Relativistic Classical Mechanics and Electrodynamics

This book presents classical relativistic mechanics and electrodynamics in the Feynman-Stueckelberg event-oriented framework formalized by Horwitz and Piron.

The full apparatus of classical analytical mechanics is generalized to relativistic form by replacing Galilean covariance with manifest Lorentz covariance and introducing a coordinate-independent parameter to play the role of Newton's universal and monotonically advancing time. Fundamental physics is described by the -evolution of a system point through an unconstrained 8D phase space, with mass a dynamical quantity conserved under particular interactions. Classical gauge invariance leads to an electrodynamics derived from five -dependent potentials described by 5D pre-Maxwell field equations. Events trace out worldlines as advances monotonically, inducing pre-Maxwell fields by their motions, and moving under the influence of these fields. The dynamics are governed canonically by a scalar Hamiltonian that generates evolution of a 4D block universe defined at to an infinitesimally close 4D block universe defined at +. This electrodynamics, and its extension to curved space and non-Abelian gauge symmetry, is well-posed and integrable, providing a clear resolution to grandfather paradoxes. Examples include classical Coulomb scattering, electrostatics, plane waves, radiation from a simple antenna, classical pair production, classical CPT, and dynamical solutions in weak field gravitation. This classical framework will be of interest to workers in quantum theory and general relativity, as well as those interested in the classical foundations of gauge theory.

Martin Land was born in Brooklyn in 1953. He grew up in the New York City area, strongly influenced by his mother, a social worker who worked with Holocaust survivors, and his father, a second-generation engineer in small manufacturing businesses associated with the garment industry. In his school years he cleaned swimming pools and stables, worked as a carpenter on a construction site, and expedited orders in the garment center. In 1972, he entered Reed College in Portland, Oregon, where he received a Kroll Fellowship for original research which permitted him to devote an extra year to extensive study in the humanities along with his specialization in physics. After completing his BA in 1977, he returned to New York City where he received an M.S. in electrical engineering from Columbia University in 1979 as a member of the Eta Kappa Nu engineering honor society. He joined Bell Laboratories, developing specialized hardware for fiber optic communication with application in computer networks and video transmission. In 1982, he worked as a telecommunications engineer at a major Wall Street bank. Returning to theoretical physics at Hebrew University in Jerusalem, he worked with Eliezer Rabinovicci on supersymmetric quantum mechanics to receive a second M.S. in 1986. In 1985, he married Janet Baumgold, a feminist therapist and co-founder of the Counseling Center for Women. Following a year devoted to full-time fatherhood and another in compulsory national service, he began working toward a Ph.D. in high energy physics with Lawrence Horwitz at Tel Aviv University in 1988. He elaborated many aspects of the classical and quantum theories known as Stueckelberg-Horwitz-Piron (SHP) theory, producing a dissertation developing the SHP quantum field theory. Concurrently with his doctoral work, he was on the research faculty of the Computer Science Department at Hebrew University, developing specialized hardware for parallel computing. After submitting his dissertation in 1995, he taught communications engineering for three years at the Holon Institute of Technology, before joining the Department of Computer Science at Hadassah College in Jerusalem, teaching computer architecture, microprocessors, embedded systems, and computer networking. He was a founding member of the International Association for Relativistic Dynamics (IARD) in 1998 and has served as IARD president since 2006. In parallel to his activities in physics and computer science, he has enjoyed a long collaboration with Jonathan Boyarin of Cornell University in various areas of the humanities, critical theory, and Jewish studies. This collaboration has allowed him to communicate contemporary thinking in physics, especially notions of time associated with SHP theory, to scholars in other fields as modern context for philosophical consideration of temporality.

Lawrence Paul Horwitz was born in New York City on October 14, 1930. He lived in Westchester County until 1934, then went to London where his father founded and managed a chain of womens wear shops, called the Richard Shops, and then returned to the United States in 1936. After a few years in Brooklyn, NY, his family moved to Forest Hills in Queens, NY, where he learned tennis and attended Forest Hills High School, a school dedicated to teaching students how to think, where he came to love physics. He then went to the College of Engineering, New York University, where he studied Engineering Physics and graduated summa cum laude with a Tau Beta Pi key and the S.F.B. Morse medal for physics. He met a young lady, Ruth Abeles, who arrived from Germany in the U.S. in 1939 and became his wife before moving on to Harvard University in 1952 with a National Science Foundation Fellowship. He received his doctorate at Harvard working under the supervision of Julian Schwinger in 1957. He then worked at the IBM Watson Research Laboratory where he met Herman Goldstine, a former assistant to John von Neumann and, among other things, explored with him octononic and quaternionic Hilbert spaces from both physical and mathematical points of view. He then moved on to the University of Geneva in 1964, becoming involved in scattering theory as well as continuing his studies of hypercomplex systems with L. C. Biedenharn and becoming involved in particle physics with Yuval Neeman at CERN. He became full professor at the University of Denver in 1966–1972; he then accepted a full professorship at Tel Aviv University. After stopping for a year to work with C. Piron at the University of Geneva on the way to Israel, he has been at Tel Aviv University since 1973, with visits at University of Texas at Austin, Ilya Prigogine Center for Statistical Mechanics and Complex Systems in Brussels, and at CERN, ETH (Honggerberg, Zurich), University of Connecticut (Storrs, CT), IHES (Bures-sur-Yvette, Paris), and Institute for Advanced Study (Princeton, NJ), where he was a Member in Natural Sciences, 1993, 1996, 1999, 2003 with short visits in August 1990, and January 1991, working primarily with S. L. Adler. He is now Professor Emeritus at Tel Aviv University, Bar Ilan University, and Ariel University. His major interests are in particle physics, statistical mechanics, mathematical physics, theory of unstable systems, classical and quantum chaos, relativistic quantum mechanics, relativistic many body theory, quantum field theory, general relativity, representations of quantum theory on hypercomplex Hilbert modules, group theory and functional analysis, theories of irreversible quantum evolution, geometrical approach to the study of the stability of classical Hamiltonian systems, and to the dark matter problem, and classical and quantum chaos. He is a member of the American Physical Society (Particle Physics), Swiss Physical Society, European Physical Society, International Association for Mathematical Physics, Israel Physical Society, Israel Mathematics Union, European Mathematical Society, International Quantum Structures Association, Association of Members of the Institute for Advanced Study, and the International Association for Relativistic Dynamics.