# Weekly Papers on Quantum Foundations (23)

Testing Bell inequalities in Higgs boson decays. (arXiv:2106.01377v1 [hep-ph])

Higgs boson decays produce pairs of W bosons in a maximally entangled state, the spins of which can be expected to violate Bell inequalities. We show that the spin density matrix of the $W^\pm$ pair may be reconstructed experimentally from the directions of the emitted leptons, and from it the expectation values of various Bell operators determined. Simulations of $H \rightarrow W^+W^-$ indicate that violation of the CHSH inequality is unlikely to be measurable, however the CGLMP inequality is near-maximally violated, with large statistical significances which might be observable even with existing LHC data.

Can one hear a matrix? Recovering a real symmetric matrix from its spectral data. (arXiv:2106.01819v1 [math-ph])

The spectrum of a real and symmetric $N\times N$ matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove the unitary ambiguities. This work specifies the spectral and sign information required for a unique reconstruction of general matrices. More specifically, the spectral information consists of the spectra of the $N$ nested main minors of the original matrix of the sizes $1,2,\dots,N$. However, due to the complicated nature of the required sign data, improvements are needed in order to make the reconstruction procedure feasible. With this in mind, we restrict our attention to banded matrices where the amount of spectral data exceeds the number of the unknown matrix entries. It is shown that one can take advantage of this redundancy to guarantee unique reconstruction of {\it generic} matrices. The space of non-generic matrices is defined either via a set of polynomial equations or via a set of equations involving eigenvectors. Thus, the space of non-generic matrices has a positive co-dimension as a subspace of the space of all matrices. It is shown that one can optimize the ratio between redundancy and genericity by using the freedom of choice of the spectral information input. We demonstrate our constructions in detail for pentadiagonal matrices.

Background Independence and Quantum Causal Structure. (arXiv:2106.01038v2 [quant-ph] UPDATED)

One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. In fact, this appears to be one of the main conceptual obstacles to uniting the two theories. Additionally, a combination of the two theories is expected to yield non-classical, or “indefinite”, causal structures. In this paper, we present a background-independent formulation of the process matrix formalism – a form of quantum mechanics that allows for indefinite causal structure – while retaining operationally well-defined measurement statistics. We do this by postulating an arbitrary probability distribution of measurement outcomes across discrete “chunks” of spacetime, which we think of as physical laboratories, and then requiring that this distribution be invariant under any permutation of laboratories. We find (a) that one still obtains nontrivial, indefinite causal structures with background independence, (b) that we lose the idea of local operations in distinct laboratories, but can recover it by encoding a reference frame into the physical states of our system, and (c) that permutation invariance imposes surprising symmetry constraints that, although formally similar to a superselection rule, cannot be interpreted as such.

Yet another approach to the inverse square law and to the circular character of the hodograph of Kepler orbits. (arXiv:2106.01903v1 [physics.hist-ph])

The law of centripetal force governing the motion of celestial bodies in eccentric conic sections, has been established and thoroughly investigated by Sir Isaac Newton in his Principia Mathematica. Yet its profound implications on the understanding of such motions is still evolving. In a paper to the royal academy of science, Sir Willian Hamilton demonstrated that this law underlies the circular character of hodographs for Kepler orbits. A fact which was the object of ulterior research and exploration by Richard Feynman and many other authors [1]. In effect, a minute examination of the geometry of elliptic trajectories, reveals interesting geometric properties and relations, altogether, combined with the law of conservation of angular momentum lead eventually, and without any recourse to dealing with differential equations, to the appearance of the equation of the trajectory and to the derivation of the equation of its corresponding hodograph. On this respect, and for the sake of founding the approach on solid basis, I devised two mathematical theorems; one concerning the existence of geometric means, and the other is related to establishing the parametric equation of an off-center circle, altogether compounded with other simple arguments ultimately give rise to the inverse square law of force that governs the motion of bodies in elliptic trajectories, as well as to the equation of their inherent circular hodographs.

