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Register a new userSpecial Relativity in the 21$^{rm st}$ century
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This paper, which is meant to be a tribute to Minkowskis geometrical insight, rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space, which are displayed by the spacetime manifold in the limiting situation in which the effects of gravity can be neglected, leads to a formulation of special relativity based on the appearance of two universal constants: a limiting speed $c$ and a cosmological constant $Lambda$ which measures a residual curvature of the universe, which is not ascribable to the distribution of matter-energy. That these constants should exist is an outcome of the underlying symmetries and is confirmed by experiments and observations, which furnish their actual values. Specifically, it turns out on these foundations that the kinematical group of special relativity is the de Sitter group $dS(c,Lambda)=SO(1,4)$. On this basis, we develop at an elementary classical and, hopefully, sufficiently didactical level the main aspects of the theory of special relativity based on SO(1,4) (de Sitter relativity). As an application, we apply the formalism to an intrinsic formulation of point particle kinematics describing both inertial motion and particle collisions and decays.
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We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of binaries containing black holes and neutron stars, as well as simulations of black-hole formation through failed supernovae and high-mass neutron star--neutron star mergers. Modeling such events requires numerical integration of the field equations of general relativity in three spatial dimensions, coupled, in the case of neutron-star containing binaries, with increasingly sophisticated treatment of fluids, electromagnetic fields, and neutrino radiation. However, it was not until 2005 that accurate long-term evolutions of binaries containing black holes were even possible. Since then, there has been an explosion of new results and insights into the physics of strongly-gravitating system. Particular emphasis has been placed on understanding the gravitational wave and electromagnetic signatures from these extreme events. And with the recent dramatic discoveries of gravitational waves from merging black holes by the Laser Interferometric Gravitational Wave Observatory and Virgo, and the subsequent discovery of both electromagnetic and gravitational wave signals from a merging neutron star binary, numerical relativity became an indispensable tool for the new field of multimessenger astronomy.
In the history of cosmology physical paradoxes played important role for development of contemporary world models. Within the modern standard cosmological model there are both observational and conceptual cosmological paradoxes which stimulate to search their solution. Confrontation of theoretical predictions of the standard cosmological model with the latest astrophysical observational data is considered. A review of conceptual problems of the Friedmann space expending models, which are in the bases of modern cosmological model, is discussed. The main paradoxes, which are discussed in modern literature, are the Newtonian character of the exact Friedmann equation, the violation of the energy conservation within any comoving local volume, violation of the limiting recession velocity of galaxies for the observed high redshift objects. Possible observational tests of the nature of the cosmological redshift are discussed
The hodograph of a non-relativistic particle motion in Euclidean space is the curve described by its momentum vector. For a general central orbit problem the hodograph is the inverse of the pedal curve of the orbit, (i.e. its polar reciprocal), rotated through a right angle. Hamilton showed that for the Kepler/Coulomb problem, the hodograph is a circle whose centre is in the direction of a conserved eccentricity vector. The addition of an inverse cube law force induces the eccentricity vector to precess and with it the hodograph. The same effect is produced by a cosmic string. If one takes the relativistic momentum to define the hodograph, then for the Sommerfeld (i.e. the special relativistic Kepler/Coulomb problem) there is an effective inverse cube force which causes the hodograph to precess. If one uses Schwarzschild coordinates one may also define a a hodograph for timelike or null geodesics moving around a black hole. Iheir pedal equations are given. In special cases the hodograph may be found explicitly. For example the orbit of a photon which starts from the past singularity, grazes the horizon and returns to future singularity is a cardioid, its pedal equation is Cayleys sextic the inverse of which is Tschirhausens cubic. It is also shown that that provided one uses Beltrami coordinates, the hodograph for the non-relativistic Kepler problem on hyperbolic space is also a circle. An analogous result holds for the the round 3-sphere. In an appendix the hodograph of a particle freely moving on a group manifold equipped with a left-invariant metric is defined.
This research aims to introduce a new principle in the flat space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the quantum world. This limit, unattainable by the particles, represents a preferred inertial reference frame associated with a universal background field that breaks Lorentz symmetry. There emerges a new relativistic dynamics where a minimum speed forms an inferior energy barrier. One of the interesting consequences of the existence of such a minimum speed is that it prevents the absolute zero temperature for an ultracold gas according to the third law of thermodynamics. So we will be able to provide a fundamental dynamical explanation for the third law through a connection between such a phenomenological law and the new relativistic dynamics with a minimum speed.
Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson--Mansouri--Sexl parameter $|alpha|lesssim 1.1 times10^{-8}$ quantifying a violation of time dilation, thus improving by a factor of around two the best known constraint obtained with Ives--Stilwell type experiments, and by two orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this paper will improve by orders of magnitude in the near future.
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