# Weekly Papers on Quantum Foundations (10)

Observing a Superposition

Skokowski, Paul (2021) Observing a Superposition. [Preprint]

Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols. (arXiv:2103.02639v1 [quant-ph])

Device-independent quantum key distribution is a secure quantum cryptographic paradigm that allows two honest users to establish a secret key, while putting minimal trust in their devices. Most of the existing protocols have the following structure: first, a bipartite nonlocal quantum state is distributed between the honest users, who perform local projective measurements to establish nonlocal correlations. Then, they announce the implemented measurements and extract a secure key by post-processing their measurement outcomes. We show that no protocol of this form allows for establishing a secret key when implemented on certain entangled nonlocal states, namely on a range of entangled two-qubit Werner states. To prove this result, we introduce a technique for upper-bounding the asymptotic key rate of device-independent quantum key distribution protocols, based on a simple eavesdropping attack. Our results imply that either different tools — such as different reconciliation techniques or non-projective measurements — are needed for device-independent quantum key distribution in the large-noise regime, or Bell nonlocality is not sufficient for this task.

Bell-Fine theorems on complementarity. (arXiv:2103.03101v1 [quant-ph])

We provide a Bell-type analysis of complementarity via a suitably designed hidden-variables model that leads to a set of Bell-like inequalities that can be tested by easily measured observables. We show that this violation is equivalent to Fine-like theorems regarding the lack of a joint distribution for incompatible observables. This is illustrated by path-interference duality in a Young interferometer.

A non local phase field model of Bohm’s quantum potential. (arXiv:2103.03162v1 [quant-ph])

Assuming that the free energy of a gas depends non-locally on the logarithm of its mass density, the body force in the resulting equation of motion consists of the sum of density gradient terms. Truncating this series after the second term, Bohm’s quantum potential and the Madelung equation are identically obtained, showing explicitly that some of the hypotheses that led to the formulation of quantum mechanics admit a classical interpretation based on non-locality.

The quantum mechanical notion of unobservable causal loop and the anthropic principle. (arXiv:2103.03173v1 [quant-ph])

It can be argued that the ordinary description of the reversible quantum process between two one-to-one correlated measurement outcomes is incomplete because, by not specifying the direction of causality, it allows causal structures that violate the time symmetry that is required of a reversible process. This also means that it can be completed simply by time-symmetrizing it, namely by requiring that the initial and final measurements evenly contribute to the selection of their correlated pair of outcomes. This leaves the description unaltered but shows that it is the quantum superposition of unobservable time-symmetrized instances whose causal structure is completely defined. Each instance consists of a causal loop: the final measurement that changes backwards in time the input state of the unitary transformation that leads to the state immediately before it. In former works, we have shown that such loops exactly explain the quantum computational speedup and quantum nonlocality. In this work we show that they lead to a completion of the anthropic principle that allows a universe evolution with quantum speedup.

Gauge-underdetermination and shades of locality in the Aharonov-Bohm effect. (arXiv:2103.02684v1 [quant-ph])

Authors: Ruward A. Mulder

I address the view that the classical electromagnetic potentials are shown by the Aharonov-Bohm effect to be physically real (which I dub: ‘the potentials view’). I give a historico-philosophical presentation of this view and assess its prospects, more precisely than has so far been done in the literature. Taking the potential as physically real runs prima facie into ‘gauge-underdetermination’: different gauge choices represent different physical states of affairs and hence different theories. I then illustrate this theme by what I take to be the basic insight of the AB effect for the potentials view, namely that the gauge equivalence class that directly corresponds to the electric and magnetic fields (which I call the Wide Equivalence Class) is too wide, i.e., the Narrow Equivalence Class encodes additional physical degrees of freedom: these only play a distinct role in a multiply-connected space. There is a trade-off between explanatory power and gauge symmetries. Although this narrower equivalence class gives a explanation in terms of local interactions’, locality is not satisfied in the sense of signal locality. It is therefore intellectually mandatory to seek desiderata that will distinguish even within these narrower equivalence classes, i.e. will prefer some elements of such an equivalence class over others. I consider various formulations of locality, such as Bell locality, local interaction Hamiltonians, and signal locality. I show that Bell locality can only be evaluated if one fixes the gauge freedom completely. Yet, an explanation in terms of signal locality can be accommodated by the Lorenz gauge: the potentials propagate in waves at finite speed. I therefore suggest the Lorenz gauge potentials theory — an even narrower gauge equivalence relation — as the ontology of electrodynamics.

