A survey is given of the elegant physics of N-particle systems, both classical and quantal, non-relativistic (NR) and relativistic, non-gravitational (SR) and gravitational (GR). Chapter 1 deals exclusively with NR systems; the correspondence between classical and quantal systems is highlighted and summarized in two tables of Sec. 1.3. Chapter 2 generalizes Chapter 1 to the relativistic regime, including Maxwell’s theory of electromagnetism. Chapter 3 follows Einstein in allowing gravity to curve the spacetime arena; its Sec. 3.2 is devoted to the (...) yet missing theory of elementary particles, which should determine their properties and interactions. If completed, it would replace QFT; promising is the ‘metron’ approach. (shrink)

Dans cet article, nous entendons montrer que les principes d’invariance interviennent de manière essentielle pour caractériser les lois de la nature en physique. Pour ce faire, nous nous focaliserons sur les réflexions épistémologiques que Weyl et Wigner consacrent aux symétries. Nous proposerons une analyse conceptuelle de l’invariance en indiquant qu’elle permet de généraliser la première analogie de l’expérience de Kant (le principe de permanence de la substance). Nous analyserons de plus l’argument de Weyl selon lequel les principes (...) d’invariance constituent des connaissances a priori en un sens relativisé. Nous indiquerons pour finir qu’aux yeux de Wigner, les « symétries » constituent des conditions qui nous permettent de structurer notre compréhension de la réalité empirique. (shrink)

Dans cet article, nous entendons montrer que les principes d’invariance interviennent de manière essentielle pour caractériser les lois de la nature en physique. Pour ce faire, nous nous focaliserons sur les réflexions épistémologiques que Weyl et Wigner consacrent aux symétries. Nous proposerons une analyse conceptuelle de l’invariance en indiquant qu’elle permet de généraliser la première analogie de l’expérience de Kant (le principe de permanence de la substance). Nous analyserons de plus l’argument de Weyl selon lequel les principes (...) d’invariance constituent des connaissances a priori en un sens relativisé. Nous indiquerons pour finir qu’aux yeux de Wigner, les « symétries » constituent des conditions qui nous permettent de structurer notre compréhension de la réalité empirique. (shrink)

The Wigner–Weyl mapping of quantum operators to classical phase space functions preserves the algebra, when operator multiplication is mapped to the binary “*” operation. However, this isomorphism is destroyed under the quasiclassical substitution of * with conventional multiplication; consequently, an approximate mapping is required if algebraic relations are to be preserved. Such a mapping is uniquely determined by the fundamental relations of quantum mechanics, as is shown in this paper. The resultant quasiclassical approximation leads to an algebraic derivation (...) of Thomas–Fermi theory, and a new quantization rule which—unlike semiclassical quantization—is non-invariant under action transformations of the Hamiltonian, in the same qualitative manner as the true eigenvalues. The quasiclassical eigenvalues are shown to be significantly more accurate than the corresponding semiclassical values, for a variety of 1D and 2D systems. In addition, certain standard refinements of semiclassical theory are shown to be easily incorporated into the quasiclassical formalism. (shrink)

A field-theoretic version of Wigner’s friend (1961) illustrates how the quantum measurement problem arises for field theory. Similarly, considering spacelike separate measurements of entangled fields by observers akin to Wigner’s friend shows the sense in which relativistic constraints make the measurement problem particularly difficult to resolve in the context of a relativistic field theory. We will consider proposals by Wigner (1961), Bloch (1967), Helwig and Kraus (1970), and Bell (1984) for resolving the measurement problem for quantum field (...) theory. We will conclude by considering the possibility of giving up rich dynamical explanation in the context of a many-maps formulation of relativistic quantum field theory. (shrink)

An explicit expression of the “Wigner operator” is derived, such that the Wigner function of a quantum state is equal to the expectation value of this operator with respect to the same state. This Wigner operator leads to a representation-independent procedure for establishing the correspondence between the inhomogeneous symplectic group applicable to linear canonical transformations in classical mechanics and the Weyl-metaplectic group governing the symmetry of unitary transformations in quantum mechanics.

This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Hermann Weyls "Philosophie der Mathematik und Naturwissenschaft" erschien erstmals 1928 als Beitrag zu dem von A. Bäumler und M. Schröter herausgegebenen "Handbuch der Philosophie". Die amerikanische Ausgabe, auf der die deutsche Übersetzung von Gottlob Kirschmer beruht, erschien 1949 bei Princeton University Press. Das nunmehr bereits in der 8. Auflage vorliegende Werk ist längst auch in Deutschland zum Standardwerk geworden.

