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.
We present a solution for the apparent paradox regarding an incompatibility between the Lorentz force law and special relativity presented by Mansuripur [Phys. Rev. Lett. 108, 193901 (2012)]. A connection between the apparent paradox and the Abraham-Minkowski debate about the momentum of electromagnetic waves in material media is also presented.
In the first part of this paper we review the fundamental difference between the usual transformations of the three-dimensional (3D) vectors of the electric field $\mathbf{E}$, the magnetic field $\mathbf{B}$, the polarization $\mathbf{P}$, the magnetization $\mathbf{M}$ and the Lorentz transformations of the 4D geometric quantities, vectors E, B, P, M, with many additional explanations and several new results. In the second part, we have discussed the existence of the electric field vector E outside a stationary superconducting wire with a steady current and also different experiments for the…
The usual transformations of the three-dimensional (3D) fields E and B that are found in [1] ([1] A. Einstein, Ann. Physik \17, 891 (1905)) are always considered to be the relativistically correct Lorentz transformations (LT) of E and B. However, as proved in, e.g., [2] ([2] T. Ivezić, Found. Phys. Lett. 18, 301 (2005)), these transformations drastically differ from the LT of the relativistically correct 4D electric and magnetic fields. In this paper a simple proof of that difference will be presented and the consequences for EDM experiments and for some quantum phase shifts experiments are br…
The usual transformations (UT) of the 3-vectors E and B that are found by Lorentz, Poincaré and independently by Einstein in 1905. are generally considered to be the Lorentz transformations (LT) of E and B. According to the UT E in one frame is 'seen' as E' and B' in a relatively moving frame. In Minkowski's last paper, in 1908. in section 11.6, he defined the vectors (with four components) of the electric $Φ$ and magnetic $Ψ$ fields and discovered that, e.g., $Φ$ correctly transforms by the LT again to $Φ^{\prime}$. His correct LT are reinvented in, e.g., [11] ([11] Ivezić T 2005 Found. Phys.…
We present diagrams and simple calculations for the apparent (i.e. photographable) length of a moving ruler skimming the observer's position, under three different classes of model. Special relativity's predictions in this particular situation are the root-product average of the two more basic first-order predictions generated by simple "propagation timelag" arguments. We find that special relativity can legally predict either a photographable Lorentz contraction or a photographable Lorentz expansion in the "centred" ruler, depending on whether our camera is at the ruler's "apparent" or "offic…
In this paper it will be exactly proved both in the geometric algebra and tensor formalisms that the usual Maxwell equations with the three-dimensional (3D) vectors of the electric and magnetic fields, E{bold} and B{bold} respectively, are not, contrary to the general opinion, Lorentz covariant equations. Consequently they are not equivalent to the field equations with the observer independent quantities, the electromagnetic field tensor Fsup{ab} (tensor formalism) or with the bivector field F (the geometric algebra formalism). Different 4D algebric objects are used to represent the standard o…
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not spatial intervals, so breaking space-time exchange symmetry and forbidding relativity of simultaneity and length contraction. Two satellite-borne experiments to test these predictions are proposed.
Observations of the apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not spatial intervals, so breaking space time exchange symmetry and forbidding relativity of simultaneity and length contraction. A satellite cesium clock experiment to test these predictions is proposed.
For every observer, however distant, the electric field of a uniformly moving charge is always directed away from, or points towards, the instantaneous present position of the charge and not away from, or towards, the retarded position at which the observer sees it (due to the finite speed of light). This fact is a well-established consequence of, among others, the application of the Liénard-Wiechert potentials, and its significance for fundamental physics is probably not fully appreciated. Here we show how and why this property has non-negligible consequences for what we take for granted abou…
In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebric objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and consequently that the ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained res…
In this paper a geometric approach to the special relativity (SR) is used that is called the "invariant special relativity" (ISR). In the ISR it is considered that in the four-dimensional (4D) spacetime physical laws are geometric, coordinate-free relationships between the 4D geometric, coordinate-free quantities. It is mathematicaly proved that in the ISR the electric and magnetic fields are properly defined vectors on the 4D spacetime. According to the first proof the dimension of a vector field is mathematicaly determined by the dimension of its domain. Since the electric and magnetic field…
It is generally assumed in the literature that a Lorentz transformation on a neutral current loop results in a moving current loop with a nonvanishing charge distribution and an electric dipole moment. We show in this paper that this is not, in fact, correct. The derivation that leads to the charge distribution was based on an incomplete Lorentz transformation, which transforms the charge-current four-vector $j^μ=[ρ({\bf r},t),{\bf j(r},t)]$, but not the space-time four-vector $x^μ=(t,{\bf r})$. We show that completing the Lorentz transformation by using the variable $t'$ in the moving frame, …
The distinction between the real positions of moving objects in a single reference frame and the apparent positions of objects at rest in one inertial frame and viewed from another, as predicted by the space-time Lorentz Transformations, is discussed. It is found that in the Rockets-and-String paradox the string remains unstressed and does not break and that the pole in the Barn-and-Pole paradox never actually fits into the barn. The close relationship of the Lorentz-Fitzgerald Contraction and the relativity of simultaneity of Special Relativity is pointed out and an associated paradox, in whi…
The standard Lorentz transformations establish a relationship between the space-time coordinates of the same event when detected from two inertial reference frames I and I' in the standard arrangement. This event is characterized by the space-time coordinates E(x,tE) and E'(x',t'E), tE and t'E representing the readings of the standard synchronized clocks C(x) and C'(x') located in the two frames where the event takes place. We obtain the nonstandard Lorentz transformations establishing a "physically" correct relationship between the readings of the standard synchronized clocks and the readings…
The apparent nonlocality of the Coulomb gauge external field problem in electrodynamics is illustrated with an example in which nonlocality is especially striking. Explanation of this apparent nonlocal behaviour based on a purely local picture is given. A gauge invariant decomposition of the Lorentz-force into two terms with clear physical meanings is pointed out. Based on this decomposition derivation of the Aharonov-Bohm effect in terms of field strengths alone is given.
