This is the first publication (in German or English) of Hermann Minkowski's three papers on relativity together: (i) The Relativity Principle - lecture given at the meeting of the Göttingen Mathematical Society on November 5, 1907 (the first English translation); (ii) The Fundamental Equations for Electromagnetic Processes in Moving Bodies - lecture given at the meeting of the Göttingen Scientific Society on December 21, 1907 (new translation); (iii) Space and Time - lecture given at the 80th Meeting of Natural Scientists in Cologne on September 21, 1908 (new translation).

Space and Time: Minkowski's papers on relativity

Science & Math

Minkowski, Hermann

Physics

Minkowski Institute Press

This book fills a gap in the literature. So far there has been no book which deals with inertia and gravitation by explicitly addressing open questions and issues which have been hampering the proper understanding of these phenomena. The book places a strong emphasis on the physical understanding of the main aspects and features of inertia and gravitation. It discusses questions such as: (i) Are inertial forces fictitious or real? (ii) Does special relativity provide an insight into the origin of inertia? (iii) Does mass increase relativistically? (iv) Why is the inertial mass equivalent to the gravitational mass? (v) Are gravitational phenomena caused by gravitational interaction according to general relativity? (vi) Is there gravitational energy? (vii) Do gravitational waves carry gravitational energy? (viii) Can gravity be quantized? October 19, 2019: new printing -- an Appendix ``On Relativistic Mass'' is included, some notes and references are added and noticed typos are corrected.

Inertia and Gravitation: From Aristotle's Natural Motion to Geodesic Worldlines in Curved Spacetime

Petkov, Vesselin

Robert Geroch's lecture notes on general relativity are unique in three main respects. First, the physics of general relativity and the mathematics, which describes it, are masterfully intertwined in such a way that both reinforce each other to facilitate the understanding of the most abstract and subtle issues. Second, the physical phenomena are first properly explained in terms of spacetime and then it is shown how they can be “decomposed” into familiar quantities, expressed in terms of space and time, which are measured by an observer. Third, Geroch's successful pedagogical approach to teaching theoretical physics through visualization of even the most abstract concepts is fully applied in his lectures on general relativity by the use of around a hundred figures. Although the book contains lecture notes written in 1972, it is (and will remain) an excellent introduction to general relativity, which covers its physical foundations, its mathematical formalism, the classical tests of its predictions, its application to cosmology, a number of specific and important issues (such as the initial value formulation of general relativity, signal propagation, time orientation, causality violation, singularity theorems, conformal transformations, and asymptotic structure of spacetime), and the early approaches to quantization of the gravitational field. As a very helpful companion to this book can serve Geroch's "Differential Geometry: 1972 Lecture Notes". This printing (24 September 2015) corrects all discovered typos.

General Relativity: 1972 Lecture Notes (Lecture Notes Series)

Geroch, Robert

This book comprises Robert Geroch's course notes on quantum field theory. Although written in 1971 Geroch's lecture notes are still a very helpful text on quantum field theory since they contain a concise exposition of its core topics accompanied by compressed but deep and clear explanations. What also makes this book a valuable contribution to the existing textbooks on quantum field theory is Geroch's unique approach to teaching theoretical and mathematical physics - the physical concepts and the mathematics, which describes them, are masterfully intertwined in such a way that both reinforce each other to facilitate the understanding of even the most abstract and subtle issues.

Quantum Field Theory: 1971 Lecture Notes (Lecture Notes Series)

The greatest mystery in the world is its very existence. In our intellectual development, we all reach a turning point when we start asking the perennial existential questions: "What is the world?"; "What am I?"; "What is the meaning of the existence of the world and myself?". As the German philosopher Schopenhauer put it: "The lower a man stands in intellectual respects the less of a riddle does existence seem to him... but, the clearer his consciousness becomes the more the problem grasps him in its greatness." This book explores what fundamental physics tells us about the physical world and how the scientific picture of what exists often differs disturbingly from the "common sense" view based on the way our senses reflect the world. Centuries-old illusions are identified by showing that they contradict experimentally-confirmed results of modern physics, which clears the way toward deeper understanding of reality. The greatest illusion that the world exists only at the present moment of time has been realized by many great thinkers, but so far the human race has been unable to free itself from it, prompting Einstein to write this: "the distinction between past, present and future is only a stubbornly persistent illusion." Getting rid of such stubbornly persistent illusions by open-mindedly examining the implications of modern physics for the physical world can help us rise above the fog of everyday life and see Nature the way she herself is.

