# Weekly Papers on Quantum Foundations (14)

 上午8:37 | E. Martins, M. F. Savi, R. M. Angelo | quant-ph updates on arXiv.org

Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource in tasks involving quantum state discrimination and quantum programmability. Here we link quantum incompatibility with the amount of information that can be extracted from a system upon successive measurements of noncommuting observables, a scenario related to communication tasks. This approach leads us to characterize incompatibility as a resource encoded in a physical context, which involves both the quantum state and observables. Moreover, starting with a measure of context incompatibility we derive a measurement-incompatibility quantifier that is easily computable, admits a geometrical interpretation, and is maximum only if the eigenbases of the involved observables are mutually unbiased.

 上午8:37 | Jianhua Ren, Lupei Qin, Wei Feng, Xin-Qi Li | quant-ph updates on arXiv.org

The weak-value (WV) measurement proposed by Aharonov, Albert and Vaidman (AAV) has attracted a great deal of interest in connection with quantum metrology. In this work, we extend the analysis beyond the AAV limit and obtain a few main results. (i) We obtain non-perturbative result for the signal-to-noise ratio (SNR). In contrast to the AAV’s prediction, we find that the SNR asymptotically gets worse when the AAV’s WV $A_w$ becomes large, i.e., in the case $g|A_w|^2>>1$, where $g$ is the measurement strength. (ii) With the increase of $g$ (but also small), we find that the SNR is comparable to the result under the AAV limit, while both can reach — actually the former can slightly exceed — the SNR of the standard measurement. However, along a further increase of $g$, the WV technique will become less efficient than the standard measurement, despite that the postselection probability is increased. (iii) We find that the Fisher information can characterize the estimate precision qualitatively well as the SNR, yet their difference will become more prominent with the increase of $g$. (iv) We carry out analytic expressions of the SNR in the presence of technical noises and illustrate the particular advantage of the imaginary WV measurement. The non-perturbative result of the SNR manifests a favorable range of the noise strength and allows an optimal determination.

The International Gamma-Ray Astrophysics Laboratory (INTEGRAL) satellite has yielded unprecedented measurements of the soft gamma-ray spectrum of our Galaxy. Here we use those measurements to set constraints on dark matter (DM) that decays or annihilates into photons with energies $E\approx 0.02-2$ MeV. First, we revisit the constraints on decaying and annihilating particle DM. For DM decaying to two photons, we find that previous limits were overstated by roughly an order of magnitude. Our new, conservative analysis finds that the DM lifetime must satisfy $\tau\gtrsim 10^{27}\,{\rm s}\times (m_{\chi}/\rm MeV)^{-1}$ for DM masses $m_{\chi}=0.054-3.6$ MeV. For MeV-scale DM that annihilates into photons INTEGRAL sets the strongest constraints to date, whereas for annihilations to electron-positron pairs, INTEGRAL only improves upon current limits when assuming $p$-wave annihilation. Second, we target ultralight primordial black holes (PBHs) through their Hawking radiation. This makes them appear as decaying DM with a photon spectrum peaking at $E\approx 5/(8\pi G M_{\rm PBH})$, for a PBH of mass $M_{\rm PBH}$. We use the INTEGRAL data to demonstrate that PBHs with masses less than 2 $\times 10^{17}$ g cannot comprise all of the DM, setting the tightest bound to date on ultralight PBHs.

Two of the dominant channels to produce the black-hole binary mergers observed by LIGO and Virgo are believed to be the isolated evolution of stellar binaries in the field and dynamical formation in star clusters. Their relative efficiency can be characterized by a “mixing fraction.” Pair instabilities prevent stellar collapse from generating black holes more massive than about $45 M_\odot$. This “mass gap” only applies to the field formation scenario, and it can be filled by repeated mergers in clusters. A similar reasoning applies to the binary’s effective spin. If black holes are born slowly rotating, the high-spin portion of the parameter space (the “spin gap”) can only be populated by black hole binaries that were assembled dynamically. Using a semianalytical cluster model, we show that future gravitational-wave events in either the mass gap, the spin gap, or both can be leveraged to infer the mixing fraction between the field and cluster formation channels.

