Weyl and the Problem of Space

Weyl and the Problem of Space
Author: Julien Bernard
Publisher: Springer Nature
Total Pages: 418
Release: 2019-10-09
Genre: Science
ISBN: 3030115275

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This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington). This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.

Space, Time, Matter

Space, Time, Matter
Author: Hermann Weyl
Publisher:
Total Pages: 380
Release: 1922
Genre: Relativity (Physics)
ISBN:

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Mind and Nature

Mind and Nature
Author: Hermann Weyl
Publisher: University of Pennsylvania Press
Total Pages: 112
Release: 2015-09-30
Genre: Philosophy
ISBN: 1512819328

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A new study of the mathematical-physical mode of cognition.

Phenomenological Approaches to Physics

Phenomenological Approaches to Physics
Author: Harald A. Wiltsche
Publisher: Springer Nature
Total Pages: 263
Release: 2020-06-23
Genre: Science
ISBN: 3030469735

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This book offers fresh perspective on the role of phenomenology in the philosophy of physics which opens new avenues for discussion among physicists, "standard" philosophers of physics and philosophers with phenomenological leanings. Much has been written on the interrelations between philosophy and physics in the late 19th and early 20th century, and on the emergence of philosophy of science as an autonomous philosophical sub-discipline. This book is about the under-explored role of phenomenology in the development and the philosophical interpretation of 20th century physics. Part 1 examines questions about the origins and value of phenomenological approaches to physics. Does the work of classical phenomenologists such as Husserl, Merleau-Ponty or Heidegger contain elements of systematic value to both the practice and our philosophical understanding of physics? How did classical phenomenology influence “standard” philosophy of science in the Anglo-American and other traditions? Part 2 probes questions on the role of phenomenology in the philosophies of physics and science: - Can phenomenology help to solve “Wigner’s puzzle”, the problem of the "unreasonable effectiveness" of mathematics in describing, explaining and predicting empirical phenomena? - Does phenomenology allow better understanding of the principle of gauge invariance at the core of the standard model of contemporary particle physics? - Does the phenomenological notion of “Lifeworld” stand in opposition to the “scientific metaphysics” movement, or is there potential for dialogue? Part 3 examines the measurement problem. Is the solution outlined by Fritz London and Edmond Bauer merely a re-statement of von Neumann’s view, or should it be regarded as a distinctively phenomenological take on the measurement problem? Is phenomenology a serious contender in continuing discussions of foundational questions of quantum mechanics? Can other interpretational frameworks such as quantum Bayesianism benefit from implementing phenomenological notions such as constitution or horizonal intentionality?

Concepts of Space

Concepts of Space
Author: Max Jammer
Publisher: Courier Corporation
Total Pages: 289
Release: 2013-08-16
Genre: Science
ISBN: 0486166473

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Historical surveys consider Judeo-Christian notions of space, Newtonian absolute space, perceptions from 18th century to the present, more. Numerous quotations and references. "Admirably compact and swiftly paced style." — Philosophy of Science.

The Concept of a Riemann Surface

The Concept of a Riemann Surface
Author: Hermann Weyl
Publisher: Courier Corporation
Total Pages: 210
Release: 2013-12-31
Genre: Mathematics
ISBN: 048613167X

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This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.

Thinking About Space and Time

Thinking About Space and Time
Author: Claus Beisbart
Publisher: Springer Nature
Total Pages: 277
Release: 2020-09-25
Genre: Mathematics
ISBN: 3030477827

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This volume offers an integrated understanding of how the theory of general relativity gained momentum after Einstein had formulated it in 1915. Chapters focus on the early reception of the theory in physics and philosophy and on the systematic questions that emerged shortly after Einstein's momentous discovery. They are written by physicists, historians of science, and philosophers, and were originally presented at the conference titled Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity, held at the University of Bern from September 12-14, 2017. By establishing the historical context first, and then moving into more philosophical chapters, this volume will provide readers with a more complete understanding of early applications of general relativity (e.g., to cosmology) and of related philosophical issues. Because the chapters are often cross-disciplinary, they cover a wide variety of topics related to the general theory of relativity. These include: Heuristics used in the discovery of general relativity Mach's Principle The structure of Einstein's theory Cosmology and the Einstein world Stability of cosmological models The metaphysical nature of spacetime The relationship between spacetime and dynamics The Geodesic Principle Symmetries Thinking About Space and Time will be a valuable resource for historians of science and philosophers who seek a deeper knowledge of the (early and later) uses of general relativity, as well as for physicists and mathematicians interested in exploring the wider historical and philosophical context of Einstein's theory.

Hermann Weyl’s Raum - Zeit - Materie and a General Introduction to His Scientific Work

Hermann Weyl’s Raum - Zeit - Materie and a General Introduction to His Scientific Work
Author: Erhard Scholz
Publisher: Birkhäuser
Total Pages: 406
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034882785

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Historical interest and studies of Weyl's role in the interplay between 20th-century mathematics, physics and philosophy have been increasing since the middle 1980s, triggered by different activities at the occasion of the centenary of his birth in 1985, and are far from being exhausted. The present book takes Weyl's "Raum - Zeit - Materie" (Space - Time - Matter) as center of concentration and starting field for a broader look at his work. The contributions in the first part of this volume discuss Weyl's deep involvement in relativity, cosmology and matter theories between the classical unified field theories and quantum physics from the perspective of a creative mind struggling against theories of nature restricted by the view of classical determinism. In the second part of this volume, a broad and detailed introduction is given to Weyl's work in the mathematical sciences in general and in philosophy. It covers the whole range of Weyl's mathematical and physical interests: real analysis, complex function theory and Riemann surfaces, elementary ergodic theory, foundations of mathematics, differential geometry, general relativity, Lie groups, quantum mechanics, and number theory.

Space - Time - Matter

Space - Time - Matter
Author: Hermann Weyl
Publisher: Createspace Independent Publishing Platform
Total Pages: 348
Release: 2018-01-19
Genre:
ISBN: 9781984040251

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From the PREFACE TO THE FOURTH EDITION. IN this edition the book has on the whole preserved its general form, but there are a number of small changes and additions, the most important of which are: (1) A paragraph added to Chapter II in which the problem of space is formulated in conformity with the view of the Theory of Groups; we endeavour to arrive at an understanding of the inner necessity and uniqueness of Pythagorean space metrics based on a quadratic differential form. (2) We show that the reason that Einstein arrives necessarily at uniquely determined gravitational equations is that the scalar of curvature is the only invariant having a certain character in Riemann's space. (3) In Chapter IV the more recent experimental researches dealing with the general theory of relativity are taken into consideration, particularly the deflection of rays of light by the gravitational field of the sun, as was shown during the solar eclipse of 29th May, 1919, the results of which aroused great interest in the theory on all sides. (4) With Mie's view of matter there is contrasted another (vide particularly � 32 and �36), according to which matter is a limiting singularity of the field, but charges and masses are force-fluxes in the field. This entails a new and more cautious attitude towards the whole problem of matter. Thanks are due to various known and unknown readers for pointing out desirable modifications, and to Professor Nielsen (at Breslau) for kindly reading the proof-sheets. --HERMANN WEYL

The Continuum

The Continuum
Author: Hermann Weyl
Publisher: Courier Corporation
Total Pages: 165
Release: 1994-01-01
Genre: Mathematics
ISBN: 0486679829

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Concise classic by great mathematician and physicist deals with logic and mathematics of set and function, concept of number and the continuum. Bibliography. Originally published 1918.