Weyl׳s search for a difference between ‘physical’ and ‘mathematical’ automorphisms

Scholz, Erhard

doi:10.1016/j.shpsb.2017.04.003

Cited by 6 publications

(3 citation statements)

References 41 publications

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“…This confrontation with nature 'as a whole', concerns the harmony, or "concordance" (p. 62), that a given theoretical construction brings to our understanding of nature, and not all extensions of the basic group structures of modern physics will lead to novel physical insight (e.g. see Scholz (2018)). Thus, on Weyl's view, physics is in a continual process of development, searching the domain of structural extensions for those that lead to a more encompassing picture of 'reality'.…”

Section: Weyl's Philosophy Of Science and The Gauge Argumentmentioning

confidence: 99%

Mathematical Analogies in Physics: The Curious Case of Gauge Symmetries

Hetzroni

Stemeroff

2022

Jerusalem Studies in Philosophy and History of Science

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Gauge symmetries provide one of the most puzzling examples of the applicability of mathematics in physics. The presented work focuses on the role of analogical reasoning in the gauge argument, motivated by Mark Steiner's claim that the application of the gauge principle relies on a Pythagorean analogy whose success undermines naturalist philosophy. In this paper, we present two different views concerning the analogy between gravity, electromagnetism, and nuclear interactions, each providing a different philosophical response to the problem of the applicability of mathematics in the natural sciences. The first is based on an account of Weyl's original work, which first gave rise to the gauge principle. Drawing on his later philosophical writings, we develop an idelaist reading of the mathematical analogies in the gauge argument. On this view, mathematical analogies serve to ensure a conceptual harmony in our scientific account of nature. We further discuss the construction of Yang and Mills's gauge theory in light of this idealist reading. The second account presents a naturalist alternative, formulated in terms of John Norton's account of a material analogy, according to which the analogy succeeds in virtue of a physical similarity between the different interactions. This account is based on the methodological equivalence principle, a simple conceptual extension of the gauge principle that allows us to understand the relation between coordinate transformations and gravity as a manifestation of the same method. The physical similarity between the different cases is based on attributing the success of this method to the dependence of the coupling on relational physical quantities. We conclude by reflecting on the advantages and limits of the idealist, naturalist, and anthropocentric

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Section: Weyl's Philosophy Of Science and The Gauge Argumentmentioning

confidence: 99%

Mathematical Analogies in Physics: The Curious Case of Gauge Symmetries

Hetzroni

Stemeroff

2022

Jerusalem Studies in Philosophy and History of Science

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“…Operational-invariance in physical theories capture exactly this requirement in mathematical terms. In this case, the mathematical representation of the state of a system (i.e., the object in a specific situation) is given from a specific reference frame (or basis) which can be consistently translated into any other reference frame (or basis) (see for a detailed analysis [29,30,66]). While in the case of classical mechanics this translation is provided by the Galilean transformations, in the case of relativity theory this is given through the Lorentz transformations.…”

Section: An Objective Relational Definition Of Quantum Entanglementmentioning

confidence: 99%

Relational Quantum Entanglement Beyond Non-Separable and Contextual Relativism

Ronde¹,

Massri²

2020

Preprint

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In this paper we address the relativist-perspectival nature of the orthodox definition of quantum entanglement in terms of preferred factorizations. We also consider this aspect aspect within the generalized definition of entanglement proposed by Barnum et al. [6,7] in terms of preferred observables. More specifically, we will discuss the non-separable relativism implied by the orthodox definition of entanglement, the contextual relativism implied by its generalization as well as some other serious problems presently discussed within the specialized literature. In the second part of this work, we address a recently proposed objective-invariant definition of entanglement understood as the actual and potential coding of effective and intensive relations [32]. Through the derivation of two theorems we will show explicitly how this new objective definition of entanglement is able to escape both non-separable relativism and contextual relativism. According to these theorems, within this proposed relational definition, all possible subsets of observables as well as all possible factorizations can be globally considered as making reference to the same (potential) state of affairs. The conclusion is that, unlike with the orthodox definitions, this new objective-relational notion of entanglement is able to bypass relativism right from the start opening the door to a realist understanding of quantum correlations.

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“…14 Cf. (Scholz 2016b) 15 (Cogliati 2015, Nabonnand 2016, Scholz 2016a; for a modern mathematical introduction to Cartan geometry see (Sharpe 1997). geometry (homogeneous in the sense of F. Klein) by motivating T. Levi-Civita's concept of infinitesimal parallelism, he did not yet see the gap closed. 16 Cartan alluded to the Kleinean understanding of homogeneity and indicated the idea underlying his approach:…”

Section: Homogeneity Characterizations Given By Weylmentioning

confidence: 99%

The Changing Faces of the Problem of Space in the Work of Hermann Weyl

Scholz

2019

Studies in History and Philosophy of Science

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During his life Weyl approached the problem of space (PoS) from various sides. Two aspects stand out as permanent features of his different approaches: the unique determination of an affine connection (i.e., without torsion in the terminology of Cartan) and the question which type of group characterizes physical space. The first feature came up in 1919 (commentaries to Riemann's inaugural lecture) and played a crucial role in Weyl's work on the PoS in the early 1920s. He defended the central role of affine connections even in the light of Cartan's more general framework of connections with torsion. In later years, after the rise of the Dirac field, it could have become problematic, but Weyl saw the challenge posed to Einstein gravity by spin coupling primarily in the possibility to allow for non-metric affine connections. Only after Weyl's death Cartan's approach to infinitesimal homogeneity and torsion became revitalized in gravity theories.

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Weyl׳s search for a difference between ‘physical’ and ‘mathematical’ automorphisms

Cited by 6 publications

References 41 publications

Mathematical Analogies in Physics: The Curious Case of Gauge Symmetries

Mathematical Analogies in Physics: The Curious Case of Gauge Symmetries

Relational Quantum Entanglement Beyond Non-Separable and Contextual Relativism

The Changing Faces of the Problem of Space in the Work of Hermann Weyl

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