Is Electromagnetic Field Momentum Due to the Flow of Field Energy?. (arXiv:2105.05355v2 [physics.hist-ph] UPDATED)

Authors: Oliver Davis Johns

Momentum and energy conservation require electromagnetic field momentum and energy to be treated as physically real, even in static fields. This motivates the conjecture that field momentum might be due to the flow of a relativistic mass density (defined as energy density divided by the square of the speed of light). This article investigates the velocity of such a mass flow and finds a conflict between two different definitions of it, both of which originally seem plausible if the flow is to be taken as real. This investigation is careful to respect the transformation rules of special relativity throughout. The paper demonstrates that the consensus definition of the flow velocity of electromagnetic energy is inconsistent with the transformation rules of special relativity, and hence is incorrect. A replacement flow velocity is derived which is completely consistent with those transformation rules. The conclusion is that these conflicting definitions of flow velocity cannot be resolved in a way that is consistent with special relativity and also allows electromagnetic field momentum density to be the result of relativistic mass flow. Though real, field momentum density cannot be explained as the flow of a relativistic mass density. As a byproduct of the study, it is also shown that there is a comoving system in which the electromagnetic energy-momentum tensor is reduced to a simple diagonal form, with two of its diagonal elements equal to the energy density and the other two diagonal elements equal to plus and minus a single parameter derived from the electromagnetic field values, a result that places constraints on possible fluid models of electromagnetism.

Exploring black holes as particle accelerators in realistic scenarios. (arXiv:2106.01385v1 [gr-qc])

The possibility that rotating black holes could be natural particle accelerators has been subject of intense debate. While it appears that for extremal Kerr black holes arbitrarily high center of mass energies could be achieved, several works pointed out that both theoretical as well as astrophysical arguments would severely dampen the attainable energies. In this work we study particle collisions near Kerr–Newman black holes, by reviewing and extending previously proposed scenarios. Most importantly, we implement the hoop conjecture for all cases and we discuss the astrophysical relevance of these collisional Penrose processes. The outcome of this investigation is that scenarios involving near-horizon target particles are in principle able to attain, sub-Planckian, but still ultra high, center of mass energies of the order of $10^{21}-10^{23}$ eV. Thus, these target particle collisional Penrose processes could contribute to the observed spectrum of ultra high-energy cosmic rays, even if the hoop conjecture is taken into account, and as such deserve further scrutiny in realistic settings.

Hearts of Darkness: the inside out probing of black holes. (arXiv:2106.01530v1 [gr-qc])

Classical black holes shield us from the singularities that inevitably appear in general relativity. Being singularity regularization one of the main landmarks for a successful theory of quantum gravity, quantum black holes are not obliged to hide their inner core from the outside world. Notwithstanding the aforesaid, it is often implicitly assumed that quantum gravity effects must remain confined to black hole interiors. In this essay we argue in the opposite direction, discussing theoretical evidence for the existence of strong correlations between the physics inside and outside non-singular black holes. We conclude that astronomical tests of the surroundings of black holes can provide invaluable information about their so-far unexplored interiors.

On the visibility of singularities in general relativity and modified gravity theories. (arXiv:2106.01773v1 [gr-qc])

We argue that the global causal structure of the singularity is not a purely geometric property but also depends on the collapsing matter-field leading to its formation. To show this, we investigate the global visibility of the end state of a spherically symmetric marginally bound Lemaitre-Tolman-Bondi collapsing cloud (which is well studied in general relativity) in the framework of modified gravity having the generalized Lagrangian $R+\alpha R^2$ in the Einstein-Hilbert action. Here $R$ is the Ricci scalar, and $\alpha>0$ is a constant. As an example, we depict that for the same LTB metric governing the spacetime formed due to two different matter-fields, i.e., dust in general relativity and imperfect viscous fluid in $f(R)$ gravity, the singularity is locally visible in the former case, and globally visible in the latter case.

Intuition in Einsteinian Physics. (arXiv:2106.01820v1 [gr-qc])

Authors: Bernard F. Schutz

This chapter sets the stage for the rest of the book by exploring the role of intuition as a tool to deepen understanding in Einsteinian physics. Drawing on examples from the history of general relativity, we argue that the development of physical intuition is a crucial goal in physics education in parallel with any mathematical development of a physics subject.

