The non-commutativity and the non-associativity of the composition law of the non-colinear velocities lead to an apparent paradox, which in turn is solved by the Thomas rotation. A 3×3 parametric, unimodular and orthogonal matrix elaborated by Ungar is able to determine the Thomas rotation. However, the algebra involved in the derivation of the Thomas rotation matrix is overwhelming. The aim of this paper is to present a direct derivation of the Thomas angle as the angle between the composite vectors of the non-colinear velocities, thus obtaining a simplicity with which the rotation can be expressed. This allows the formulation of an alternative to the statement related to the necessity of the Thomas rotation of the Cartesian axes by the statement implying the necessity of the rotation of the direct (inverse) relativistic composite velocity to coincide with the inverse (direct) relativistic composite velocity.

On the relativistic velocity composition paradox and the Thomas rotation

Antibodies in the sera of patients with lacaziosis recognized an approximately 193-kDa antigen and other Lacazia loboi antigens. Paracoccidioides brasiliensis gp43 antigen was detected by all evaluated sera, but they failed to detect a protein with the same molecular mass in L. loboi extracts. This study is the first to examine the humoral response to L. loboi antigens by using multiple host sera.

Use of sera from humans and dolphins with lacaziosis and sera from experimentally infected mice for Western Blot analyses of Lacazia loboi antigens.

We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell’s equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material invariance is established and shown to be a true covariance principle, unlike the Lorentz covariance, which is valid only for non-deforming frames in rectilinear relative motion. Thus, this paper establishes that electrodynamics can be fully explained if one assumes that it is the manifestation of the internal forces of an underlying elastic material which we term the metacontinuum. The new frame-indifferent formulation of electrodynamics is shown to incorporate the Lorentz force as an integral part of Faraday’s law, rather than as an additional empirical variable. Respectively, if the upper-convected derivative is added in Maxwell’s displacement current it can explain Biot–Savart’s and Oersted–Ampere’s laws. An immediate corollary of the material invariance is the Galilean invariance of the model. The possible detection of the absolute continuum is also discussed. First, the famous experiment of Ives and Stilwell is reexamined with a modified Bohr–Rydberg formula for the emitted frequencies from a moving atom, and it is shown that the results are fully compatible with the presence of an absolute medium. Second, a new interferometry experiment is proposed in which the first-order Doppler effect can be measured, and thus the presence of a medium at rest can be unequivocally established.

On the nonlinear continuum mechanics of space and the notion of luminiferous medium

Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative Assuming that the electromagnetic field should follow the general requirements for a material field, we show that if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell’s electrodynamics becomes material invariant Note, that the material invariance of Faraday’s law is automatically established if the Lorentz force is admitted as an integral part of the model The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum

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Jeff Nicoll

Papers

Heretical Verities: Mathematical Themes in Physical Description