相关论文: The language of Einstein spoken by optical instrum…
Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics,…
We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
We show that the standard Lorentz transformations admit an invariant mass (length) scale, such as the Planck scale. In other words, the frame independence of such scale is built-in within those transformations, and one does not need to…
Invariance of the counted number of photons and the Lorentz-Einstein transformations enable us to derive transformation equations for the physical quantities introduced in order to characterize energy emission and transport in a plane and…
The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
The ``little group'' for massless particles (namely, the Lorentz transformations $\Lambda$ that leave a null vector invariant) is isomorphic to the Euclidean group E2: translations and rotations in a plane. We show how to obtain explicitly…
Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current…
The study of light lensed by cosmic matter has yielded much information about astrophysical questions. Observations are explained using geometrical optics following a ray-based description of light. After deflection the lensed light…
We show that the image by the Lorentz transformation of a spherical (circular) light wave, emitted by a moving source, is not a spherical (circular) light wave but an ellipsoidal (elliptical) light wave. Poincare's ellipsoid (ellipse) is…
We propose a reformulation of general relativity by making the Abelian decomposition of Einstein's theory. Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the Einstein's…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
Starting with a thought experiment proposed by Kard, which derives the formula that accounts for the relativistic effect of length contraction, we present a "two line" transparent derivation of the Lorentz-Einstein transformations for the…
Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take…
Lorentz symmetry is the fundamental symmetry of Einstein's theory of Special Relativity and has been tested to great precision. Nevertheless, the possibility remains that it is violated at the Planck scale, as predicted by some theories of…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily…
In previous work, the author extended the Poincare Lie algebra to include a four position operator as a natural extension to a large fifteen parameter Lie algebra of operators. We here propose to generalize the metric contained in those…
In this paper, we discuss the role of Mathematics in articulating reality in theoretical Physics. We propose a parallel between empirical and theoretical work and investigate how scientists can also speak about reality without performing…