# Weekly Papers on Quantum Foundations (26)

Gao, Shan (2022) On Bell’s Everett (?) theory. [Preprint]

Earman, John (2022) Trace-Free Gravitational Theory (aka Unimodular Gravity) for Philosophers. [Preprint]

Chen, Eddy Keming and Goldstein, Sheldon (2022) Governing Without A Fundamental Direction of Time: Minimal Primitivism about Laws of Nature. Ben-Menahem, Y. (eds.). Rethinking the Concept of Law of Nature. pp. 21-64.

Baker, David John (2022) The Epiphenomena Argument for Symmetry-to-Reality Inference. In: UNSPECIFIED.

Generalized Gleason theorem and finite amount of information for the context. (arXiv:2206.11830v1 [quant-ph])

Quantum processes cannot be reduced, in a nontrivial way, to classical processes without specifying the context in the description of a measurement procedure. This requirement is implied by the Kochen-Specker theorem in the outcome-deterministic case and, more generally, by the Gleason theorem. The latter establishes that there is only one non-contextual classical model compatible with quantum theory, the one that trivially identifies the quantum state with the classical state. However, this model requires a breaking of the unitary evolution to account for macroscopic realism. Thus, a causal classical model compatible with the unitary evolution of the quantum state is necessarily contextual at some extent. Inspired by well-known results in quantum communication complexity, we consider a particular class of hidden variable theories by assuming that the amount of information about the measurement context is finite. Aiming at establishing some general features of these theories, we first present a generalized version of the Gleason theorem and provide a simple proof of it. Assuming that Gleason’s hypotheses hold only locally for small’ changes of the measurement procedure, we obtain almost the same conclusion of the original theorem about the functional form of the probability measure. An additional constant and a relaxed property of the density operator’ are the only two differences from the original result. By this generalization of the Gleason theorem and the assumption of finite information for the context, we prove that the probabilities over three or more outcomes of a projective measurement must be linear functions of the projectors associated with the outcomes, given the information on the context.

The double doors of the horizon. (arXiv:2206.11870v1 [gr-qc])

In statistical mechanics entropy is a measure of disorder obeying Boltzmann’s formula $S=\log{\cal N}$, where ${\cal N}$ is the accessible phase space volume. In black hole thermodynamics one associates to a black hole an entropy Bekenstein-Hawking $S_{BH}$. It is well known that $S_{BH}$ is very large for astrophysical black holes, much larger than any collection of material objects that could have given rise to the black hole. If $S_{BH}$ is an entropy the question is thus what is the corresponding ${\cal N}$, and how come this very large phase space volume is only opened up to the universe by a gravitational collapse, which from another perspective looks like a massive loss of possibilities. I advance a hypothesis that the very large increase in entropy can perhaps be understood as an effect of classical gravity, which eventually bottoms out when quantum gravity comes into play. I compare and discuss a selection of the very rich literature around these questions.

The Topology and Geometry of Causality. (arXiv:2206.08911v2 [quant-ph] UPDATED)

We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our investigation proceeds from two complementary fronts: a topological one, using tools from sheaf theory, and a geometric one, based on polytopes and linear programming. From the topological perspective, we understand experimental outcome probabilities as bundles of compatible contextual data over certain topological spaces, encoding causality constraints. From the geometric perspective, we understand the same experimental outcome probabilities as points in high-dimensional causal polytopes, which we explicitly construct and fully characterise.

Our work is a significant extension of both the established Abramsky-Brandenburger framework for contextuality and the current body of work on indefinite causality. We provide definitions of causal fraction and causal separability for empirical models relative to a broad class of causal constraints: this allows us to construct and characterise novel examples which explicitly connect causal inseparability to non-locality and contextuality. In particular, we clearly demonstrate the existence of “causal contextuality”, a phenomenon where causal structure is explicitly correlated to the classical inputs and outputs of local instruments, so that contextuality of the associated empirical model directly implies causal inseparability.

A unified quantization of gravity and other fundamental forces of nature. (arXiv:2206.11367v1 [gr-qc])

Authors: Claus Gerhardt

We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Let as abbreviate the spatial Hamilton functions of the Standard Model by $H_{SM}$ and the Hamilton function of gravity by $H_G$. Working in a fiber bundle $E$ with base space $S_0=\mathbb{R}[n]$, where the fiber elements are Riemannian metrics, we can express the Hamilton functions in the form $H_G+H_{SM}=H_G+t^{-\frac23}\tilde H_{SM}$ if $n=3$, where $\tilde H_{SM}$ depends on metrics $\sigma_{ij}$ satisfying $\det{\sigma_{ij}}=1$. In the quantization process, we quantize $H_G$ for general $\sigma_{ij}$ but $\tilde H_{SM}$ only for $\sigma_{ij}=\delta_{ij}$ by the usual methods of QFT. Let $v$ resp. $\psi$ be the spatial eigendistributions of the respective Hamilton operators, then, the solutions $u$ of the Wheeler-DeWitt equation are given by $u=wv\psi$, where $w$ satisfies an ODE and $u$ is evaluated at $(t,\delta_{ij})$ in the fibers.

Lifshitz symmetry: Lie algebras, spacetimes and particles. (arXiv:2206.11806v1 [hep-th])

We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (“particles”) of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name “Lifshitz Lie algebras”. We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes:

(1) ($d+2$)-dimensional Lifshitz spacetimes which have one additional holographic direction;

(2) ($d+1$)-dimensional Lifshitz–Weyl spacetimes which can be seen as the boundary geometry of the spacetimes in (1) and where the scalar generator is interpreted as an anisotropic dilation; and

(3) ($d+1$)-dimensional aristotelian spacetimes with one scalar charge, including exotic fracton-like symmetries that generalise multipole algebras.

