# Weekly Papers on Quantum Foundations (8)

Review of Mark Wilson, Physics Avoidance

Fraser, Doreen (2021) Review of Mark Wilson, Physics Avoidance. [Preprint]

Fundamental Nomic Vagueness

Chen, Eddy Keming (2021) Fundamental Nomic Vagueness. [Preprint]

From Ramanujan to renormalization: the art of doing away with divergences and arriving at physical results. (arXiv:2102.09371v1 [physics.hist-ph])

Authors: Wolfgang Bietenholz

A century ago Srinivasa Ramanujan – the great self-taught Indian genius of mathematics – died, shortly after returning from Cambridge, UK, where he had collaborated with Godfrey Hardy. Ramanujan contributed numerous outstanding results to different branches of mathematics, like analysis and number theory, with a focus on special functions and series. Here we refer to apparently weird values which he assigned to two simple divergent series, $\sum_{n \geq 1} n$ and $\sum_{n \geq 1} n^{3}$. These values are sensible, however, as analytic continuations, which correspond to Riemann’s $\zeta$-function. Moreover, they have applications in physics: we discuss the vacuum energy of the photon field, from which one can derive the Casimir force, which has been experimentally measured. We also discuss its interpretation, which remains controversial. This is a simple way to illustrate the concept of renormalization, which is vital in quantum field theory.

Agreement between observers: a physical principle?. (arXiv:2102.08966v1 [quant-ph])

Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the post-quantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann’s seminal Agreement Theorem states that two (classical) agents cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for quantum agents, while we construct examples of (post-quantum) no-signaling boxes where agents can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.

Formalization of Bohr’s contextuality within theory of open quantum systems. (arXiv:2102.09184v1 [quant-ph])

In quantum physics, the notion of contextuality has a variety of interpretations which are typically associated with the names of their inventors, say Bohr, Bell, Kochen and Specker, and recently Dzhafarov. In fact, Bohr was the first who pointed to contextuality of quantum measurements as a part of formulation of his principle of complementarity. (Instead of “contextuality”, he considered dependence on “experimental conditions.”) Unfortunately, the contextuality counterpart of the complementarity principle was overshadowed by the issue of incompatibility of observables. And the interest for contextuality of quantum measurements rose again only in connection with the Bell inequality. The original Bohr’s contextuality, as contextuality of each quantum measurement, was practically forgotten. It was highlighted in the works of the author of this paper, with applications both to physics and cognition. In this note, the theory of open quantum systems is applied to formalization of Bohr’s contextuality within the the scheme of indirect measurements. This scheme is widely used in quantum information theory and it leads to the theory of quantum instruments (Davis-Lewis-Ozawa). In this scheme, Bohr’s viewpoint on contextuality of quantum measurements is represented in the formal mathematical framework.

The Wavefunction of Continuous-Time Recurrent Neural Networks. (arXiv:2102.09399v1 [cs.LG])

In this paper, we explore the possibility of deriving a quantum wavefunction for continuous-time recurrent neural network (CTRNN). We did this by first starting with a two-dimensional dynamical system that describes the classical dynamics of a continuous-time recurrent neural network, and then deriving a Hamiltonian. After this, we quantized this Hamiltonian on a Hilbert space $\mathbb{H} = L^2(\mathbb{R})$ using Weyl quantization. We then solved the Schrodinger equation which gave us the wavefunction in terms of Kummer’s confluent hypergeometric function corresponding to the neural network structure. Upon applying spatial boundary conditions at infinity, we were able to derive conditions/restrictions on the weights and hyperparameters of the neural network, which could potentially give insights on the the nature of finding optimal weights of said neural networks.

Putting a Spin on Language: A Quantum Interpretation of Unary Connectives for Linguistic Applications. (arXiv:2004.04128v2 [cs.CL] UPDATED)

Extended versions of the Lambek Calculus currently used in computational linguistics rely on unary modalities to allow for the controlled application of structural rules affecting word order and phrase structure. These controlled structural operations give rise to derivational ambiguities that are missed by the original Lambek Calculus or its pregroup simplification. Proposals for compositional interpretation of extended Lambek Calculus in the compact closed category of FVect and linear maps have been made, but in these proposals the syntax-semantics mapping ignores the control modalities, effectively restricting their role to the syntax. Our aim is to turn the modalities into first-class citizens of the vectorial interpretation. Building on the directional density matrix semantics, we extend the interpretation of the type system with an extra spin density matrix space. The interpretation of proofs then results in ambiguous derivations being tensored with orthogonal spin states. Our method introduces a way of simultaneously representing co existing interpretations of ambiguous utterances, and provides a uniform framework for the integration of lexical and derivational ambiguity.

Unitarity in quantum cosmology: symmetries protected and violated. (arXiv:1911.11839v2 [gr-qc] UPDATED)

Authors: Sachin PandeyNarayan Banerjee

This work deals with the violation or retention of symmetries associated with the self-adjoint extension of the Hamiltonian for homogeneous but anisotropic Bianchi I cosmological model. This extension is required to make sure the quantum evolution is unitary. It is found that the scale invariance is lost, but the Noether symmetries are preserved.

