Download or read book Weyl and the Problem of Space written by Julien Bernard and published by Springer. This book was released on 2019-09-13 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Weyl and the Problem of Space written by Julien Bernard and published by Springer Nature. This book was released on 2019-10-09 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Space Time Matter written by Hermann Weyl and published by . This book was released on 1922 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Thinking About Space and Time written by Claus Beisbart and published by Springer Nature. This book was released on 2020-09-25 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Phenomenological Approaches to Physics written by Harald A. Wiltsche and published by Springer Nature. This book was released on 2020-06-23 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?
Download or read book Hermann Weyl s Raum Zeit Materie and a General Introduction to His Scientific Work written by Erhard Scholz and published by Springer Science & Business Media. This book was released on 2001-01-01 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Concept of a Riemann Surface written by Hermann Weyl and published by Courier Corporation. This book was released on 2013-12-31 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mind and Nature written by Hermann Weyl and published by University of Pennsylvania Press. This book was released on 2015-09-30 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new study of the mathematical-physical mode of cognition.
Download or read book Philosophy of Mathematics and Natural Science written by Hermann Weyl and published by Princeton University Press. This book was released on 2009-05-17 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: History of mathematics.
Download or read book The Concepts of Space and Time written by M. Capek and published by Springer. This book was released on 2014-11-14 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Continuum written by Hermann Weyl and published by Courier Corporation. This book was released on 1994-01-01 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Weyl Operator and its Generalization written by Leon Cohen and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar. This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner.
Download or read book Levels of Infinity written by Hermann Weyl and published by Courier Corporation. This book was released on 2013-09-26 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.
Download or read book Symmetry written by Hermann Weyl and published by Princeton University Press. This book was released on 2015-07-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations—as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.
Download or read book Radical Markets written by Eric A. Posner and published by Princeton University Press. This book was released on 2019-10-08 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revolutionary ideas on how to use markets to achieve fairness and prosperity for all Many blame today's economic inequality, stagnation, and political instability on the free market. The solution is to rein in the market, right? Radical Markets turns this thinking on its head. With a new foreword by Ethereum creator Vitalik Buterin and virtual reality pioneer Jaron Lanier as well as a new afterword by Eric Posner and Glen Weyl, this provocative book reveals bold new ways to organize markets for the good of everyone. It shows how the emancipatory force of genuinely open, free, and competitive markets can reawaken the dormant nineteenth-century spirit of liberal reform and lead to greater equality, prosperity, and cooperation. Only by radically expanding the scope of markets can we reduce inequality, restore robust economic growth, and resolve political conflicts. But to do that, we must replace our most sacred institutions with truly free and open competition—Radical Markets shows how.
Download or read book On Space and Time written by Alain Connes and published by Cambridge University Press. This book was released on 2012-03-26 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gets to the heart of science by asking a fundamental question: what is the true nature of space and time?
Download or read book Weyl Transforms written by M.W. Wong and published by Springer Science & Business Media. This book was released on 2006-03-31 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the functional analytic properties of Weyl transforms as bounded linear operators on $ L2ü(äBbb Rünü) $ in terms of the symbols of the transforms. Further, the boundedness, the compactness, the spectrum and the functional calculus of the Weyl transform are proved in detail, while new results and techniques on the boundedness and compactness of the Weyl transforms in terms of the symbols in $ Lrü(äBbb Rü2nü) $ and in terms of the Wigner transforms of Hermite functions are given. The roles of the Heisenberg group and the symplectic group in the study of the structure of the Weyl transform are explained, and the connections of the Weyl transform with quantization are highlighted throughout the book. Localisation operators, first studied as filters in signal analysis, are shown to be Weyl transforms with symbols expressed in terms of the admissible wavelets of the localisation operators. The results and methods mean this book is of interest to graduates and mathematicians working in Fourier analysis, operator theory, pseudo-differential operators and mathematical physics.
