Dimensions and units in electrodynamics

Hehl, Friedrich W.; Obukhov, Yuri N.

doi:10.1007/s10714-005-0059-2

Cited by 31 publications

(29 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the absolute dimensions approach [11], we have [J] = [ρ] = charge. The 2-form j is the electric current density with the absolute dimension of [j] = charge/time.…”

Section: Electric Charge Conservationmentioning

confidence: 99%

Backwards on Minkowski's road. From 4D to 3D Maxwellian electromagnetism

Itin¹,

Friedman²

2008

Ann. Phys.

View full text Add to dashboard Cite

Abstract. Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of the covariant four-dimensional form unique? How do the different sign assumptions of electrodynamics emerge from this decomposition? Which of these assumptions are fundamental and which of them may be modified? How does the Minkowski space-time metric emerge from this preliminary metricfree construction? In this paper we are looking for answers to the problems mentioned. Our main result is the derivation of four different possible sets of electrodynamic equations which may occur in different types of isotropic electromagnetic media. The wave propagation in each of these media is described by the Minkowskian optical metrics. Moreover, the electric and magnetic energies are nonnegative in all cases. We also show that the correct directions of the Lorentz force (as a consequence of the Dufay and the Lenz rules) hold true for all these cases. However, the differences between these four types of media must have a physical meaning. In particular, the signs of the three electromagnetic invariants are different.

show abstract

“…In the absolute dimensions approach [11], we have [J] = [ρ] = charge. The 2-form j is the electric current density with the absolute dimension of [j] = charge/time.…”

Section: Electric Charge Conservationmentioning

confidence: 99%

Backwards on Minkowski's road. From 4D to 3D Maxwellian electromagnetism

Itin¹,

Friedman²

2008

Ann. Phys.

View full text Add to dashboard Cite

show abstract

“…The dimension of a 0 doesn't point to its universality. Remember that universal constants usually have the dimensions of q n 1 h n 2 , where q denotes the dimension of a charge and h that of an action, see Post [60] and [41]. Constants built according to this rule, are 4-dimensional scalars, since q and h carry exactly this property.…”

Section: Evans' Ansatzmentioning

confidence: 99%

An Assessment of Evans’ Unified Field Theory I

Hehl

Obukhov

2007

Found Phys

Self Cite

View full text Add to dashboard Cite

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ α and a (metric compatible) Lorentz connection Γ αβ . These two potentials yield the field strengths torsion T α and curvature R αβ . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ α to be proportional to four extended electromagnetic potentials A α ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.

show abstract

“…Further, by introducing the von Klitzing constant (the quantized Hall resistance) (Klitzing et al (1980)) R K = h/e 2 , the fine-structure constant can be expressed as α = Z 0 /2R K (Hehl & Obukhov (2005)). We have learned that the use of Z 0 helps to keep SI-formulae in simple forms.…”

Section: The Fine-structure Constantmentioning

confidence: 99%

Reformulation of Electromagnetism with Differential Forms

Kitano¹

2012

Trends in Electromagnetism - From Fundamentals to Applications

View full text Add to dashboard Cite

Japan IntroductionClassical electromagnetism is a well-established discipline. However, there remains some confusions and misunderstandings with respect to its basic structures and interpretations. For example, there is a long-lasting controversy on the choice of unit systems. There are also the intricate disputes over the so-called EH or EB formulations. In some textbooks, the authors respect the fields E and B as fundamental quantities and understate D and H as auxiliary quantities. Sometimes the roles of D and H in a vacuum are totally neglected.These confusions mainly come from the conventional formalism of electromagnetism and also from the use of the old unit systems, in which distinction between E and D,o rB and H is blurred, especially in vacuum. The standard scalar-vector formalism, mainly due to Heaviside, greatly simplifies the electromagnetic (EM) theory compared with the original formalism developed by Maxwell. There, the field quantities are classified according to the number of components: vectors with three components and scalars with single component. But this classification is rather superficial. From a modern mathematical point of view, the field quantities must be classified according to the tensorial order. The field quantities D and B are the 2nd-order tensors (or 2 forms), while E and H are the 1st-order tensors (1 forms). (The anti-symmetric tensors of order n are called n-forms.)The constitutive relations are usually considered as simple proportional relations between E and D, and between B and H. But in terms of differential forms, they associate the conversion of tensorial order, which is known as the Hodge dual operation. In spite of the simple appearance, the constitutive relations, even for the case of vacuum, are the non-trivial part of the EM theory. By introducing relativistic field variables and the vacuum impedance, the constitutive relation can be unified into a single equation.The EM theory has the symmetry with respect to the space inversion, therefore, each field quantity has a definite parity, even or odd. In the conventional scalar-vector notation, the parity is assigned rather by hand not from the first principle: the odd vectors E and D are named the polar vectors and the even vectors B and H are named the axial vectors. With respect to differential forms, the parity is determined by the tensorial order and the pseudoness (twisted or untwisted). The pseudoness is flipped under the Hodge dual operation. The way of parity assignment in the framework of differential forms is quite natural in geometrical point of view.

show abstract

Dimensions and units in electrodynamics

Cited by 31 publications

References 43 publications

Backwards on Minkowski's road. From 4D to 3D Maxwellian electromagnetism

Backwards on Minkowski's road. From 4D to 3D Maxwellian electromagnetism

An Assessment of Evans’ Unified Field Theory I

Reformulation of Electromagnetism with Differential Forms

Contact Info

Product

Resources

About