An Experiment for Observing Quantum Gravity Phenomena using Twin Table-Top 3D Interferometers. (arXiv:2008.04957v2 [gr-qc] UPDATED)

Theories of quantum gravity based on the holographic principle predict the existence of quantum fluctuations of distance measurements that accumulate and exhibit correlations over macroscopic distances. This paper models an expected signal due to this phenomenology, and details the design and estimated sensitivity of co-located twin table-top 3D interferometers being built to measure or constrain it. The experiment is estimated to be sensitive to displacements $\sim10^{-19}\,\rm{m}/\sqrt{\rm{Hz}}$ in a frequency band between 1 and 250 MHz, surpassing previous experiments and enabling the possible observation of quantum gravity phenomena. The experiment will also be sensitive to MHz gravitational waves and various dark matter candidates.

Quick thinking: how Einstein did (and did not) refute the ether frame of reference

Abstract

This paper addresses and proposes to resolve a longstanding problem in the philosophy of physics: whether and in what sense Albert Einstein’s Chasing the Light thought experiment was significant in the development of the theory of special relativity. Although Einstein granted this thought experiment pride of place in his 1949 Autobiographical Notes, philosophers and physicists continue to debate about what, if anything, the experiment establishes. I claim that we ought to think of Chasing the Light as Einstein’s first attempt to problematize the very idea of the electromagnetic ether frame, and that it thereby contributed to his eventual adoption of one of special relativity’s two foundational axioms: the “light postulate”. This interpretation requires the assumption that Einstein had presupposed special relativity’s other axiom, the “principle of relativity”, when initially considering Chasing the Light. This argument is novel insofar as it provides evidence that such a presupposition by Einstein is both conceptually and historically plausible. Moreover, this paper directly challenges John D. Norton’s compelling claim that Chasing the Light is best understood as a refutation of emission theories of light propagation; while both interpretations of the experiment are conceptually coherent, I argue that the interpretation found in this paper is supported more straightforwardly by historical evidence.

The visibility of philosophy of science in the sciences, 1980–2018

Abstract

In this paper, we provide a macro level analysis of the visibility of philosophy of science in the sciences over the last four decades. Our quantitative analysis of publications and citations of philosophy of science papers, published in 17 main journals representing the discipline, contributes to the longstanding debate on the influence of philosophy of science on the sciences. It reveals the global structure of relationships that philosophy of science maintains with science, technology, engineering and mathematics (STEM) and social sciences and humanities (SSH) fields. Explored at the level of disciplines, journals and authors, this analysis of the relations between philosophy of science and a large and diversified array of disciplines allows us to answer several questions: what is the degree of openness of various disciplines to the specialized knowledge produced in philosophy of science? Which STEM and SSH fields and journals have privileged ties with philosophy of science? What are the characteristics, in terms of citation and publication patterns, of authors who get their philosophy of science papers cited outside their field? Complementing existing qualitative inquiries on the influence of specific authors, concepts or topics of philosophy of science, the bibliometric approach proposed in this paper offers a comprehensive portrait of the multiple relationships that links philosophy of science to the sciences.

“Super-Heisenberg” and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field

Author(s): Zhibo Hou, Yan Jin, Hongzhen Chen, Jun-Feng Tang, Chang-Jiang Huang, Haidong Yuan, Guo-Yong Xiang, Chuan-Feng Li, and Guang-Can Guo

The Heisenberg scaling, which scales as N−1 in terms of the number of particles or T−1 in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as “super-Heisenberg scaling,” however, can also arise when the generator of the parameter involves many-…

[Phys. Rev. Lett. 126, 070503] Published Thu Feb 18, 2021

Probing theoretical statements with thought experiments

Abstract

Many thought experiments (TEs) are used to probe theoretical statements. One crucial strategy for doing this, or so I will argue, is the following. A TE reveals an inconsistency in part of our previously held, sometimes empirically well-established, theoretical statements. A TEer or her critic then proposes a resolution in the form of a conjecture, a hypothesis that merits further investigation. To explore this characterisation of the epistemic function of such TEs, I clarify the nature of the inconsistencies revealed by TEs, and how TEs reveal and resolve them. I argue that this can be done without settling the question of which cognitive processes are involved in performing a TE; be they propositional or non-propositional. The upshot is that TEs’ reliability, like real experiments, is to be found, in part, in their replicability by the epistemic community, not in their cognitive underpinnings.

On Absolute Units

Dewar, Neil (2020) On Absolute Units. [Preprint]

A critical analysis of Markovian monism

Abstract

Free Energy Principle underlies a unifying framework that integrates theories of origins of life, cognition, and action. Recently, FEP has been developed into a Markovian monist perspective (Friston et al. in BC 102: 227–260, 2020). The paper expresses scepticism about the validity of arguments for Markovian monism. The critique is based on the assumption that Markovian models are scientific models, and while we may defend ontological theories about the nature of scientific models, we could not read off metaphysical theses about the nature of target systems (self-organising conscious systems, in the present context) from our theories of nature of scientific models (Markov blankets). The paper draws attention to different ways of understanding Markovian models, as material entities, fictional entities, and mathematical structures. I argue that none of these interpretations contributes to the defence of a metaphysical stance (either in terms of neutral monism or reductive physicalism). This is because scientific representation is a sophisticated process, and properties of Markovian models—such as the property of being neither physical nor mental—could not be projected onto their targets to determine the ontological properties of targets easily.

Mathematical Anti-Realism and Explanatory Structure

Whittle, Bruno (2021) Mathematical Anti-Realism and Explanatory Structure. [Preprint]

Sensitive spin seeks single magnon

Nature Physics, Published online: 15 February 2021; doi:10.1038/s41567-021-01176-5

A quantum dot has been used to detect a single excitation among the tens of thousands of atomic nuclear spins comprising it. This result is an important step towards treating nuclear spins as a quantum memory rather than a troublesome source of noise.