This chapter is for readers who wish to learn how expert physicists think conceptually about their subjects to understand them plus readers who wish to see how we can introduce Einsteinian physics to students by developing their intuition as well as teaching them the mathematics.

Information recovery from evaporating black holes. (arXiv:2105.00198v2 [gr-qc] UPDATED)

We show that the apparent horizon and the region near $r=0$ of an evaporating charged, rotating black hole are timelike. It then follows that for black holes in nature, which invariably have some rotation, have a channel, via which classical or quantum information can escape to the outside, while the black hole shrinks in size. We discuss implications for the information loss problem.

Quantum imprints of gravitational shockwaves. (arXiv:2105.09337v2 [hep-th] UPDATED)

Gravitational shockwaves are simple exact solutions of Einstein equations representing the fields of ultrarelativistic sources and idealized gravitational waves (shocks). Historically, much work has focused on shockwaves in the context of possible black hole formation in high energy particle collisions, yet they remain at the forefront of research even today. Representing hard modes in the bulk, shocks give rise to the gravitational memory effect at the classical level and implant supertranslation (BMS) hair onto a classical spacetime at the quantum level. The aim of this paper is to further our understanding of the `information content’ of such supertranslations. Namely, we show that, contrary to the several claims in the literature, a gravitational shockwave does leave a quantum imprint on the vacuum state of a test quantum field and that this imprint is accessible to local observers carrying Unruh–DeWitt (UDW) detectors in this spacetime.

Do gamma-ray burst measurements provide a useful test of cosmological models?. (arXiv:2105.12692v2 [astro-ph.CO] UPDATED)

We study eight different gamma-ray burst (GRB) data sets to examine whether current GRB measurements — that probe a largely unexplored part of cosmological redshift ($z$) space — can be used to reliably constrain cosmological model parameters. We use three Amati-correlation samples and five Combo-correlation samples to simultaneously derive correlation and cosmological model parameter constraints. The intrinsic dispersion of each GRB data set is taken as a goodness measurement. We examine the consistency between the cosmological bounds from GRBs with those determined from better-established cosmological probes, such as baryonic acoustic oscillation (BAO) and Hubble parameter $H(z)$ measurements. We use the Markov chain Monte Carlo method implemented in \textsc{MontePython} to find best-fit correlation and cosmological parameters, in six different cosmological models, for the eight GRB samples, alone or in conjunction with BAO and $H(z)$ data. For the Amati correlation case, we compile a data set of 118 bursts, the A118 sample, which is the largest — about half of the total Amati-correlation GRBs — current collection of GRBs suitable for constraining cosmological parameters. This updated GRB compilation has the smallest intrinsic dispersion of the three Amati-correlation GRB data sets we examined. We are unable to define a collection of reliable bursts for current Combo-correlation GRB data. Cosmological constraints determined from the A118 sample are consistent with — but significantly weaker than — those from BAO and $H(z)$ data. They also are consistent with the spatially-flat $\Lambda$CDM model as well as with dynamical dark energy models and non-spatially-flat models. Since GRBs probe a largely unexplored region of $z$, it is well worth acquiring more and better-quality burst data which will give a more definitive answer to the question of the title.

Information Causality without Concatenation

Author(s): Nikolai Miklin and Marcin Pawłowski

Information causality is a physical principle which states that the amount of randomly accessible data over a classical communication channel cannot exceed its capacity, even if the sender and the receiver have access to a source of nonlocal correlations. This principle can be used to bound the nonl…

[Phys. Rev. Lett. 126, 220403] Published Fri Jun 04, 2021

Quantum metametaphysics

Abstract

Say that metaphysical indeterminacy occurs just when there is a fact such that neither it nor its negation obtains. The aim of this work is to shed light on the issue of whether orthodox quantum mechanics provides any evidence of metaphysical indeterminacy by discussing the logical, semantic, and broadly methodological presuppositions of the debate. I argue that the dispute amounts to a verbal disagreement between classical and quantum logicians, given Eli Hirsch’s account of substantivity; but that it need not be so if Ted Sider’s naturalness-based account of substantivity is adopted instead. Given the latter approach, can anything be said in order to tip the balance of the dispute either way? Some prima facie reasonable constraints on naturalness entail that the classicist is right, and the quantum world is therefore determinate. Nevertheless, there are reasons for weakening those constraints, to the effect that the dispute remains very much open. Finally, I discuss alternative accounts of metaphysical indeterminacy, and argue that they are unsuitable for framing the quantum indeterminacy debate.