The present discussion arose from the desire to explain, to an audience of non-physicists, the epistemology to which one is forced if one pursues the quantum mechanical theory of observation to its ultimate consequences. However, the conclusions will not be derived from the aforementioned theory but obtained on the basis of a rather general analysis of what we mean by real. Quantum theory will form the background but not the basis for the analysis. The concept of the real to be (...) arrived at shows considerable similarity to that of the idealist. As the title indicates, it is formulated as a dualism. It is quite possible that it will soon be rejected not only by the community of the philosophers but also by that of the scientists. If this should be the case, the attempt to derive an epistemology from physics will prove to have been premature. Naturally, the author hopes that this will not be the case because, quite apart from the quantum theoretical background, the concepts to be presented appear natural also as an outgrowth of common sense considerations. They have been arrived at by many who did not accept the epistemology of quantum mechanics. (shrink)

It is proposed to consider present-day physics as dealing with a special situation, the situation in which the phenomena of life and consciousness play no role. It is pointed out that physical theory has often dealt, in the past, with similarly special situations. Planetary theory neglects all but gravitational forces, macroscopic physics neglects fluctuations due to the atomic structure of matter, nuclear physics disregards weak and gravitational interactions. In some of these cases, physicists were well aware of dealing with special (...) situations, or limiting cases as they are called in the article; in other cases, they were not. It is pointed out that, even if it were true that present-day physics accurately describes the motion of the physical constituents of living bodies, it would not give the whole story. Arguments are adduced, however, to show that the laws of physics, applicable for inanimate matter, will have to be modified when dealing with the more general situation in which life and consciousness play significant roles. (shrink)

The quantum transition probability assignment is an equiareal transformation from the annulus of symplectic spinorial amplitudes to the disk of complex state vectors, which makes it equivalent to the equiareal projection of Archimedes. The latter corresponds to a symplectic synchronization method, which applies to the quantum phase space in view of Weyl’s quantization approach involving an Abelian group of unitary ray rotations. We show that Archimedes’ method of synchronization, in terms of a measure-preserving transformation to an equiareal disk, imposes (...) the integrality of the quantum of action, and requires the extension of the classical moment map from the real line to the circle. Additionally, the same synchronization method is encoded in the structure of the Heisenberg group, viewed as a principal bundle with a connection, whose curvature and anholonomy is expressed in terms of area bounding loops in relation to the underlying Abelian shadow on a symplectic plane. In this manner, we show that the geometric phase pertains to the minimal synchronized area \ of the 2-d symplectic Abelian shadow of the symplectic ball, modulo \. The integrality condition naturally leads to the consideration of modular commutative observables pertaining to the role of the discrete Heisenberg group. We prove that the structural transition from non-commutativity to modular commutativity in accordance to Weyl’s group-theoretic commutation relations takes place via universal factorization through the discrete Heisenberg group. In this way, we derive a homology-theoretic formulation of the synchronization method in terms of the area-bounding cells of the modular lattice \ in relation to any Abelian symplectic shadow. Thus, we finally obtain the physical interpretation of the analytic representation of quantum states as theta functions corresponding to the sections of a complex line bundle with an integral symplectic structure. (shrink)

The book should be a gem for all those interested in the history and philosophy of science.

O presente trabalho objetiva fazer uma análise sobre algumas das principais temáticas elaboradas pelo pensador argentino Luis Alberto Warat, quais sejam: o antropofagismo waratiano, o reencontro com a subjetividade perdida e a carnavalização. Para isso, analisou- se uma das obras mais caras do pensamento waratiano: A ciência jurídica e seus dois maridos. Buscou-se através da análise empreendida, elaborar uma crítica sobre paradigmas tradicionais de ciência, incluindo aqui, a própria Ciência do Direito. Sobreleva-se o caráter de indisciplina das atividades artístico-literárias para (...) insinuar as falhas históricas das disciplinas bem instituídas, do pensamento e da cultura dominantes. Visa-se, portanto, maior interação entre aquilo que se entende como ciência e a subjetividade humana como um todo. (shrink)

Hermann Weyl was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any (...) language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World and Mind and Nature, each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life. (shrink)

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

"-- Norman Sieroka, ETH Zurich"This is an important complement to Weyl's Philosophy of Mathematics and Natural Science because most of the pieces in this new..

El filósofo español José Ortega y Gasset y su traductora al alemán Helene Weyl intercambiaron correspondencia entre los años 1923 y 1946. José Ortega y Gasset y Helene Weyl formaron parte de dos grandes comunidades de intelectuales europeos: Ortega, representante de la filosofía académica en España y Helene Weyl, representante de una intelectualidad vivida más allá de cualquier corsé academicista. Su correspondencia documenta el desarrollo de dos grandes espíritus europeos así como la singular intersección de estos dos (...) mundos y culturas a través de un momento histórico difícil y turbulento del siglo XX. (shrink)

I argue that individuals may be as problematic political agents as groups are. In doing so, I draw on theory from economics, philosophy, and computer science and evidence from psychology, neuroscience, and biology. If successful, this argument undermines agency-based justifications for embracing strong notions of individual rights while rejecting the possibility of similar rights for groups. For concreteness, I critique these mistaken views by rebutting arguments given by Chandran Kukathas in his article `Are There Any Cultural Rights?' that groups lack (...) the temporal coherence, political independence, and indivisibility of individuals. I also show how formal critiques of group agency from social science (in particular, Arrow's Impossibility Theorem) can be applied as reasonably to individuals as groups. Because these symmetries between groups and individuals undermine common implicit assumptions in political philosophy, I argue that they may have broader implications for liberal political theory, as they emphasize the importance of intrapersonal justice. (shrink)