arXiv subjects

Tomislav Ivezic

Publications and source records attributed to Tomislav Ivezic.

At least 37 records · Page 2Linked to original sources

arXiv2006

Trouton-Noble paradox revisited

An apparent paradox is obtained in all previous treatments of the Trouton-Noble experiment; there is a three-dimensional torque in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque in S', the rest frame of the capacitor. In this paper instead of using 3D quantities and their ``apparent'' transformations we deal with 4D geometric quantities their Lorentz transformations and equations with them. We introduce a new decomposition of the torque N (bivector) into 1-vectors N_{s} and N_{t}. It is shown that in the frame of ``fiducial'' observers, in which the observers who measure N_{s} and N_{t} are at rest, and in the standard basis, only the spatial components N_{s}^{i} and N_{t}^{i} remain, which can be associated with components of two 3D torques. In such treatment with 4D geometric quantities the mentioned paradox does not appear. The presented explanation is in a complete agreement with the principle of relativity and with the Trouton-Noble experiment without the introduction of any additional torque.

physics.gen-ph↗

arXiv2006

Lorentz Invariant Majorana Formulation of the Field Equations and Dirac-like Equation for the Free Photon

In this paper we present a new geometric formulation (Clifford algebra formalism) of the field equations, which is independent of the reference frame and of the chosen system of coordinates in it. This formulation deals with the complex 1-vector $Ψ=E-icB$ ($i$ is the unit imaginary), which is four-dimensional (4D) geometric generalization of Majorana's complex 3D quantity $\mathbfΨ=\mathbf{E}-ic\mathbf{B}$. When the sources are absent the field equations with the complex $Ψ$ become Dirac-like relativistic wave equations for the free photon. In the frame of ``fiducial'' observers (the observers who measure fields are at rest) and in the standard basis the component form of the field equations with 4D $Ψ$ reproduces the component form of Majorana-Maxwell equations with 3D field $\mathbfΨ$. The important differences between the approach with the 4D $Ψ$ and that one with the 3D $\mathbfΨ$ are discussed.

physics.gen-ph↗

arXiv2006

The 4D geometric quantities versus the usual 3D quantities. The resolution of Jackson's paradox

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N_{s}, N_{t} and M_{s}, M_{t} respectively are given. The torques N_{s}, N_{t} (the angular momentums M_{s}, M_{t}), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities $\mathbf{E}$, $\mathbf{B}$, $\mathbf{F}$, $\mathbf{L}$, $\mathbf{N}$, etc. and their transformations are objected from the viewpoint of the invariant special relativity (ISR). In the ISR it is considered that 4D geometric quantities are well-defined both theoretically and \emph{experimentally} in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities.

physics.gen-ph↗

arXiv2005

Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment

In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The new observer independent expressions for the stress-energy vector T(n)(1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K (1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1-vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment.

physics.gen-ph↗

arXiv2005

Comment on ``Torque or no torque? Simple charged particle motion observed in different inertial frames,'' by J. D. Jackson [Am. J. Phys. 72 (12), 1484-1487 (2004)]

In this paper it is shown that the real cause of the apparent electrodynamic paradox discussed by Jackson [J. D. Jackson, Am. J. Phys. 72, 1484 (2004)] is the use of three-dimensional (3D) quantities E, B, F, L, N, .. . When 4D geometric quantities are used then there is no paradox and the principle of relativity is naturally satisfied.

physics.gen-ph↗

arXiv2005

Torque or no torque?! The resolution of the paradox using 4D geometric quantities with the explanation of the Trouton-Noble experiment

In this paper we have resolved the apparent paradox of different mechanical equations for force and torque governing the motion of a charged particle in different inertial frames. The same paradox arises in all usual ``explanations'' of the Trouton-Noble experiment. It is shown that the real cause of the paradoxes is - \emph{the use of three dimensional (3D) quantities}, e.g., $\mathbf{E}$, $\mathbf{B}$, $\mathbf{F}$, $\mathbf{L}$, $% \mathbf{N}$, \emph{their transformations and equations with them.} Instead of using 3D quantities we deal with \emph{4D geometric quantities, their Lorentz transformations and equations with them}. In such treatment the paradoxes do not appear. The explanation with \emph{4D geometric quantities}% is in a complete agreement with the principle of relativity and with the Trouton-Noble experiment.

