On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics

In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler's program succeeds here without provisos. In Kottler's approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the metric. However, one can hope to bring the Kottler idea to work by using the teleparallelism equivalent of general relativity, where the gravitational potential, the coframe, can be chosen in a premetric way.Comment: 72 pages latex with 6 figures; based on an invited talk given at the Annual Meeting of the German Physical Society (DPG) in Berlin on 20 March 2015, Working Group on Philosophy of Physics (AGPhil); a short version will be submitted to IJMP

Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation

The Lorentz law of force is the fifth pillar of classical electrodynamics, the other four being Maxwell's macroscopic equations. The Lorentz law is the universal expression of the force exerted by electromagnetic fields on a volume containing a distribution of electrical charges and currents. If electric and magnetic dipoles also happen to be present in a material medium, they are traditionally treated by expressing the corresponding polarization and magnetization distributions in terms of bound-charge and bound-current densities, which are subsequently added to free-charge and free-current densities, respectively. In this way, Maxwell's macroscopic equations are reduced to his microscopic equations, and the Lorentz law is expected to provide a precise expression of the electromagnetic force density on material bodies at all points in space and time. This paper presents incontrovertible theoretical evidence of the incompatibility of the Lorentz law with the fundamental tenets of special relativity. We argue that the Lorentz law must be abandoned in favor of a more general expression of the electromagnetic force density, such as the one discovered by A. Einstein and J. Laub in 1908. Not only is the Einstein-Laub formula consistent with special relativity, it also solves the long-standing problem of "hidden momentum" in classical electrodynamics.Comment: 7 pages, 1 figur

A new approach in classical electrodynamics to protect principle of causality

In classical electrodynamics, electromagnetic effects are calculated from solution of wave equation formed by combination of four Maxwell’s equations. However, along with retarded solution, this wave equation admits advanced solution in which case the effect happens before the cause. So, to preserve causality in natural events, the retarded solution is intentionally chosen and the advance part is just ignored. But, an equation or method cannot be called fundamental if it admits a wrong result (that violates principle of causality) in addition to the correct result. Since it is the Maxwell’s form of equations that gives birth to this acausal advanced potential, we rewrite these equations in a different form using the recent theory of reaction at a distance (Biswaranjan Dikshit, Physics essays, 24(1), 4-9, 2011) so that the process of calculation does not generate any advanced effects. Thus, the long-standing causality problem in electrodynamics is solved

How does the electromagnetic field couple to gravity, in particular to metric, nonmetricity, torsion, and curvature?

The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in the laboratory or by observing outer space. (ii) One desires to test out alternatives to Einstein's gravitational theory, in particular those of a gauge-theoretical nature, like Einstein-Cartan theory or metric-affine gravity. A clean discussion requires a reflection on the foundations of electrodynamics. If one bases electrodynamics on the conservation laws of electric charge and magnetic flux, one finds Maxwell's equations expressed in terms of the excitation H=(D,H) and the field strength F=(E,B) without any intervention of the metric or the linear connection of spacetime. In other words, there is still no coupling to gravity. Only the constitutive law H= functional(F) mediates such a coupling. We discuss the different ways of how metric, nonmetricity, torsion, and curvature can come into play here. Along the way, we touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld, Heisenberg-Euler, Plebanski), linear ones, including the Abelian axion (Ni), and find a method for deriving the metric from linear electrodynamics (Toupin, Schoenberg). Finally, we discuss possible non-minimal coupling schemes.Comment: Latex2e, 26 pages. Contribution to "Testing Relativistic Gravity in Space: Gyroscopes, Clocks, Interferometers ...", Proceedings of the 220th Heraeus-Seminar, 22 - 27 August 1999 in Bad Honnef, C. Laemmerzahl et al. (eds.). Springer, Berlin (2000) to be published (Revised version uses Springer Latex macros; Sec. 6 substantially rewritten; appendices removed; the list of references updated

The relation between classical and quantum electrodynamics

In this article it is presented the idea that quantum electrodynamics presents intrinsic limitations in the description of physical processes that makes it impossible to recover from it the type of description we have with classical electrodynamics. In this way I cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as an independent theory but just as an upgrade of classical electrodynamics and the theory of relativity, which permits an extension of classical theory in the description of phenomena that, while being clearly related to the conceptual framework of the classical theory – the description of matter, radiation, and their interaction –, cannot be properly addressed from the classical theory