Demons in Black Hole Thermodynamics: Bekenstein and Hawking. (arXiv:2102.11209v2 [physics.hist-ph] UPDATED)

Authors: Galina Weinstein

This paper comprehensively explores Stephen Hawking’s interaction with Jacob Bekenstein. Both Hawking and Bekenstein benefited from the interaction with each other. It is shown that Hawking’s interaction with Bekenstein drove him to solve the problems in Bekenstein’s black hole thermodynamics in terms of a new thermal radiation mechanism. Hawking derived the thermal radiation using a semiclassical approximation in which the matter fields are treated quantum mechanically on a classical spacetime background. Hawking’s semiclassical approximation yielded a simple formula for the entropy of the black hole, which turned out to be equivalent to Bekenstein’s equation for entropy.

Influence of gravitational waves upon light. Part I. Null geodesics, radar distance and frequency shift. (arXiv:2103.02632v1 [gr-qc])

We explore different facets of the action of linearized gravitational waves in Minkowski spacetime background upon light, under the electromagnetic geometrical optics limit, covering the main aspects: light trajectory perturbations, radar distance and light frequency shift. For this purpose, we consider observers comoving with the transverse traceless gauge coordinates. We compute the parametrized null geodesics exchanged between two of these observers, presenting explicitly the constants of motion as functions of observables, determining therefrom both the radar distance between the observers and the electromagnetic round-trip frequency shift caused by the gravitational wave. Also, a comparison is made between these results and what one would obtain by using a frequently adopted hybrid model in which the spatial trajectory of light is unchanged. Finally, we revisit and provide an explanation, resorting to the constancy of the phase along a light ray, to the fundamental puzzling question of how one is able to detect gravitational waves by means of interferometry if both light wavelength and detector arms are stretched.

Influence of gravitational waves upon light. Part II. Electric field propagation and interference pattern in a gravitational wave detector. (arXiv:2103.02688v1 [gr-qc])

In this second article of the series, we apply our recently derived equation for the electric field propagation along light rays [arXiv:2004.03496], valid on the electromagnetic geometrical optics limit, to the special case of a toy interferometer used to detect gravitational waves in a flat background. Such an equation shows that, assuming the detector is in the transverse-traceless frame, which has a local shearing relative motion due to the gravitational wave perturbations, the electric field does not propagate as in an inertial reference frame in Minkowski spacetime. We present the electric field at the end of the interferometric process, for arbitrary arm configurations with respect to the plane gravitational wave packet propagation direction. Then, for normal incidence, we compute the interference pattern and, in addition to the usual term associated with the difference in path traveled by light in the arms, we deduce two new contributions to the final intensity, arising from: (i) the round-trip electromagnetic frequency shift and (ii) the divergence of the light beam. Their quantitative relevance is compared to the traditional contribution and shown to be typically negligible due to the geometrical optics regime of light. Moreover, a non-parallel transport of the polarization vector takes place, in general, because of the gravitational wave, a feature which could generate further contributions. However, we conclude that for the normal incidence case such vector is parallel transported, preventing this kind of correction.