 上午8:37 | gr-qc updates on arXiv.org

Authors: Maria Okounkova

Recently, it has been shown that with the inclusion of overtones, the post-merger gravitational waveform at infinity of a binary black hole system is well-modelled using pure linear theory. However, given that a binary black hole merger is expected to be highly non-linear, where do these non-linearities, which do not make it out to infinity, go? We visualize quantities measuring non-linearity in the strong-field region of a numerical relativity binary black hole merger in order to begin to answer this question.

 上午8:37 | gr-qc updates on arXiv.org

We present a model for the coupling of non-relativistic quantum systems with a linearized gravitational field from a Lagrangian formulation. The coupling strongly resembles the light-matter interaction models that are known to be well approximated by the Unruh-DeWitt detector model for interactions with quantum fields. We then apply our model to linearized quantum gravity, which allows us to propose a detector based setup that can in principle probe the quantum nature of the gravitational field.

 上午8:37 | gr-qc updates on arXiv.org

Authors: Jingbo Wang

Information loss paradox is still a challenging problem in theoretical physics. In this essay, for statics BTZ black holes and Schwarzschild black holes, we propose a simple solution based on the similarity between black holes and topological insulators. That is, the Hawking radiation is pure due to the entanglement between the left-moving sector and right-moving sector of the Hawking radiation. And this entanglement may be detected in an analogue black hole in the near future.

We study local-gravity tests on unified models of inflation and dark energy in $f(R)$ gravity. In this paper, we consider three unified models, which are combination of the known dark energy models and the same inflationary term. During inflation, all unified models reduce to the model $f(R)=R + \alpha R^n$, which is a generalization of the $R^2$ inflation model proposed by Starobinsky. From the observational constraint on the tensor-to-scalar ratio and the spectral index, we obtain $1.977<n<2.003$. We then investigate local-gravity tests for these unified models. The inflationary term becomes important at extremely high curvature in the action. However, we point out that it can be important at much lower curvature for the scalaron’s potential and then its mass. Investigating how it works in the chameleon screening mechanism, we nonetheless find that the inflationary term does not relax or tighten the constraints on the three unified models in relevant density scales.

 上午8:37 | gr-qc updates on arXiv.org

Authors: Barak Shoshany

We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting phase space is precisely that of spin networks, the quantum states of discrete spacetime in loop quantum gravity, with additional degrees of freedom called edge modes, which control the gluing between cells. This work establishes, for the first time, a rigorous proof of the equivalence between spin networks and piecewise-flat geometries with curvature and torsion degrees of freedom. In addition, it demonstrates that careful consideration of edge modes is crucial both for the purpose of this proof and for future work in the field of loop quantum gravity. It also shows that spin networks have a dual description related to teleparallel gravity, where gravity is encoded in torsion instead of curvature degrees of freedom. Finally, it sets the stage for collaboration between the loop quantum gravity community and theoretical physicists working on edge modes from other perspectives, such as quantum electrodynamics, non-abelian gauge theories, and classical gravity.