We also classify the possible central extensions of Lifshitz Lie algebras and we discuss the homogeneous symplectic manifolds of Lifshitz Lie groups in terms of coadjoint orbits.

Cosmological bounce and the cosmological constant problem. (arXiv:2112.09523v3 [gr-qc] UPDATED)

Authors: Petar PavlovićMarko Sossich

We discuss how the modifications of the standard Einstein’s equations needed to support the cosmological bounce can at the same time lead to vanishing of the well known cosmological constant problem, while also studying the effects of spacetime fluctuations. We first concentrate on the case of the classical FLRW spacetime and show that in a bouncing cosmology, where the modification of the Einstein-Hilbert action can be represented by the most general function needed to support the bounce, the cosmological constant problem is absent if this function at late cosmological times approaches a sufficiently large value. We show that this result is general and does not depend on the details of modifications needed to support the cosmological bounce. Motivated by the recent studies of cosmological constant problem in the context of quantum vacuum and spacetime fluctuations in the standard cosmology, we then generalize our study to incorporate the effects of spacetime fluctuations. We show that some problems of the earlier proposals, like singularities and negative values of the scale factor, are also naturally resolved in the approach proposed here.

The Status of the Born Rule and the Role of Gleason’s Theorem and Its Generalizations: How the Leopard Got Its Spots and Other Just-So Stories

Earman, John (2022) The Status of the Born Rule and the Role of Gleason’s Theorem and Its Generalizations: How the Leopard Got Its Spots and Other Just-So Stories. [Preprint]

The Local Validity of Special Relativity, Part 2: Matter Dynamics

Fletcher, Samuel C. and Weatherall, James Owen (2022) The Local Validity of Special Relativity, Part 2: Matter Dynamics. [Preprint]

The Local Validity of Special Relativity, Part 1: Geometry

Fletcher, Samuel C. and Weatherall, James Owen (2022) The Local Validity of Special Relativity, Part 1: Geometry. [Preprint]

On the Common Logical Structure of Classical and Quantum Mechanics

Oldofredi, Andrea and Carcassi, Gabriele and Aidala, Christine A (2022) On the Common Logical Structure of Classical and Quantum Mechanics. [Preprint]

How analogy helped create the new science of thermodynamics

Abstract

Sadi Carnot’s 1824 Reflections on the Motive Power of Fire created the new science of thermodynamics. It succeeded in its audacious goal of finding a very general theory of the efficiency of heat engines, by introducing and exploiting the strange and unexpected notion of a thermodynamically reversible process. The notion is internally contradictory. It requires the states of these processes to be both in unchanging equilibrium, with a perfect balance of driving forces, while also changing. The work of Sadi’s father, Lazare Carnot, on the efficiency of ordinary machines provided Sadi with a template of a very general theory of the efficiency of ordinary machines; and a characterization of the most efficient processes in them as those that minimize differences of driving forces and can be run in reverse. Lazare’s work could provide these resources because of its choice of a dissipative ontology of inelastic collisions among hard bodies. This historically ill-fated choice meant that Lazare’s machines were analogous to Sadi’s heat engines in their key aspects: they are built from essentially dissipative processes. Lazare’s strategies for controlling dissipation and optimizing his machines were transferrable to the analogous problems Sadi found in heat engines. The unanswerable historical question is whether Sadi would have sought a general theory of heat engines at all or found these general theoretical devices without the template provided in analogy by the prior work of Lazare.

Empirical Study of PhilSci Archive Postings from Three Journals

Chattoraj, Ananya and Hanley, Brian J and Waters, C. Kenneth (2022) Empirical Study of PhilSci Archive Postings from Three Journals. [Preprint]

Emergent Realities: Diffracting Barad within a quantum-realist ontology of matter and politics

Everth, Thomas and Gurney, Laura (2022) Emergent Realities: Diffracting Barad within a quantum-realist ontology of matter and politics. [Preprint]

Believing Conspiracy Theories: A Bayesian Approach to Belief Protection

Poth, Nina and Dolega, Krzysztof (2022) Believing Conspiracy Theories: A Bayesian Approach to Belief Protection. [Preprint]

The Origins of Consciousness or the War of the Five Dimensions (Preprint)

Veit, Walter (2022) The Origins of Consciousness or the War of the Five Dimensions (Preprint). [Preprint]

Mathematical formalism for nonlocal spontaneous collapse in quantum field theory

Snoke, David (2022) Mathematical formalism for nonlocal spontaneous collapse in quantum field theory. [Preprint]

Entanglement Detection with Imprecise Measurements

Author(s): Simon Morelli, Hayata Yamasaki, Marcus Huber, and Armin Tavakoli

We investigate entanglement detection when the local measurements only nearly correspond to those intended. This corresponds to a scenario in which measurement devices are not perfectly controlled, but nevertheless operate with bounded inaccuracy. We formalize this through an operational notion of i…

[Phys. Rev. Lett. 128, 250501] Published Tue Jun 21, 2022

arXiv:2206.11055 (quant-ph)[Submitted on 22 Jun 2022]

C Dedes

Born’s rule and permutation invariance

It is shown that the probability density satisfies a hyperbolic equation of motion with the unique characteristic that in its many-particle form it contains derivatives acting at spatially remote regions. Based on this feature we explore inter-particle correlations and the relation between the quantum equilibrium condition and the permutation invariance of the probability density. Some remarks with respect to the quantum to classical transition are also presented.