Continued exploration of theoretical physics presents new questions about the nature of space, time, and matter. At the center lies an evolving integration with advanced mathematics. These fields demand new insights and often inspire the development of new mathematical frameworks. From the symmetries of string theory to the structures of quantum spacetime and the geometry of cosmology, mathematical innovation is essential for navigating the complexities of modern physics. Further examinati...

The author of Doing Mathematics explores the concepts of physics by demonstrating how physicists think and approach their work.Doing Physics makes concepts of physics easier to grasp by relating them to everyday knowledge. Addressing some of the models and metaphors that physicists use to explain the physical world, Martin H. Krieger describes the conceptual world of physics by means of analogies to economics, anthropology, theater, carpentry, mechanical sy...

Does the future exist already? What is space? Are time machines physically possible? What is quantum mechanical reality like? Are there many universes? Is there a ‘true’ geometry of the universe? Why does there appear to be an arrow of time? Do humans play a special role in the world?In this unique introductory book, Dean Rickles guides the reader through these and other core questions that keep philosophers of physics up at night. He discusses the three pillars of modern physics (...

Metaphysicians should pay attention to quantum mechanics. Why? Not because it provides definitive answers to many metaphysical questions-the theory itself is remarkably silent on the nature of the physical world, and the various interpretations of the theory on offer present conflicting ontological pictures. Rather, quantum mechanics is essential to the metaphysician because it reshapes standard metaphysical debates and opens up unforeseen new metaphysical possibilities. Even if quantum me...

The US economy today is confronted with the prospect of extended stagnation. This book explores why. Thomas I. Palley argues that the Great Recession and destruction of shared prosperity is due to flawed economic policy over the past thirty years. One flaw was the growth model adopted after 1980 that relied on debt and asset price inflation to fuel growth instead of wages. A second flaw was the model of globalization that created an economic gash. Third, financial deregulation and the hous...

Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical me...

This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics.The authors'...

Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deep...

May of us harbour deep questions on subjects such as the origin of the universe, the concepts of time and causality, the nature of consciousness and free will, the mind-body problems of philosophy, the relationship between mathematics and physics, and more. Conventional answers will usually be from fundamental physics (often deeply mathematical) or philosophy (often very abstract). This work takes a different view of reality by substituting mathematical determinism for causal determinism, ...

The problems of indeterminism, uncertainty and statistics in quantum theory are legend and have spawned a wide-variety of interpretations, none too satisfactory.The key issue of discontent is the conflict between the microscopic and the macroscopic worlds: How does a classically certain world emerge from a world of uncertainty and probability? To attempt to solve this riddle, we must first understand the nature of atoms.What If Atoms Are Not Things But Ideas?

This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we sho...

Physics and Mathematics: Collaboration, Contradiction, and the Quest for Truth:Physics and mathematics, twin pillars of human understanding, have built our greatest theories and deepest paradoxes. From Newton’s laws to Einstein’s spacetime, from quantum mechanics to string theory, their partnership has revealed profound insights while exposing sharp contradictions.But what happens when mathematics speaks a language nature doesn’t obey? Or when physics demands answers no formu...