Unheard Harmonies

2014 ◽  
Author(s):  
Peter Pesic
Keyword(s):  
Twentieth Century ◽  
String Theory ◽  
Scientific Work ◽  
High Energy ◽  
Mathematical Formalism ◽  
Color Theory ◽  
Web Browsers ◽  
Wave Mechanics ◽  
Erwin Schrödinger ◽  
Cosmic Order

Among early twentieth-century physicists, many considered their musical experiences formative of their relation to science. Albert Einstein’s famous devoted to music seems linked to his scientific work mainly through a general quest for harmony. Werner Heisenberg was a skilled musician who embraced a Platonic search for cosmic order after a revelatory performance of Bach. Even the unmusical Erwin Schrödinger found himself relying on musical analogies (as well as color theory) when he formulated his wave mechanics. The development of string theory reengages the mathematics of vibration, though the reality of the “strings” rests on analogy built on analogy, as shown in the progression Yoichiro Nambu described in his early work on this theory. Indeed, the concept of resonance remains important throughout physics, such as high-energy experiments. The Pythagorean theme of harmony remains potent in contemporary physics, though its harmonies are more and more unhearable and embedded in mathematical formalism. Throughout the book where various sound examples are referenced, please see http://mitpress.mit.edu/musicandmodernscience (please note that the sound examples should be viewed in Chrome or Safari Web browsers).

scholarly journals Unimodular vs nilpotent superfield approach to pure dS supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sukruti Bansal ◽  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
String Theory ◽  
General Framework ◽  
Recent Progress ◽  
High Energy ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
New Approach ◽  
Sitter Spacetime ◽  
Novel Approach ◽  
De Sitter Vacua

Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

scholarly journals High-energy scattering and D-pair creation in Matrix string theory

1999 ◽  
Vol 537 (1-3) ◽  
pp. 260-296 ◽  
Author(s):  
Steven B. Giddings ◽  
Feike Hacquebord ◽  
Herman Verlinde
Keyword(s):  
String Theory ◽  
High Energy ◽  
Pair Creation ◽  
Energy Scattering ◽  
High Energy Scattering

Political Matrix and Political Representation: Prolegomenon to a New Departure from an Old Problem

1969 ◽  
Vol 63 (2) ◽  
pp. 427-441 ◽  
Author(s):  
Kenneth Prewitt ◽  
Heinz Eulau
Keyword(s):  
Twentieth Century ◽  
Empirical Research ◽  
Political Representation ◽  
Scientific Work ◽  
The Other ◽  
Past Century ◽  
City Councils ◽  
Political Units ◽  
The One ◽  
Special District

Scholars interested in theorizing about political representation in terms relevant to democratic governance in mid-twentieth century America find themselves in a quandary. We are surrounded by functioning representative institutions, or at least by institutions formally described as representative. Individuals who presumably “represent” other citizens govern some 90 thousand different political units—they sit on school and special district boards, on township and city councils, on county directorates, on state and national assemblies, and so forth. But the flourishing activity of representation has not yet been matched by a sustained effort to explain what makes the representational process tick.Despite the proliferation of representative governments over the past century,theoryabout representation has not moved much beyond the eighteenth-century formulation of Edmund Burke. Certainly most empirical research has been cast in the Burkean vocabulary. But in order to think in novel ways about representative government in the twentieth-century, we may have to admit that present conceptions guiding empirical research are obsolete. This in turn means that the spell of Burke's vocabulary over scientific work on representation must be broken.To look afresh at representation, it is necessary to be sensitive to the unresolved tension between the two main currents of contemporary thinking about representational relationships. On the one hand, representation is treated as a relationship between any one individual, the represented, and another individual, the representative—aninter-individualrelationship. On the other hand, representatives are treated as a group, brought together in the assembly, to represent the interest of the community as a whole—aninter-grouprelationship. Most theoretical formulations since Burke are cast in one or the other of these terms.

scholarly journals IVAN SLESHYNSKY AS A POPULARIZER OF THE IDEAS OF MATHEMATICAL LOGIC IN UKRAINE

2020 ◽  
pp. 99-107
Keyword(s):  
Twentieth Century ◽  
Mathematical Logic ◽  
Mathematical Reasoning ◽  
Mathematical Proof ◽  
Scientific Work ◽  
The United States ◽  
Late Nineteenth Century ◽  
Common Belief ◽  
Early Twentieth Century ◽  
Mathematical Sciences

