Formulation of electromagnetism in a six dimensional space-time

Dattoli, G.; Mignani, Roberto

doi:10.1007/bf02786138

Cited by 28 publications

(5 citation statements)

References 3 publications

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“…in the frame of four-dimensional spacetime and we can extend this similarity to six-dimensional space as such as relativistic mass, momentum and energy of moving particles can't easily be measured. However, we can explain the effect of the anisotropy of the six-dimensional Lorentz scaling factor on the various physical properties with the help of the idea proposed by Recami and Mignani [12]; Demers [13]; Mignani and Recami [14]; Cole [15]; Dattoli and Mingani [16]; Pappas [17]; Teli [18]; Guy [19]; Franco and Jorge [20]. S massive frame is written as:…”

Section: Resultsmentioning

confidence: 99%

“…Some time ago, Recami and Mignani [12]; Demers [13]; Mignani and Recami [14]; Cole [15]; Dattoli and Mingani [16]; Pappas [17]; Teli [18]; Guy [19]; Franco and Jorge [20] added two extra time coordinates to the 4-dimensional spacetime coordinates to interpret the imaginary quantities in the superluminal Lorentz transformations. Time is taken as a vector in the Euclidian 3-dimensional space 3 T , so that an event can be represented in Euclidian 6-dimensional space…”

Section: A Six-dimensional Voigt-lorentz Transformationmentioning

confidence: 99%

“…Figure 3 shows the azimuthal angle variation of normalized As pointed out by Recami and Mignani [12]; Demers [13]; Mignani and Recami [14]; Cole [15]; Dattoli and Mingani [16]; Pappas [17]; Teli [18]; Guy [19]; Franco and Jorge [20] the magnitude of the time vector ( )…”

Section: Time Dilationmentioning

confidence: 99%

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Special Relativity in Six Dimensions

Sama

2022

5003

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In the four-dimensional spacetime theory of special relativity, the space coordinate is time contracted along the motion, while perpendicular coordinates are invariant and time varies with position. This leads to a velocity transformation valid at speed of light and used in showing invariance electric and magnetic fields which are invariant along x-axis but change occur along y, and z-axes, contrary to the classical electrodynamics. In this work we introduce a new six-dimensional spacetime theory which allows time (position) change of position (time) in three coordinate axes and still satisfy the Lorentz invariance conditions of metric and Maxwell’s wave equations between two frames. We derive a new velocity transformation rule which is valid at any relative speed of massive frames moving with respect to each other. We derived expressions for relativistic mass, energy, Doppler shift, time dilation, length contraction, photon rest mass, and used the conservation of relativistic power to prove that the electric and magnetic fields and consequently, Maxwell wave equations are Lorentz invariant between two massive frames with and without nonzero photon mass in vacuum and materials medium. Calculated photon mass is in excellent agreement with the measured and observed upper bounds of 1.24x10-54 kg and1.75x 10-53 kg, respectively.

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Section: Resultsmentioning

confidence: 99%

Section: A Six-dimensional Voigt-lorentz Transformationmentioning

confidence: 99%

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Special Relativity in Six Dimensions

Sama

2022

5003

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“…In this paper we consider a six dimensional spacetime structure having three time-like and three space-like coordinates which is left invariant under the "rotation" group SO (3,3). The introduction of a six-dimensional spacetime with three time coordinates originated from the seminal works by Mignani and Recami [40], Dattoli [41] and G. Ziino [42][43][44][45] as an attempt to solve the problem of superluminal motion in four-dimensional relativity theory [46][47][48][49][50][51]. E.A.B.…”

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confidence: 99%

The Dirac Equation in Six-dimensional SO(3,3) Symmetry Group and a Non-chiral “Electroweak” Theory

Dartora

Cabrera

2009

Int J Theor Phys

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We propose a model of electroweak interactions without chirality in a sixdimensional spacetime with 3 time-like and 3 space-like coordinates, which allows a geometrical meaning for gauge symmetries. The spacetime interval ds 2 = dx μ dx μ is left invariant under the symmetry group SO(3, 3). We obtain the six-dimensional version of the Dirac gamma matrices, μ , and write down a Dirac-like Lagrangian density, L = iψ μ ∇ μ ψ. The spinor ψ can be decomposed into two Dirac spinors, ψ 1 and ψ 2 , interpreted as the electron and neutrino fields, respectively. In six-dimensional spacetime the electron and neutrino fields appear as parts of the same entity in a natural manner. The SO(3, 3) Lorentz symmetry group is locally broken to the observable SO(1, 3) Lorentz group, with only one observable time component, t z . The t z -axis may not be the same at all points of the spacetime, and the effect of breaking the SO(3, 3) spacetime symmetry group locally to an SO(1, 3) Lorentz group, is perceived by the observers as the existence of the gauge fields. We interpret the origin of mass and gauge interactions as a consequence of extra time dimensions, without the need of introducing the so-called Higgs mechanism for the generation of mass. Further, in our 'toy' model, we are able to give a geometric meaning to the electromagnetic and non-Abelian gauge symmetries.

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“…These equations are different from those obtained earlier by Negi-Rajput [23] derived for electric charge only. These are also not exactly same as given by equations (3) for generalized subluminal electric and magnetic fields of dyons but shows the striking symmetry between the electric and magnetic fields of dyons under superluminal transformations and may thus be visualized as the generalized superluminal electromagnetic field of dyons in frame K when viewed from subluminal frame K. As such, it may be concluded that though the roles of electric and magnetic charges are not changed while passing from subluminal to superluminal realm under the superluminal transformations, a dyon interacting with superluminal electromagnetic fields containing symmetrical electromagnetic fields behaves neither as electric charge nor as pure magnetic monopole [32,33] but with mixed behaviors of electric and magnetic charges rather namely a tachyonic dyon. As such we agree with Negi-Rajput [23] that even in the case of a dyon interacting with generalized superluminal electromagnetic fields, a tachyonic electric charge can not behave as a bradyonic magnetic monopole or vice versa.…”

Section: Dyonic Field Equations Under Superluminal Lorentz Transmentioning

confidence: 99%