Authors: Gabriele U. Varieschi

This paper introduces a possible alternative model of gravity based on fractional calculus and its applications to Newtonian gravity. In particular, Gauss’s law for gravity as well as Laplace’s equation and other fundamental classical laws are extended to a $D$-dimensional metric space, where $D$ can be a non-integer dimension. We show a possible connection between this Newtonian Fractional Gravity (NFG) and Modified Newtonian Dynamics (MOND), the leading alternative gravity model, which accounts for the observed properties of galaxies and other astrophysical structures without requiring the dark matter hypothesis. The MOND acceleration constant $a_{0} \simeq 1.2 \times 10^{ -10}\mbox{m}\thinspace \mbox{s}^{ -2}$ can be related to a natural scale length $l_{0}$ in NFG, i.e., $a_{0} \approx GM/l_{0}^{2}$, for astrophysical structures of mass $M$, and the deep-MOND regime is present in regions of space where the dimension is reduced to $D \approx 2$. For several fundamental spherically-symmetric structures, we compare MOND results such as the empirical Radial Acceleration Relation (RAR), circular speed plots, and logarithmic plots of the observed radial acceleration $g_{obs}$ vs. the baryonic radial acceleration $g_{bar}$, showing that NFG is capable of reproducing these results using a variable local dimension $D\left (w\right )$, where $w =r/l_{0}$ is a dimensionless radial coordinate. At the moment, we are unable to derive explicitly this dimension function $D\left (w\right )$ from first principles, but it can be obtained empirically in each case from the general RAR. Additional work on the subject, including studies of axially-symmetric structures, detailed galactic rotation curves fitting, and a possible relativistic extension, will be needed to establish NFG as a viable alternative model of gravity.

 2020年4月2日 星期四 下午4:39 | Philsci-Archive: No conditions. Results ordered -Date Deposited.
Pitts, J. Brian (2020) Conservation of Energy: Missing Features in Its Nature and Justification and Why They Matter. Foundations of Science. ISSN 1233-1821
 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

This special issue of Foundations of Physics collects together articles representing some recent new perspectives on the hole argument in the history and philosophy of physics. Our task here is to introduce those new perspectives.

 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

We address a recent proposal concerning ‘surplus structure’ due to Nguyen et al. (Br J Phi Sci, 2018). We argue that the sense of ‘surplus structure’ captured by their formal criterion is importantly different from—and in a sense, opposite to—another sense of ‘surplus structure’ used by philosophers. We argue that minimizing structure in one sense is generally incompatible with minimizing structure in the other sense. We then show how these distinctions bear on Nguyen et al.’s arguments about Yang-Mills theory and on the hole argument.

 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

The Hole Argument was originally formulated by Einstein and it haunted him as he struggled to understand the meaning of spacetime coordinates in the context of the diffeomorphism invariance of general relativity. This argument has since been put to philosophical use by Earman and Norton (Br J Philos Sci 515–525, 1987) to argue against a substantival conception of spacetime. In the present work I demonstrate how Earman and Norton’s Hole Argument can be extended to exclude everything and not merely substantival manifolds. These casualties of the hole demonstrate that the Hole Argument hinges essentially on our notion of determinism and not on the diffeomorphic freedom of general relativity. Just as Earman and Norton argue that we should not let our metaphysics run roughshod over the structure of our physical theories, so I will argue that, in particular, we should not uncritically allow our metaphysics to dictate what our physical theories must determine. The central conviction which drives the arguments of this paper is that deterministic theories are not required to determine for future moments what they cannot determine for any present or past moments. I provide two arguments to the effect that a physically informed notion of determinism does not require general relativity to determine substantival facts. Consequently the Hole Argument cannot be used against substantival spacetime. The position that I advocate is an instance of “sophisticated determinism.”

 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

The Hole Argument is primarily about the meaning of general covariance in general relativity. As such it raises many deep issues about identity in mathematics and physics, the ontology of space–time, and how scientific representation works. This paper is about the application of a new foundational programme in mathematics, namely homotopy type theory (HoTT), to the Hole Argument. It is argued that the framework of HoTT provides a natural resolution of the Hole Argument. The role of the Univalence Axiom in the treatment of the Hole Argument in HoTT is clarified.

 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

This is an essay about general covariance, and what it says (or doesn’t say) about spacetime structure. After outlining a version of the dynamical approach to spacetime theories, and how it struggles to deal with generally covariant theories, I argue that we should think about the symmetry structure of spacetime rather differently in generally-covariant theories compared to non-generally-covariant theories: namely, as a form of internal rather than external symmetry structure.

