Related papers: The Lorentz Force Law and Spacetime Symmetries
We show that the kinematics underlying Poincare's elongated ellipse, immediately deduced from Lorentz Transformation (LT), is not the same as Einstein's kinematics. The two main differences are : On one hand the relationship of Lorentz…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
Empirical understanding teaches us that space is three dimensional while relativity merges space with time. We tried to show that it is possible to model space as three complex coordinates. In our construction, the usual spatial coordinate…
We extend de la Fuente and Romero's defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit…
Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…
Fields of Lorentz transformations on a space--time are related to tangent bundle self isometries. In other words, a gauge transformation with respect to the Minkowski metric on each fibre. Any such isometry can be expressed, at least…
When a charge accelerates, its field-lines curve in a typical pattern. This pattern resembles the curvature induced on the field-lines by a neighboring charge. Not only does the latter case involve a similar curvature, it moreover results…
Original abstract: Consider the worldline of a charged particle in a static spacetime. Contraction of the time-translation Killing field with the retarded electromagnetic energy-momentum tensor gives a conserved electromagnetic energy…
While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed…
There exist several approaches that investigate the connectedness of spacetime events through solutions of the Lorentz force equation. These approaches separate into three categories, that consider different equations. We clarify the…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
It is first shown that the scalar product on any orthogonal space (V, g) allows one to define linear isomorphisms of the vector spaces of bivectors and 2-forms on V with the underlying vector spaces of the Lie algebra so(p, q) and its dual,…
In this part of the series I show how five-tensors can be used for describing in a coordinate-independent way finite and infinitesimal Poincare transformations in flat space-time. As an illustration, I reformulate the classical mechanics of…
The vector form of a Lorentz transformation which is separated with time and space parts is studied. It is necessary to introduce a new definition of the relative velocity in this transformation, which plays an important role for the…
The theory of linear acceleration emission is developed for a large amplitude electrostatic wave in which all particles become highly relativistic in much less than a wave period. An Airy integral approximation is shown to apply near the…
In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analog of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
It is generally expected from intuition that the electromagnetic force exerted on a charged particle should remain unchanged when observed in different reference frames in uniform translational motion. In the special relativity, this…
A motion of a classical free charge in an electromagnetic plane wave can be found exactly in a fully relativistic case. We have found an approximate non-parameter form of the suitable equations of motion. In a linearly polarized wave, in…
Defining the electric and magnetic field vectors in curved spacetime requires a proper choice of the observer's frame four-vector. Related literature shows that this fundamental issue in physics still needs to be properly resolved. In…