Formal and physical equivalence in two cases in contemporary quantum physics

The application of analytic continuation in quantum field theory (QFT) is juxtaposed to T-duality and mirror symmetry in string theory. Analytic continuation—a mathematical transformation that takes the time variable t to negative imaginary time—it—was initially used as a mathematical technique for solving perturbative Feynman diagrams, and was subsequently the basis for the Euclidean approaches within mainstream QFT (e.g., Wilsonian renormalization group methods, lattice gauge theories) and the Euclidean field theory program for rigorously constructing non-perturbative models of interacting QFTs. A crucial difference between theories related by duality transformations and those related by analytic continuation is that the former are judged to be physically equivalent while the latter are regarded as physically inequivalent. There are other similarities between the two cases that make comparing and contrasting them a useful exercise for clarifying the type of argument that is needed to support the conclusion that dual theories are physically equivalent. In particular, T-duality and analytic continuation in QFT share the criterion for predictive equivalence that two theories agree on the complete set of expectation values and the mass spectra and the criterion for formal equivalence that there is a “translation manual” between the physically significant algebras of observables and sets of states in the two theories. The analytic continuation case study illustrates how predictive and formal equivalence are compatible with physical inequivalence, but not in the manner of standard underdetermination cases. Arguments for the physical equivalence of dual theories must cite considerations beyond predictive and formal equivalence. The analytic continuation case study is an instance of the strategy of developing a physical theory by extending the formal or mathematical equivalence with another physical theory as far as possible. That this strategy has resulted in developments in pure mathematics as well as theoretical physics is another feature that this case study has in common with dualities in string theory.     

New tools for theory choice and theory diagnosis

Theory choice can be approached in at least four ways. One of these calls for the application of decision theory, and this article endorses this approach. But applying standard forms of decision theory imposes an overly demanding standard of numeric information, supposedly satisfied by point-valued utility and probability functions. To ameliorate this difficulty, a version of decision theory that requires merely comparative utilities and plausibilities is proposed. After a brief summary of this alternative, the article illustrates how comparative decision theory affords a rational reconstruction of decisions made by exemplary scientists in two cases of theory choice: Buffon’s law and the luminiferous ether. It also offers a rational reconstruction of two cases of theory diagnosis: Mendeleev’s anomalies and the Pioneer anomaly.     

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II: The search of the interface between QFT and QG

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior.Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper.     

Failure of ontological excess baggage as a criterion of the ontic approaches to quantum theory

This article presents a discussion of the notion of quantum ontological excess baggage, first proposed by Hardy. It is argued here that this idea does not have the significance suggested in his paper. It is shown that if this concept is properly analyzed, it fails to pose any threat to the ontic approach to quantum theory in general.     

Reduction and emergence in the fractional quantum Hall state

We present the fractional quantum Hall (FQH) effect as a candidate emergent phenomenon. Unlike some other putative cases of condensed matter emergence (such as thermal phase transitions), the FQH effect is not based on symmetry breaking. Instead FQH states are part of a distinct class of ordered matter that is defined topologically. Topologically ordered states result from complex long-ranged correlations between their constituent parts, such that the system displays strongly irreducible, qualitatively novel properties.     

信息几何理论与应用研究进展

信息几何是在Riemann流形上采用现代微分几何方法来研究统计学问题的基础性、前沿性学科,被誉为是继Shannon开辟现代信息理论之后的又一新的理论变革,在信息科学与系统理论研究领域展现出了巨大的发展潜力．本文首先从参数化概率分布族的内蕴几何结构特征与信息的几何性质出发,精炼了信息几何的科学内涵,指出信息几何相比于经典统计学与信息论的理论优势与方法的革新．然后简要阐述了信息几何与微分几何的联系,综述了信息几何理论的发展历史与近20年来信息几何在神经网络、统计推断、通信编码、系统理论、物理学和医学成像等各领域应用的研究现状,归纳和总结了其中所体现的信息几何的基本原理和基本方法,并对信息几何的发展给予注记．特别地,对信息几何在信号处理领域中的应用成果进行了较全面的总结和概括,阐述了信息几何在信号检测、参数估计与滤波等方面的最新研究成果．最后,展望信息几何的发展前景,提出了信息几何在信号处理领域中的若干开放性问题．     

Constraints and divergent assessments of fertility in non-empirical physics in the history of the string theory controversy

This paper examines historic appraisals of string theory to develop a less abstract understanding of the string theory controversy and assessment in non-empirical physics. This historical approach reveals several points of conflict in the controversy, each centring on a constraint. By proceeding stepwise through these constraints, I reveal the role that constraints played in determining divergent assessments of string theory. Rather than disagreement between two competing methods, a level of agreement is found amongst those critical and supportive of string theory as to the commitment to the relevant constraints, but disagreement as to the sufficiency of consistency, the path to background independence and a non-perturbative formulation, and how to interpret the significance of applications. Furthermore, the string theory community itself is shown to be divided in its commitment to the necessity of uniqueness and the legitimacy of anthropic reasoning. These varied assessments, guided by considerations of constraints, have informed divergent claims as to the past and future fertility of string theory. These are claims as to the value of string theory in guiding research in quantum gravity: claims as to whether string theory has and will be valuable as a means rather than an end.     

String theory,Einstein, and the identity of physics: Theory assessment in absence of the empirical

String theorists are certain that they are practicing physicists. Yet, some of their recent critics deny this. This paper argues that this conflict is really about who holds authority in making rational judgment in theoretical physics. At bottom, the conflict centers on the question: who is a proper physicist? To illustrate and understand the differing opinions about proper practice and identity, we discuss different appreciations of epistemic virtues and explanation among string theorists and their critics, and how these have been sourced in accounts of Einstein's biography. Just as Einstein is claimed by both sides, historiography offers examples of both successful and unsuccessful non-empirical science. History of science also teaches that times of conflict are often times of innovation, in which novel scholarly identities may come into being. At the same time, since the contributions of Thomas Kuhn historians have developed a critical attitude towards formal attempts and methodological recipes for epistemic demarcation and justification of scientific practice. These are now, however, being considered in the debate on non-empirical physics.