physics.gen-ph↗

arXiv2004

The Proof that the Standard Transformations of E and B are not the Lorentz Transformations. Application to Motional EMF

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 ST are the result of the application of the LT only to the part of E_{f}, i.e., to F, but leaving gamma_{0} unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.

physics.gen-ph↗

arXiv2004

The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations. The New Lorentz Invariant Field Equations

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 results do not depend on the character of the 4D algebric objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors E_{Hv} and B_{Hv} and the abstract tensors, the 4-vectors E^{a} and B^{a}. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D E and B and their ST.

physics.gen-ph↗

arXiv2003

The exact proof that Maxwell equations with the 3D E and B are not Lorentz covariant equations. The new Lorentz invariant field equations

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 observer dependent and the new observer independent electric and magnetic fields. The proof of a fundamental disagreement between the standard electromagnetism and the special relativity does not depend on the character of the 4D algebric object used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors Esub{HL} and Bsub{HL} and the abstract tensors, the 4-vectors Esup{a} and Bsup{a}. All these quantities are defined without reference frames. Such field equations are in a complete agreement with experiments.

physics.gen-ph↗

arXiv2003

The Proof that the Standard Transformations of E and B are not the Lorentz Transformations. Clifford Algebra Formalism

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.

physics.gen-ph↗

arXiv2003

Lorentz invariant relativistic electrodynamics in the Clifford algebra formalism. The formulation with bivector field F

In this paper we present the formulation of relativistic electrodynamics (independent of the reference frame and of the chosen system of coordinates in it) that uses the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames or, when some basis is introduced, every quantity is represented as a coordinate-based geometric quantity comprising both components and a basis. The new, observer independent, expressions for the stress-energy vector T(n), the energy density U, the Poynting vector S and the momentum density g, the angular momentum density M and the Lorentz force K are directly derived from the field equations with F.

physics.gen-ph↗

arXiv2003

The Proof that the Standard Transformations of E and B and the Maxwell Equations with E and B are not Relativistically Correct

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D spacetime and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E^a and B^a, as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms.

hep-th↗

arXiv2002

Invariant Relativistic Electrodynamics. Clifford Algebra Approach

In the usual Clifford algebra formulation of electrodynamics the Faraday bivector field F is decomposed into the observer dependent sum of a relative vector E and a relative bivector e_5 B by making a space-time split, which depends on the observer velocity. (E corresponds to the three-dimensional electric field vector, B corresponds to the three-dimensional magnetic field vector and e_5 is the (grade-4) pseudoscalar.) In this paper it is proved that the space-time split and the relative vectors are not relativistically correct, which means that the ordinary Maxwell equations with E and B and the field equations (FE) with F are not physically equivalent. Therefore we present the observer independent decomposition of F by using the 1-vectors of electric E and magnetic B fields. The equivalent, invariant, formulations of relativistic electrodynamics (independent of the reference frame and of the chosen coordinatization for that frame) which use F, E and B, the real multivector Psi = E - e_5 cB and the complex 1-vector Psi = E - icB are developed and presented here. The new observer independent FE are presented in formulations with E and B, with real and complex Psi. When the sources are absent the FE with real and complex Psi become Dirac like relativistic wave equations for the free photon. The expressions for the observer independent stress-energy vector T(v) (1-vector), energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K (1-vector) are directly derived from the FE. The local conservation laws are also directly derived from the FE and written in an invariant way.

hep-th↗

arXiv2002

The invariant formulation of special relativity, or the "true transformations relativity", and electrodynamics

