# Weekly Papers on Quantum Foundations (35)

Authors: Palemkota MaithreshTejinder P. Singh

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.

Authors: Walter F. Wreszinski

We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by Robinson and Ruelle and Lanford and Robinson. An example is provided by a class of models of quantum spin systems introduced by Emch and Radin. Consequences regarding irreversibility and the time arrow, as well as possible extensions to quantum continuous systems are discussed.

Direct measurement of wave functions has attracted great interests and many different methods have been developed. However, the precision of current techniques is limited by the use of Fourier transform lenses. These measurements require to shear cut the part of particles with momentum P=0, which greatly restricts the efficiency and application of the approaches. Here, we propose and experimentally demonstrate a method to directly measure two-dimensional photonic wave functions by combining the momentum weak measurement technology and the zonal wavefront restoration algorithm. Both the Gaussian and Laguerre-Gaussian wave functions are experimentally well reconstructed. Our method avoids using the Fourier lens and post selection on the momentum P=0. We further apply it to measure wavefronts with ultra-high spatial frequency, which is difficult for traditional Shack-Hartmann wavefront sensing technologies. Our work extends the ability of quantum weak measurement and would be useful for wavefront sensing.

 下午12:42 | gr-qc updates on arXiv.org

According to the classical Penrose inequality, the mass at spatial infinity is bounded from below by a function of the area of certain trapped surfaces. We exhibit quantum field theory states that violate this relation at the semiclassical level. We formulate a Quantum Penrose Inequality, by replacing the area with the generalized entropy of the lightsheet of an appropriate quantum trapped surface. We perform a number of nontrivial tests of our proposal, and we consider and rule out alternative formulations. We also discuss the relation to weak cosmic censorhip.

There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit (observer dependent) thermal properties and possess a heat density. This suggests that spacetime, like matter, has microscopic degrees of freedom and its long wavelength limit should be described in thermodynamic language and not in a geometric language. Second clue is related to the existence of the cosmological constant. Its understanding from first principles will require the dynamical principles of the theory to be invariant under the shift $T^a_b \to T^a_b + (constant) \delta^a_b$. This puts strong constraints on the nature of gravitational dynamics and excludes metric tensor as a fundamental dynamical variable. In fact, these two clues are closely related to each other. When the dynamical principles are recast, respecting the symmetry $T^a_b \to T^a_b + (constant) \delta^a_b$, they automatically acquire a thermodynamic interpretation related to the first clue. The first part of this review provides a pedagogical introduction to thermal properties of the horizons, including some novel derivations. The second part describes some aspects of cosmological constant problem and the last part provides a perspective on gravity which takes into account these principles.

Authors: John F. DonoghueGabriel Menezes

Causality in quantum field theory is defined by the vanishing of field commutators for space-like separations. However, this does not imply a direction for causal effects. Hidden in our conventions for quantization is a connection to the definition of an arrow of causality, i.e. what is the past and what is the future. If we mix quantization conventions within the same theory, we get a violation of microcausality. In such a theory with mixed conventions the dominant definition of the arrow of causality is determined by the stable states. In some quantum gravity theories, such as quadratic gravity and possibly asymptotic safety, such a mixed causality condition occurs. We discuss some of the implications.

 2019年9月5日 星期四 上午8:00 | Latest Results for Synthese

### Abstract

Must a theory of quantum gravity have some truth to it if it can recover general relativity in some limit of the theory? This paper answers this question in the negative by indicating that general relativity is multiply realizable in quantum gravity. The argument is inspired by spacetime functionalism—multiple realizability being a central tenet of functionalism—and proceeds via three case studies: induced gravity, thermodynamic gravity, and entanglement gravity. In these, general relativity in the form of the Einstein field equations can be recovered from elements that are either manifestly multiply realizable or at least of the generic nature that is suggestive of functions. If general relativity, as argued here, can inherit this multiple realizability, then a theory of quantum gravity can recover general relativity while being completely wrong about the posited microstructure. As a consequence, the recovery of general relativity cannot serve as the ultimate arbiter that decides which theory of quantum gravity that is worthy of pursuit, even though it is of course not irrelevant either qua quantum gravity. Thus, the recovery of general relativity in string theory, for instance, does not guarantee that the stringy account of the world is on the right track; despite sentiments to the contrary among string theorists.

 2019年9月3日 星期二 上午8:00 | Latest Results for Foundations of Physics

### Abstract

The debate on the conventionality of simultaneity and the debate on the dimensionality of the world have been central in the philosophy of special relativity. The link between both debates however has rarely been explored. The purpose of this paper is to gauge what implications the former debate has for the latter. I show the situation to be much more subtle than was previously argued, and explain how the ontic versus epistemic distinction in the former debate impacts the latter. Despite claims to the contrary, I conclude that special relativity leaves the debate on the dimensionality of the world underdetermined.

 2019年9月3日 星期二 上午8:00 | Latest Results for Synthese

### Abstract

We critically analyze the rationale of arguments from finetuning and naturalness in particle physics and cosmology, notably the small values of the mass of the Higgs-boson and the cosmological constant. We identify several new reasons why these arguments are not scientifically relevant. Besides laying out why the necessity to define a probability distribution renders arguments from naturalness internally contradictory, it is also explained why it is conceptually questionable to single out assumptions about dimensionless parameters from among a host of other assumptions. Some other numerological coincidences and their problems are also discussed.

 2019年9月3日 星期二 上午8:00 | Saleem Denholme | Nature Physics – Issue – nature.com science feeds

Nature Physics, Published online: 03 September 2019; doi:10.1038/s41567-019-0654-x

Conditional convergence of maths and physics

 2019年9月3日 星期二 上午12:25 | Philsci-Archive: No conditions. Results ordered -Date Deposited.
Shaw, Robert (2019) Stern-Gerlach: conceptually clean or acceptably vague? [Preprint]
 2019年9月1日 星期日 上午10:55 | Philsci-Archive: No conditions. Results ordered -Date Deposited.
Bacciagaluppi, Guido (2019) Unscrambling Subjective and Epistemic Probabilities. [Preprint]
 2019年9月1日 星期日 上午10:53 | Philsci-Archive: No conditions. Results ordered -Date Deposited.
Suárez, Mauricio (2019) Explanatory Chance. [Preprint]