El Principio de Relatividad y el problema del conocimiento Segunda edición con correcciones y ampliaciones (original) (raw)

2019

This is a second Spanish edition, corrected and slightly augmented, of a book published in 2011. It is intended for an audience interested in the problems that arise around scientific knowledge in the so-called post-modern era, and at the same time willing to study with some depth the physical mathematical bases of the theory of relativity, as well as some of its applications in astrophysics and cosmology. It is assumed that the reader has basic knowledge of algebra, infinitesimal calculus of one and several variables, and general physics (elements of mechanics, electromagnetism and optics, thermal and quantum physics), such as those that can be acquired during the first two years of university studies of science or engineering. Bearing this in mind, some complementary topics of mathematics and physics are presented with which the reader may not be familiar. On this basis the foundations of the restricted and generalized theories of relativity are developed. The results of experiments and confirmatory observations are considered. Some difficulties of the theory are pointed out and alternative paths that have been or are being explored are mentioned. The reader is not supposed to be familiar with epistemology or other branches of philosophy. Philosophical contents, particularly epistemological ones, are introduced as they are needed, beginning with the first chapter that is completely dedicated to them. Chapters two, three and four describe the development of ideas in Newtonian particle mechanics and classical field theory, including electromagnetism, using Galileo's relativity principle as the guiding thread. In chapter five we examine the crisis in the foundations of nineteenth-century physics that led to the restricted theory of relativity. Chapters six, seven and eight are intended to study the foundations, limitations and some applications of restricted theory. The experiments reported in 2012 that debunk the results reported in 2011 (and mentioned in the first edition of the book) about faster-than-light neutrinos are taken into account. A problem related with the slowing down of accelerated clocks, posed in 1985, is treated with more detail in this second edition of the book, both in chapter eight and in chapter thirteen, where its relation with the “unus mundus” problem is considered. At the end of chapter eight, the epistemological relations between the theories of classical physics are examined after the restricted theory of relativity was accepted. Chapter nine is intended to supplement the knowledge of mathematics. In particular, this chapter presents elements of differential geometry of surfaces and their extension to manifolds in n dimensions, including notions of tensor calculation, parallel transport, geodesics and curvature of manifolds. Chapter ten is intended to expose the foundations of the generalized theory of relativity. The epistemological relations between the theories of classical physics after the generalized theory of relativity was accepted are considered at the end of the chapter. Chapter eleven presents some applications of David Hilbert´s version of Schwartzschild solution of gravitational field equations and summarizes the confirmatory evidence available in relation to generalized theory. In addition, the basics of the calculus of variations are introduced. In chapters twelve and thirteen, astronomical applications and topics of relativistic physical cosmology, accompanied by historical and epistemological considerations, are then developed in some detail. In this second edition of the book the recent observation of an object with the Event Horizon Telescope, considered as the first black hole registered image, is mentioned. Some critical bibliography related with black holes is given. In chapter fourteen, the structure of the restricted theory of relativity, generalized theory and physical cosmology are examined from the epistemological point of view. In chapter fifteen some aspects of the work of scientific research from the psychological and sociological points of view are briefly considered. Emphasis is placed on the topics that allow us to understand avatars in the development of scientific ideas, until they disappear definitively into oblivion or become part of a stabilized and dominant paradigm. In chapter sixteen, the principle of relativity and some of its consequences are discussed from a broader philosophical perspective, emphasizing the self-imposed limitations of science. The detailed bibliographical references and some important complements appear in the form of footnotes. At the end a list of books and web pages is suggested that may be of interest to reaffirm some concepts or to deepen in the subjects of physical-mathematical sciences, cosmology and philosophy presented here. It has been sought, as far as it has been possible, that the development of the subject be self-contained, that the physical and philosophical ideas, as well as the basic hypotheses, be highlighted and explained, and that their consequences naturally arise during the development of the themes. Likewise, an attempt has been made to involve the reader in the construction of the theory, avoiding two extremes equally. One of them consists in making reference to advanced mathematical tools, which usually the reader does not know, but which are not explained to him, and that therefore he is forced to accept or study elsewhere. The other extreme avoids the necessary mathematical foundation by resorting to purely verbal statements and graphic representations, suggestive but often close to a systematized fantasy. To the extent that these objectives are achieved, the book should be useful as an introductory study material and as a basis for accessing more advanced treatments, in books and research articles, some of which include bibliographical references on foot of page