 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

I apply homotopy type theory (HoTT) to the hole argument as formulated by Earman and Norton. I argue that HoTT gives a precise sense in which diffeomorphism-related Lorentzian manifolds represent the same spacetime, undermining Earman and Norton’s verificationist dilemma and common formulations of the hole argument. However, adopting this account does not alleviate worries about determinism: general relativity formulated on Lorentzian manifolds is indeterministic using this standard of sameness and the natural formalization of determinism in HoTT. Fixing this indeterminism results in a more faithful mathematical representation of general relativity as used by physicists. It also gives a substantive notion of general covariance.

 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

I illustrate a challenge to a view that is a response to the Hole Argument. The view, sophisticated substantivalism, has been claimed to be the received view. While sophisticated substantivalism has many defenders, there is a fundamental tension in the view that has not received the attention it deserves. Anyone who defends or endorses sophisticated substantivalism, should acknowledge this challenge, and should either show why it is not serious or explain how to respond to it.

 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

Recent work on the hole argument in general relativity by Weatherall (Br J Philos Sci 69(2):329–350, 2018) has drawn attention to the neglected concept of (mathematical) models’ representational capacities. I argue for several theses about the structure of these capacities, including that they should be understood not as many-to-one relations from models to the world, but in general as many-to-many relations constrained by the models’ isomorphisms. I then compare these ideas with a recent argument by Belot (Noûs, 2017http://sci-hub.tw/10.1111/nous.12200) for the claim that some isometries “generate new possibilities” in general relativity. Philosophical orthodoxy, by contrast, denies this. Properly understanding the role of representational capacities, I argue, reveals how Belot’s rejection of orthodoxy does not go far enough, and makes better sense of our practices in theorizing about spacetime.

 2020年4月1日 星期三 上午8:00 | Latest Results for Foundations of Physics

### Abstract

Leibniz Equivalence is a principle of applied mathematics that is widely assumed in both general relativity textbooks and in the philosophical literature on Einstein’s hole argument. In this article, I clarify an ambiguity in the statement of this Leibniz Equivalence, and argue that the relevant expression of it for the hole argument is strictly false. I then show that the hole argument still succeeds as a refutation of manifold substantivalism; however, recent proposals that the hole argument is undermined by principles of representational equivalence do not fare so well.

 2020年3月30日 星期一 下午6:00 | Juliette Monsel, Marco Fellous-Asiani, Benjamin Huard, and Alexia Auffèves | PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

Author(s): Juliette Monsel, Marco Fellous-Asiani, Benjamin Huard, and Alexia Auffèves

We analyze work extraction from a qubit into a waveguide (WG) acting as a battery, where work is the coherent component of the energy radiated by the qubit. The process is stimulated by a wave packet whose mean photon number (the battery’s charge) can be adjusted. We show that the extracted work is …

[Phys. Rev. Lett. 124, 130601] Published Mon Mar 30, 2020

 2020年3月30日 星期一 下午4:23 | Philsci-Archive: No conditions. Results ordered -Date Deposited.
Chen, Eddy Keming and Tumulka, Roderich (2020) Uniform Probability Distribution Over All Density Matrices. [Preprint]
 2020年3月30日 星期一 上午8:00 | James Analytis | Nature Physics – Issue – nature.com science feeds

Nature Physics, Published online: 30 March 2020; doi:10.1038/s41567-020-0861-5

An ultra-cold atomic gas is used to image a phase transition in an iron pnictide with micrometre resolution.

 2020年3月30日 星期一 上午8:00 | Jörg Wrachtrup | Nature Physics – Issue – nature.com science feeds

Nature Physics, Published online: 30 March 2020; doi:10.1038/s41567-020-0871-3

Single rare-earth ions are hard to observe and even harder to use as qubits. However, with the help of coupling to an optical cavity and clever engineering of selection rules, a big step has been taken to establish their new role in the quantum world.