The first half of the twentieth century was marked by the simultaneous development of logic and mathematics. Logic offered the necessary means to justify the foundations of mathematics and to solve the crisis that arose in mathematics in the early twentieth century. In European science in the late nineteenth century, the ideas of symbolic logic, based on the works of J. Bull, S. Jevons and continued by C. Pierce in the United States and E. Schroeder in Germany were getting popular. The works by G. Frege and B. Russell should be considered more progressive towards the development of mathematical logic. The perspective of mathematical logic in solving the crisis of mathematics in Ukraine was noticed by Professor of Mathematics of Novorossiysk (Odesa) University Ivan Vladislavovich Sleshynsky. Sleshynsky (1854 –1931) is a Doctor of Mathematical Sciences (1893), Professor (1898) of Novorossiysk (Odesa) University. After studying at the University for two years he was a Fellow at the Department of Mathematics of Novorossiysk University, defended his master’s thesis and was sent to a scientific internship in Berlin (1881–1882), where he listened to the lectures by K. Weierstrass, L. Kronecker, E. Kummer, G. Bruns. Under the direction of K. Weierstrass he prepared a doctoral dissertation for defense. He returned to his native university in 1882, and at the same time he was a teacher of mathematics in the seminary (1882–1886), Odesa high schools (1882–1892), and taught mathematics at the Odesa Higher Women’s Courses. Having considerable achievements in the field of mathematics, in particular, Pringsheim’s Theorem (1889) proved by Sleshinsky on the conditions of convergence of continuous fractions, I. Sleshynsky drew attention to a new direction of logical science. The most significant work for the development of national mathematical logic is the translation by I. Sleshynsky from the French language “Algebra of Logic” by L. Couturat (1909). Among the most famous students of I. Sleshynsky, who studied and worked at Novorossiysk University and influenced the development of mathematical logic, one should mention E. Bunitsky and S. Shatunovsky. The second period of scientific work of I. Sleshynsky is connected with Poland. In 1911 he was invited to teach mathematical disciplines at Jagiellonian University and focused on mathematical logic. I. Sleshynsky’s report “On Traditional Logic”, delivered at the meeting of the Philosophical Society in Krakow. He developed the common belief among mathematicians that logic was not necessary for mathematics. His own experience of teaching one of the most difficult topics in higher mathematics – differential calculus, pushed him to explore logic, since the requirement of perfect mathematical proof required this. In one of his further works of this period, he noted the promising development of mathematical logic and its importance for mathematics. He claimed that for the mathematics of future he needed a new logic, which he saw in the “Principles of Mathematics” by A. Whitehead and B. Russell. Works on mathematical logic by I. Sleszynski prompted many of his students in Poland to undertake in-depth studies in this field, including T. Kotarbiński, S. Jaśkowski, V. Boreyko, and S. Zaremba. Thanks to S. Zaremba, I. Sleshynsky managed to complete the long-planned concept, a two-volume work “Theory of Proof” (1925–1929), the basis of which were lectures of Professor. The crisis period in mathematics of the early twentieth century, marked by the search for greater clarity in the very foundations of mathematical reasoning, led to the transition from the study of mathematical objects to the study of structures. The most successful means of doing this were proposed by mathematical logic. Thanks to Professor I. Sleshynsky, who succeeded in making Novorossiysk (Odesa) University a center of popularization of mathematical logic in the beginning of the twentieth century the ideas of mathematical logic in scientific environment became more popular. However, historical events prevented the ideas of mathematical logic in the domestic scientific space from the further development.

Introductory Considerations

2018 ◽  
Author(s):  
John von Neumann
Keyword(s):  
Quantum Theory ◽  
Theoretical Description ◽  
Statistical Interpretation ◽  
Wave Mechanics ◽  
Transformation Theory ◽  
Max Born ◽  
Erwin Schrödinger ◽  
Physical Problems ◽  
Starting Point ◽  
New System

This chapter presents the origins of the transformation theory and related concepts. It shows how, in 1925, a procedure initiated by Werner Heisenberg was developed by himself, Max Born, Pascual Jordan, and a little later by Paul Dirac, into a new system of quantum theory—the first complete system of quantum theory which physics has possessed. A little later Erwin Schrödinger developed the “wave mechanics” from an entirely different starting point. This accomplished the same ends, and soon proved to be equivalent to the Heisenberg, Born, Jordan, and Dirac system. On the basis of the Born statistical interpretation of the quantum theoretical description of nature, it was possible for Dirac and Jordan to join the two theories into one, the “transformation theory,” in which they make possible a grasp of physical problems which is especially simple mathematically.

scholarly journals The Unsolved Problem of Stellar Origins

1996 ◽  
Vol 169 ◽  
pp. 533-549
Author(s):  
Charles J. Lada
Keyword(s):  
Twentieth Century ◽  
Science Fiction ◽  
High Energy Physics ◽  
Gamma Ray ◽  
High Energy ◽  
Giant Molecular Clouds ◽  
Observational Astronomy ◽  
History Of ◽  
Large Telescopes ◽  
The Universe

We now stand at the threshold of the 21st century having witnessed perhaps the greatest era of astronomical discovery in the history of mankind. During the twentieth century the subject of astronomy was revolutionized and completely transformed by technology and physics. Advances in technology that produced radio astronomy, infrared astronomy, UV, X and γ ray astronomy, large telescopes on the ground, in balloons, aircraft and space coupled with advances in nuclear, atomic and high energy physics forever changed the way in which the universe is viewed. Indeed, it is altogether likely that future historians of science will consider the twentieth century as the Golden Age of observational astronomy. As a measure of how far we have come in the last 100 years, recall that at the turn of this century the nature of spiral nebulae and of the Milky Way itself as an island universe were not yet revealed. The expansion of the universe and the microwave background were not yet discovered and exotic objects such as quasars, pulsars, gamma-ray bursters and black holes were not even envisioned by the most imaginative authors of science fiction. The interstellar medium, with its giant molecular clouds, magnetic fields and obscuring dust was unknown. Not even the nature of stars, these most fundamental objects of the astronomical universe, was understood.

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