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This text brings history and the key fields of physics together to present a unique technical discussion of the principles of least action.

This edited volume features essays written in honor of Ernst Mach. It explores his life, work, and legacy. Readers will gain a better understanding of this natural scientist and scholar who made major contributions to physics, the philosophy of science, and physiological psychology. The essays offer a critical inventory of Mach’s lifework in line with state-of-the-art research and historiography. It begins with physics, where he paved the way for Einstein’s Theory of Relativity. The account continues with Mach's contributions in biology, psychology, and physiology pioneering with an empiricist and gestalthaft Analysis of Sensations. Readers will also discover how in the philosophy of science he served as a model for the Vienna Circle with the Ernst Mach Society as well as paved the way for an integrated history and theory of science. Indeed, his influence extends far beyond the natural sciences -- to the Vienna Medical School and psychoanalysis (R. Bárány, J. Breuer, S. Freud), to literature (Jung Wien, R. Musil), to politics (F. Adler, Austro-Marxism and the Viennese adult education), to arts between Futurism and Minimal Art as well as to social sciences between the liberal school (J. Schumpeter, F. A. von Hayek) and empirical social research (P. Lazarsfeld und M. Jahoda).

This volume is the first English resource to shed light on the philosophy of Joseph Petzoldt (1862-1929), the main pupil of Ernst Mach and founder of the Gesellschaft für wissenschaftliche Philosophie, later the association of Berlin logical positivists. A central figure in the early debate on the theory of relativity, his work was praised by Einstein himself. Tracing the development of Petzoldt's ideas, starting from his early acceptance of materialism and Kantian agnosticism, Chiara Russo Krauss presents a comprehensive reconstruction of his philosophy in the context of the German milieu. She examines his attempt to develop a new philosophy following Gustav Fechner and the empiriocriticism of Richard Avenarius and Ernst Mach. In the final chapter, she sets out how Petzoldt proposed relativistic positivism as the official interpretation of Einstein's relativity. By illuminating key elements of Petzoldt's work, this is a valuable case study for students and scholars of philosophy of science and late 19th-century and early 20th-century philosophy. It reveals the complex interplay of two different tendencies of the time: neo-Kantianism and its struggle to overcome the notion of thing-in-itself, as well as the need for an epistemological foundation for the new advances of science.