020) Clarifying the New Problem for Quantum Mechanics: Reply to Vaidman. [Preprint]

Probing Theoretical Statements with Thought Experiments

El Skaf, Rawad (2021) Probing Theoretical Statements with Thought Experiments. [Preprint]