How does the Planck scale affect qubits?. (arXiv:2103.03093v1 [quant-ph])

Authors: Matthew J. Lake

Gedanken experiments in quantum gravity motivate generalised uncertainty relations (GURs) implying deviations from the standard quantum statistics close to the Planck scale. These deviations have been extensively investigated for the non-spin part of the wave function but existing models tacitly assume that spin states remain unaffected by the quantisation of the background in which the quantum matter propagates. Here, we explore a new model of nonlocal geometry in which the Planck-scale smearing of classical points generates GURs for angular momentum. These, in turn, imply an analogous generalisation of the spin uncertainty relations. The new relations correspond to a novel representation of {\rm SU(2)} that acts nontrivially on both subspaces of the composite state describing matter-geometry interactions. For single particles each spin matrix has four independent eigenvectors, corresponding to two $2$-fold degenerate eigenvalues $\pm (\hbar + \beta)/2$, where $\beta$ is a small correction to the effective Planck’s constant. These represent the spin states of a quantum particle immersed in a quantum background geometry and the correction by $\beta$ emerges as a direct result of the interaction terms. In addition to the canonical qubits states, $\ket{0} = \ket{\uparrow}$ and $\ket{1} = \ket{\downarrow}$, there exist two new eigenstates in which the spin of the particle becomes entangled with the spin sector of the fluctuating spacetime. We explore ways to empirically distinguish the resulting geometric’ qubits, $\ket{0′}$ and $\ket{1′}$, from their canonical counterparts.

Interpreting Mass via Riemannian Polyhedra. (arXiv:2103.03201v1 [math.DG])

Authors: Pengzi Miao

We give an account of some recent development that connects the concept of mass in general relativity to the geometry of large Riemannian polyhedra, in the setting of both asymptotically flat and asymptotically hyperbolic manifolds.

Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies. (arXiv:2009.11525v2 [astro-ph.GA] UPDATED)

The strong equivalence principle (SEP) distinguishes General Relativity from other viable theories of gravity. The SEP demands that the internal dynamics of a self-gravitating system under free-fall in an external gravitational field should not depend on the external field strength. We test the SEP by investigating the external field effect (EFE) in Milgromian dynamics (MOND), proposed as an alternative to dark matter in interpreting galactic kinematics. We report a detection of this EFE using galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. Our detection is threefold: (1) the EFE is individually detected at $8\sigma$ to $11\sigma$ in “golden” galaxies subjected to exceptionally strong external fields, while it is not detected in exceptionally isolated galaxies, (2) the EFE is statistically detected at more than $4\sigma$ from a blind test of 153 SPARC rotating galaxies, giving a mean value of the external field consistent with an independent estimate from the galaxies’ environments, and (3) we detect a systematic downward trend in the weak gravity part of the radial acceleration relation at the right acceleration predicted by the EFE of the MOND modified gravity. Tidal effects from neighboring galaxies in the $\Lambda$CDM context are not strong enough to explain these phenomena. They are not predicted by existing $\Lambda$CDM models of galaxy formation and evolution, adding a new small-scale challenge to the $\Lambda$CDM paradigm. Our results point to a breakdown of the SEP, supporting modified gravity theories beyond General Relativity.

A Wavefunction Description for a Localized Quantum Particle in Curved Spacetimes. (arXiv:2012.08539v2 [gr-qc] UPDATED)

Authors: T. Rick PercheJonas Neuser

We reduce Dirac’s spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and curvature around the center of mass of the system, generalizing the results of [Phys. Rev. D 22, 1922]. Under a non-relativistic approximation, one obtains a quantum description in a Hilbert space of complex wavefunctions defined in the rest space of the system. The wavefunction of the particle then evolves according to a modified Schr\”odinger equation associated with a symmetric Hamiltonian. When compared to the standard Schr\”odinger equation for a wavefunction, we obtain corrections in terms of the acceleration of the system’s center of mass and curvature of spacetime along its trajectory. In summary, we provide a formalism for the use of a complex wavefunction to describe a localized quantum particle in curved spacetimes.