Recovering General Relativity from a Planck scale discrete theory of quantum gravity

Butterfield, Jeremy and Dowker, Fay (2021) Recovering General Relativity from a Planck scale discrete theory of quantum gravity. [Preprint]

Newton’s experimental proofs

Lampert, Timm (2021) Newton’s experimental proofs. THEORIA. An International Journal for Theory, History and Foundations of Science, 36 (2). pp. 261-283. ISSN 2171-679X

Reflections off a relativistic mirror

Nature Physics, Published online: 03 June 2021; doi:10.1038/s41567-021-01259-3

High-order harmonics of laser pulses yield spectral components with shorter wavelength and duration and tighter focus than the original pulse. Precise spatiotemporal characterization of this radiation from a relativistic plasma mirror is relevant for ultrafast science.

John Bell on ‘Subject and Object’: an Exchange

Halvorson, Hans and Butterfield, Jeremy (2021) John Bell on ‘Subject and Object’: an Exchange. [Preprint]

The Strong Arm of the Law – A Unified Account of Necessary and Contingent Laws of Nature

Hirèche, Salim and Linnemann, Niels and Michels, Robert and Vogt, Lisa (2021) The Strong Arm of the Law – A Unified Account of Necessary and Contingent Laws of Nature. [Preprint]

A Dialogue on the Ethics of Science: Henri Poincaré and Pope Francis

Danne, Nicholas (2021) A Dialogue on the Ethics of Science: Henri Poincaré and Pope Francis. [Preprint]

Bilocal Bell Inequalities Violated by the Quantum Elegant Joint Measurement

Author(s): Armin Tavakoli, Nicolas Gisin, and Cyril Branciard

Network Bell experiments give rise to a form of quantum nonlocality that conceptually goes beyond Bell’s theorem. We investigate here the simplest network, known as the bilocality scenario. We depart from the typical use of the Bell state measurement in the network central node and instead introduce…

[Phys. Rev. Lett. 126, 220401] Published Tue Jun 01, 2021

Theoretical equivalence and duality

Abstract

Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical equivalence. I argue that duality suggests a construal of theoretical equivalence in the physical sciences. The construal is in terms of the isomorphism of models, as defined by the schema. This construal gives interpretative constraints that should be useful for discussions of theoretical equivalence more generally. I illustrate the construal in various formulations of Maxwell’s electromagnetic theory.

Humeans are out of this world

Abstract

I defend the following argument in this paper. Premise 1: Laws of nature are intrinsic to the universe. Premise 2: Humeanism maintains that laws of nature are extrinsic to the universe. Conclusion: Humeanism is false. This argument is inspired by Hawthorne’s (Noûs 38(2):351–358, 2004) argument in “Humeans are out of their Minds”. My argument differs from his; Hawthorne focuses on Humean views of causation and how they interact with judgments about consciousness. He thinks Humeans are forced to treat certain mental properties (insofar as they involve causal features) as extrinsic to conscious minds. I do not discuss causation or consciousness here. I focus on Humean accounts of laws. I argue that Humean laws are extrinsic to the entire universe. As such, Humeans are not just out of their minds; they are out of this world. I aim to show that premises 1 and 2 are well-supported and that denying either of them comes at a cost. Nevertheless, some Humeans may prefer to reject 1 or 2 rather than give up Humeanism. Even if the Humean takes one of these routes, the argument above has philosophical import: it shows that Humeanism involves surprising commitments.

Are non-accidental regularities a cosmic coincidence? Revisiting a central threat to Humean laws

Abstract

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked on many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws.