Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation

In ZM theory the direction of time has a non-zero projection onto space and this projection corresponds to the local velocity relative to the observer. Classical trajectories can be obtained by following the local direction of time. The relationship of time to space enables the change in momentum over time to be related to the spatial change in energy and momentum. Previously Hamilton's equations-of-motion were derived by considering trajectories in one space and one time dim...

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 distributio...

Special relativity is reformulated as a symmetry property of space-time: Space-Time Exchange Invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the traditional form of the Principle of Special Relativity. The kinematical version of the latter is shown to be a consequence of the Lorentz transformation. As a dynamical application, the laws of electrodynamics and magnetodynamics are derived fr...

We analyze the transformation properties of Faraday law in an empty space and its relationship with Maxwell equations. In our analysis we express the Faraday law via the four-potential of electromagnetic field and the field of four-velocity, defined on a circuit under its deforming motion. The obtained equations show one more facet of the physical meaning of electromagnetic potentials, where the motional and transformer parts of the flux rule are incorporated into a common ph...

The unification of electricity and magnetism achieved by special relativity has remained for decades a model of unification in theoretical physics. We discuss the relationship between electric and magnetic fields from a classical point of view, and then examine how the four main relevant authors (Lorentz, Poincar\'e, Einstein, Minkowski) dealt with the problem of establishing the transformation laws of the fields in different inertial systems. We argue that Poincar\'e's deriv...

In this paper it is proved by using the Clifford algebra formalism that the standard transformations (ST) of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer ...

After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is involved via the addition law of parallel speeds or via the Lorentz transformations for the space-time coordinates of the same event. Electricity and magnetism are involved via Gauss's and Ampere's laws. In this way we avoid the transformatio...

It is recently discovered that the usual transformations of the three-dimensional (3D) vectors of the electric and magnetic fields differ from the Lorentz transformations (LT) (boosts) of the corresponding 4D quantities that represent the electric and magnetic fields. In this paper, using geometric algebra formalism, this fundamental difference is examined representing the electric and magnetic fields by bivectors.

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamic quantities are derived from the pre-assumption that the equations of electrodynamics are covariant against these---unknown---transformation rules. There are several problems to be raised concerning these derivations. This is, however, not our main concern in this paper. Even if these derivations are regarded as unquestionable, they leave...

This Comment addresses a recent paper by M. Mansuripur (Phys. Rev. Lett. 108, 193901 (2012)), who claims that the Lorentz law of force should be abandoned because it violates relativity. The Comment argues that this is not necessarily the case and also takes issue with Manusripur's approach to classical electromagnetism.