In the invariant approach to special relativity (SR), which we call the ''true transformations (TT) relativity,'' a physical quantity in the four-dimensional spacetime is mathematically represented either by a true tensor or equivalently by a coordinate-based geometric quantity comprising both components and a basis. This invariant approach differs both from the usual covariant approach, which mainly deals with the basis components of tensors in a specific, i.e., Einstein's coordinatization of the chosen inertial frame of reference,.and the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rather quantities from ''3+1'' space and time, e.g., the synchronously determined spatial length. This noncovariant formulation of SR is called the ''apparent transformations (AT) relativity.'' The principal difference between the ''TT relativity'' and the ''AT relativity'' arises from the difference in the concept of sameness of a physical quantity for different observers. In the second part of this paper we present the invariant formulation of electrodynamics with the electromagnetic field tensor F^{ab}, and also the equivalent formulation in terms of the four-vectors of the electric E^{a} and magnetic B^{a} fields.

hep-ph↗

arXiv2002

Relativistic Electrodynamics without Reference Frames. Clifford Algebra Formulation

In the usual Clifford algebra formulation of electrodynamics the Faraday bivector field $F$ is expressed in terms of \QTR{em}{the observer dependent} relative vectors $\QTR{bf}{E}$ and $\QTR{bf}{B.}$ In this paper we present \QTR{em}{the observer independent}decomposition of $F$ by using the vectors (grade-1) of electric $E$ and magnetic $B$ fields and we develop the formulation of relativistic electrodynamics which is independent of the reference frame and of the chosen coordinatization. We also present equivalent formulations by using the multivector (Clifford aggregate) $Ψ=E-e_{5}cB$ for the real Clifford algebra; $e_{5}$ is the (grade-4) pseudoscalar) or the complex 1-vector $Ψ=E-icB$ (for the complex Clifford algebra; $i$ is the unit imaginary). In such formulations the Maxwell equations become a Dirac like relativistic wave equation for the free photon.

hep-ph↗

arXiv2002

About the Simultaneous Co-Existence of Instantaneous and Retarded Interactions in Classical Electrodynamics

In this paper it is proved that, contrary to the results found by A.E. Chubykalo and S.J. Vlaev (Int. J. Mod. Phys. A 14, 3789 (1999)), the retarded electric and magnetic fields for an uniformly accelerated charge exactly satisfy Maxwell equations (ME). Furthermore it is shown that ME are correctly written in the usual form with the partial derivatives and thus not, as proposed by Chubykalo and Vlaev, with the total derivatives.

hep-ph↗

arXiv2001

An Invariant Formulation of Special Relativity, or the "True Transformation Relativity," and its Comparison with Experiments

Different formulations of special relativity are theoretically discussed. First an invariant formulation, i.e., the ''true transformations (TT) relativity,'' is exposed. There a physical quantity is represented by a true tensor which comprises both components and a basis. Also the usual covariant formulation and the ''apparent transformations (AT) relativity'' are considered. It is shown that all the experiments are in agreement with the ''TT relativity'' but not always with the ''AT relativity.''

physics.gen-ph↗

arXiv2001

Covariant Formulation of Electromagnetic 4-Momentum in Terms of 4-Vectors E^αand B^α

The fundamental difference between the true transformations (TT) and the apparent transformations (AT) is explained. The TT refer to the same quantity, while the AT refer, e.g., to the same measurement in different inertial frames of reference. It is shown that the usual transformations of the three-vectors E and B are - the AT. The covariant electrodynamics with the four-vectors E(sup alpha) and B(sup alpha) of the electric and magnetic field is constructed. It is also shown that the conventional synchronous definitions of the electromagnetic energy and momentum contain both, the AT of the volume, i.e.,the Lorentz contraction, and the AT of E and B, while Rohrlich's expressions contain only the AT of E and B. A manifestly covariant expression for the energy-momentum density tensor and the electromagnetic 4-momentum is constructed using E(sup alpha) and B(sup alpha). The "4/3" problem is discussed and it is shown that all previous treatments either contain the AT of the volume, or the AT of E and B, or both of them. In our approach all quantities are four-dimensional spacetime tensors whose transformations are the TT.

physics.gen-ph↗