Is the Lorentz signature of the metric of spacetime electromagnetic in origin?
نویسندگان
چکیده
We formulate a premetric version of classical electrodynamics in terms of the excitation H = (H,D) and the field strength F = (E,B). A local, linear, and symmetric spacetime relation between H and F is assumed. It yields, if electric/magnetic reciprocity is postulated, a Lorentzian metric of spacetime thereby excluding Euclidean signature (which is, nevertheless, discussed in some detail). Moreover, we determine the Dufay law (repulsion of like charges and attraction of opposite ones), the Lenz rule (the relative sign in Faraday’s law), and the sign of the electromagnetic energy. In this way, we get a systematic understanding of the sign rules and the sign conventions in electrodynamics. The question in the title of the paper is answered affirmatively.
منابع مشابه
Electromagnetic Field Tensor and Lorentz Force as Consequence of the Geometry of Minkowskian Spacetime
We show that the electromagnetic field tensor and the Lorentz Force are both a natural consequence of the geometric structure of Minkowskian space, being related to infinitesimal boost and rotations in spacetime. The longstanding issue about the apparent empirical origin of the Lorentz Force is clarified.
متن کاملFrom the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups
The Lorentz transformation of order $(m=1,n)$, $ninNb$, is the well-known Lorentz transformation of special relativity theory. It is a transformation of time-space coordinates of the pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and $n$ space dimensions ($n=3$ in physical applications). A Lorentz transformation without rotations is called a {it boost}. Commonly, the ...
متن کاملSpacetimes admitting quasi-conformal curvature tensor
The object of the present paper is to study spacetimes admitting quasi-conformal curvature tensor. At first we prove that a quasi-conformally flat spacetime is Einstein and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying Einstein's field equation with cosmological constant is covariant constant. Next, we prove that if the perfect flui...
متن کاملOn the energy - momentum current of the electromagnetic field in a pre - metric axiomatic approach
We complete a metric-free axiomatic framework for electrodynamics by introducing the appropriate energy-momentum current Σα of the electromagnetic field. We start from the Lorentz force density and motivate the form of Σα. Then we postulate it (fourth axiom) and discuss its properties. In particular, it is found that Σα is traceless and invariant under an electric-magnetic reciprocity transform...
متن کاملBi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups
The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B and a subgroup $H$ of $Gamma$ induces, under general conditions, a group-like structure for B, known as a gyrogroup. The famous concrete realization of a gyrogroup, which motivated the emergence of gyrogroups into the mainstream, is the space of all relativistically admissible velocities along with a binary mbox{...
متن کامل