From Illusions to Reality: Time, Spacetime and the Nature of Reality (Understanding Reality Series)

Could the day ever come when mathematics proceeds in a purely mechanistic fashion - that it requires no genuinely new insights? This sounds like a good question for an afternoon's debate. But, strange as it may seem, there is actually a theorem in mathematics to the effect that this subject can never become routine! This result, called Godel's theorem, is one of the greatest discoveries in mathematics of the twentieth century. And - perhaps even more remarkable - the proof of this theorem can be understood by anyone, without any knowledge at all of mathematics. The statement and proof of Godel's theorem is the subject of this book. The idea is quite simple, but it requires thinking about things in a new way. The book includes homework problems and exams with solutions and comments.

Unsolvable Problems: 1990 Lecture Notes

Robert Geroch's lecture notes on differential geometry reflect his original and successful style of teaching - explaining abstract concepts with the help of intuitive examples and many figures. The book introduces the most important concepts of differential geometry and can be used for self-study since each chapter contains examples and exercises, plus test and examination problems which are given in the Appendix. As these lecture notes are written by a theoretical physicist, who is an expert in general relativity, they can serve as a very helpful companion to Geroch's excellent "General Relativity: 1972 Lecture Notes."

Differential Geometry: 1972 Lecture Notes

Mathematics

This book is roughly divided in three parts. The first one is a general introduction to theories with extra dimensions and, more specifically, to brane worlds. Both old-fashioned topics (such as Kaluza-Klein theories) and more modern aspects (e.g. Large Extra Dimensions and Randall-Sundrum models) are discussed. The second and third parts (which we refer to as Part I and II respectively) are essentially two monographs. There, the reader is guided through the construction of the 4D effective field theory derived from higher dimensional (in particular five-dimensional and six-dimensional) models. Part I is devoted to the study of how the heavy Kaluza-Klein modes contribute to the low energy dynamics of the light modes. Part II concerns instead the analysis of the spectrum arising from non-standard compactifications of six-dimensional (supersymmetric) theories, involving a warp factor and conical defects in the internal manifold. Several applications of the above mentioned topics are discussed, providing an up to date overview of these subjects.

Brane Worlds: Theories with One or Two Extra Dimensions

Salvio, Alberto

This book is about spacetime, and how, in General Relativity, it performs its widely accepted role of explaining all the phenomena of gravity. Space and time have long been contentious presences in theories of mechanics because of their metaphysical peculiarities. Philosophical worries continue to fog a clear understanding of just how spacetime performs this role. In early sections of his revolutionary paper of 1916, Einstein claimed that his use of a new style of formulation removes "the last remnant of physical objectivity from space and time". His satisfaction in banishing these metaphysical anxieties was evident. However in 1917 it was shown his claim was ungrounded. He readily accepted the criticism: it left intact all the maths and physics of the theory. These amply justify the widespread, orthodox view of spacetime's fundamental role in the theory. Einstein banished no demon but rather released a genie - spacetime. However, his hostility continued, resulting in attempts to rewrite the role of spacetime. These had some later influence but never caught on. Einstein set supreme importance on the role of imagination in scientific theory and valued it as his most significant gift. In science, perhaps in culture generally, relativity is unsurpassed in its imaginative conceptual daring. Yet he and others paused at its metaphysical novelty and radicalism: hostility to spacetime persists. This book presents an unqualified philosophical defence of the conceptual coherence and uniqueness of spatiotemporality. It offers an alternative to the relationist/substantivalist dilemma; it explains Minkowski's derivation of spacetime without the light postulate; it defends, clarifies and stresses the deep role of spacetime in the standard novelties of both relativity theories. A study of spacetime in relativity shows how an insubstantial entity can nevertheless be concrete. That solves the metaphysical worry over its intelligibility and reveals it as fundamental to ontology.

Einstein's Genie: Spacetime out of the Bottle

Politics & Social Sciences

Nerlich, Graham

Philosophy

Robert Geroch's lecture notes "Infinite-Dimensional Manifolds" provide a concise, clear, and helpful introduction to a wide range of subjects, which are essential in mathematical and theoretical physics - Banach spaces, open mapping theorem, splitting, bounded linear mappings, derivatives, mean value theorem, manifolds, mappings of manifolds, scalar and vector fields, tensor products, tensor spaces, natural tensors, tensor fields, tensor bundles, Lie derivatives, integral curves, geometry of Lie derivatives, exterior derivatives, derivative operators, partial differential equations, and Riemannian geometry. Like in his other books, Geroch explains even the most abstract concepts with the help of intuitive examples and many (over 60) figures. Like Geroch’s other books, this book too can be used for self-study since each chapter contains examples plus a set of problems given in the Appendix.

Infinite-Dimensional Manifolds: 1975 Lecture Notes

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