Hidden Symmetry of Vanishing Love. (arXiv:2103.01234v2 [hep-th] UPDATED)

We show that perturbations of massless fields in the Kerr black hole background enjoy a hidden infinite-dimensional (“Love”) symmetry in the properly defined near zone approximation. Love symmetry mixes IR and UV modes. Still, this approximate symmetry allows us to derive exact results about static tidal responses. Generators of the Love symmetry are globally well defined and have a smooth Schwarzschild limit. The Love symmetry contains an $SL(2,\mathbb{R})\times {U}(1)$ subalgebra. Generic regular solutions of the near zone Teukolsky equation form infinite-dimensional $SL(2,\mathbb{R})$ representations. In some special cases ($\hat{\ell}$ parameter is an integer), these are highest weight representations. This situation corresponds to vanishing Love numbers. In particular, static perturbations of four-dimensional Schwarzschild black holes belong to finite-dimensional representations. Other known facts about static Love numbers also acquire an elegant explanation in terms of the $SL(2,\mathbb{R})$ representation theory.

Polarization out of the vortex

Nature Physics, Published online: 04 March 2021; doi:10.1038/s41567-021-01167-6

The virtual photons that are exchanged when a free-electron vortex beam interacts with a nanoscopic target unlock an explicit connection between polarized optical spectroscopy and the inelastic scattering of scalar electron waves.

The Everett interpretation: structure

Saunders, Simon (2021) The Everett interpretation: structure. [Preprint]

The many-worlds theory of consciousness

List, Christian (2021) The many-worlds theory of consciousness. [Preprint]

Curie’s Principle and Causal Graphs

Kinney, David (2021) Curie’s Principle and Causal Graphs. [Preprint]

Abstract

This paper takes issue with an influential interpretationist argument for physicalism about intentionality based on the possibility of radical interpretation. The interpretationist defends the physicalist thesis that the intentional truths supervene on the physical truths by arguing that it is possible for a radical interpreter, who knows all of the physical truths, to work out the intentional truths about what an arbitrary agent believes, desires, and means without recourse to any further empirical information. One of the most compelling arguments for the possibility of radical interpretation, associated most closely with David Lewis and Donald Davidson, gives a central role to decision theoretic representation theorems, which demonstrate that if an agent’s preferences satisfy certain constraints, it is possible to deduce probability and utility functions that represent her beliefs and desires. We argue that an interpretationist who wants to rely on existing representation theorems in defence of the possibility of radical interpretation faces a trilemma, each horn of which is incompatible with the possibility of radical interpretation.

Dynamical Symmetries and Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems

Author(s): Georg Engelhardt and Jianshu Cao

In recent experiments, the light-matter interaction has reached the ultrastrong coupling limit, which can give rise to dynamical generalizations of spatial symmetries in periodically driven systems. Here, we present a unified framework of dynamical-symmetry-protected selection rules based on Floquet…

[Phys. Rev. Lett. 126, 090601] Published Tue Mar 02, 2021

The Measurement Problem of Consciousness

Browning, Heather and Veit, Walter (2021) The Measurement Problem of Consciousness. [Preprint]

Operational Resource Theory of Imaginarity

Author(s): Kang-Da Wu, Tulja Varun Kondra, Swapan Rana, Carlo Maria Scandolo, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo, and Alexander Streltsov

There exist real quantum states which can be perfectly distinguished via local operations and classical communication, but which cannot be distinguished with any nonzero probability if one of the parties has no access to imaginarity.

[Phys. Rev. Lett. 126, 090401] Published Mon Mar 01, 2021

A pragmatic approach to the ontology of models

Antoniou, Antonis (2021) A pragmatic approach to the ontology of models. [Preprint]

Scientific Realism and Empirical Confirmation: a Puzzle

Allzén, Simon (2021) Scientific Realism and Empirical Confirmation: a Puzzle. [Preprint]

Why We Should Be Suspicious of Conspiracy Theories. A Novel Demarcation Problem

Boudry, Maarten (2020) Why We Should Be Suspicious of Conspiracy Theories. A Novel Demarcation Problem. [Preprint]