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 dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_{f}=F\cdot γ_{0}, whereas the S…
This communication is devoted to a brief historical framework and to a comprehensive critical discussion concerning foundational issues of Electrodynamics. Attention is especially focused on the events which, about the end of XIX century, led to the notion of Lorentz force, still today ubiquitous in literature on Electrodynamics. Is this a noteworthy instance of a rule which, generated by an improper simplification of Maxwell-JJ Thomson formulation, is in fact physically untenable but, this notwithstanding, highly successful. Modelling of electromagnetic fields and fluxes in spacetime respecti…
We suppose that vacuum is filled with a kind of continuously distributed matter which may be called the $Ω(1)$ substratum, or the electromagnetic aether. Suppose that the time scale of a macroscopic observer is very large compares to the the Maxwelllian relaxation time of the $Ω(1)$ substratum. Thus, the macroscopic observer concludes that the $Ω(1)$ substratum behaves like a Newtonian-fluid. Inspired by H. A. Lorentz, we speculate that electric charges may be extremely small hard spherical sources or spherical sinks with finite radii. Based on the spherical source and spherical sink model of …
It is shown that the well-known procedure for proving the equivalence of the expressions for the electric field calculated using the Lorentz and Coulomb gauges is incorrect. The difference between the two gauges is due to the difference in the speed of propagation of a disturbance of the scalar potential. As an auxiliary result, it is proven that the solution for the electric field cannot be obtained directly from the Maxwell equations, i.e. without introducing the scalar and vector potentials.
We consider the magneto-electric optical properties of the quantum vacuum and show that all the different phenomenona are related by Lorentz invariance. As a model calculation we show how crossed fields properties can be calculated starting from single field properties by using Lorentz transformations. Using this method we have studied for the first time the case of a crossed static magnetic field and electric field applied with one of these two fields parallel to the direction of light propagation. We also show that parallel field properties can be found using general symmetry properties.
The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to nonholonomic frames with 2 (or 3) +2+2+... spacetime decompositions. This allows us to construct exact solutions with generic off--diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (un-) broken symmetry parameters. Such nonholonomic configurations/ models have a nice ultraviolet behavior and seem to be gho…
In this paper it is exactly proved by using the Clifford algebra formalism that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not the Lorentz transformations of well-defined quantities from the 4D spacetime but the 'apparent' transformations of the 3D quantities. Thence the usual Maxwell equations with the 3D E and B are not in agreement with special relativity. The 1-vectors E and B, as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B.
In this paper, we consider the apparent superluminal speed of neutrinos in their travel from CERN to Gran Susso, as measured by the OPERA experiment, within the framework of the Extended Lorentz Transformation Model. The model is based on a natural extension of Lorentz transformation by wick rotation. Scalar and Dirac's fields are considered and invariance under the new lorentz group is discussed. Moreover, an extension of quantum mechanics to accommodate new particles is considered using the newly proposed Generalized-$\mathbb{C}$ quantum mechanics. A two dimensional representation of the new…
We discuss transormation laws of electric and magnetic fields under Lorentz transformations, deduced from the Classical Field Theory. It is found that we can connect the resulting expression for a bivector formed with those fields, with the expression deduced from the Wigner transformation rules for spin-1 functions of massive particles. This mass parameter should be interpreted because the constancy of speed of light forbids the existence of the photon mass.
It is pointed out that the underlying reason why the magnetic force is similar to a Coriolis force is that it is caused by Thomas rotations, induced by successions of non-collinear Lorentz boosts. The magnetic force may even be viewed as a kind of Coriolis force (making perhaps more acceptable the apparent non-existence of magnetic monopoles). We also show that under a change of inertial frames, Faraday lines of force Lorentz contract as if 'etched' in space, while 'Coriolis' terms get added on.
