We propose two semismooth Newton methods for seeking the eigenvalues of a linear transformation relative to Lorentz cones, by the natural equation reformulation and the normal equation reformulation, respectively, and establish their local quadratic convergence results under suitable conditions. The convergence analysis shows that the method based on the natural equation formulation is not infl...

Lorentz gas as a typical distribution of velocities for more than a moment. We may take the initial momentary distribution of velocities as conforming to Lorentz, but a moment later, owing to the finite distribution of the condensing wall, the ions there will have a radial distribution of velocity with v V v not equal to zero. With v * V v not equal to zero at the points we cannot make the gas ...

We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-1/2 particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum. The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lore...

The special theory of relativity grew out of the Maxwell electromagnetic equations. So it came about that even in the derivation of the mechanical concepts and their relations the consideration of those of the electromagnetic field has played an essential role. The question as to the independence of those relations is a natural one because the Lorentz transformation, the real basis of the speci...

The origin of the FitzGerald-Lorentz length contraction (FLC) hypothesis is discussed and attempts to verify it empirically are analyzed in detail. It is pointed out that the Lorentz transformation (LT) and the FLC not only rest on Einstein's two postulates of relativity, but also depend in a crucial way upon an additional assumption that was untested experimentally at the time. It is shown tha...