String theory at order α′2 and the generalized Bergshoeff-de Roo identification

It has been shown by Marques and Nunez that the first α′-correction to the bosonic and heterotic string can be captured in the O(D, D) covariant formalism of Double Field Theory via a certain two-parameter deformation of the double Lorentz transformations. This deformation in turn leads to an infinite tower of α′-corrections and it has been suggested that they can be captured by a generalization of the Bergshoeff-de Roo identification between Lorentz and gauge degrees of freedom in an extended DFT formalism. Here we provide strong evidence that this indeed gives the correct α′2-corrections to the bosonic and heterotic string by showing that it leads to a cubic Riemann term for the former but not for the latter, in agreement with the known structure of these corrections including the coefficient of Riemann cubed.

On the Schwarzschild solution in TEGR

Conserved currents, superpotentials and charges for the Schwarzschild black hole in the Teleparallel Equivalent of General Relativity (TEGR) are constructed. We work in the covariant formalism and use the Noether machinery to construct conserved quantities that are covariant/invariant with respect to both coordinate and local Lorentz transformations. The constructed quantities depend on the vector field ξ and we consider two different possibilities, when ξ is chosen as either a timelike Killing vector or a four-velocity of an observer. We analyze and discuss the physical meaning of each choice in different frames: static and freely falling Lemaitre frame. Moreover, a new generalized free-falling frame with an arbitrary initial velocity at infinity is introduced. We derive the inertial spin connection for various tetrads in different frames and find that the “switching-off” gravity method leads to ambiguities.

Scrutiny of the So-Called Einstein’s Causality

In the present paper, the so-called Einstein’s causality is scrutinized and proven to be an illusion, a sort of mathematical fallacy. Causality as a well-established universal principle was and is absolutely valid for subluminal, luminal and superluminal signals under any natural and/or artificial circumstances. It is also shown that conceptually special relativity theory (SRT) is inapplicable to superluminality of physical phenomena since SRThas the light speed in vacuum as an upper limiting speed in its own proper domain of applications, and also because SRT is crucially based on the concept of inertial reference frames (IRFs) which are related to each other by Lorentz transformations, that is why the relative velocity of any two IRFs must be smaller than light speed.

Explicit Baker–Campbell–Hausdorff–Dynkin formula for spacetime via geometric algebra

We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations [Formula: see text] in the spin representation (a.k.a. Lorentz rotors) in terms of their generators [Formula: see text]: [Formula: see text] This formula is general to geometric algebras (a.k.a. real Clifford algebras) of dimension [Formula: see text], naturally generalizing Rodrigues’ formula for rotations in [Formula: see text]. In particular, it applies to Lorentz rotors within the framework of Hestenes’ spacetime algebra, and provides an efficient method for composing Lorentz generators. Computer implementations are possible with a complex [Formula: see text] matrix representation realized by the Pauli spin matrices. The formula is applied to the composition of relativistic 3-velocities yielding simple expressions for the resulting boost and the concomitant Wigner angle.

The CMB, Preferred Reference System, and Dragging of Light in the Earth Frame

The dominant CMB dipole anisotropy is a Doppler effect due to a particular motion of the solar system with a velocity of 370 km/s. Since this derives from peculiar motions and local inhomogeneities, one could meaningfully consider a fundamental frame of rest Σ associated with the Universe as a whole. From the group properties of Lorentz transformations, two observers, individually moving within Σ, would still be connected by the relativistic composition rules. However, the ultimate implications could be substantial. Physical interpretation is thus traditionally demanded in order to correlate some of the dragging of light observed in the laboratory with the direct CMB observations. Today, the small residuals—from those of Michelson–Morley to present experiments with optical resonators—are just considered instrumental artifacts. However, if the velocity of light in the interferometers is not the same parameter “c” of Lorentz transformations, nothing would prevent a non-zero dragging. Furthermore, the observable effects would be much smaller than what is classically expected and would most likely be of an irregular nature. We review an alternative reading of experiments that leads to remarkable correlations with the CMB observations. Notably, we explain the irregular 10−15 fractional frequency shift presently measured with optical resonators operating in vacuum and solid dielectrics. For integration times of about 1 s and a typical Central European latitude, we also predict daily variations of the Allan variance in the range (5÷12)·10−16.

New global positioning system (GPS) test falsifies the Lorentz transformations and special relativity

The time transformation governing the operation of the global positioning system (GPS) clocks and the time corrections required to ensure sustained clock synchronization are determined to be the Selleri time transformation and not the Lorentz time transformation. This condition, as well as GPS-demonstrated light speed anisotropy, falsifies the Lorentz transformations and special relativity.

New measurement method corrected a failure in special relativity

A logical reasoning problem in the Special Relativity interpretation of the Lorentz transformation was discovered and corrected by introducing an alternative interpretation of Lorentz transformations with a relativistic measuring process based on both, stretched time and length units, whereby the measurements as a consequence measure a shortened distance and time lines as variables due to used units. The space shuttles are getting longer instead of shorter and a barn-pole paradox does not occur. The spatial locations remain in their locations and space is not contracted and not changed. The failure is that by contracting both units and distance the Lorentz factor is eliminated and relativity was vanished. The elementary particles have their own measuring devices for time and length in the form of wavelengths and frequencies and they read distances and durations of different lengths from space using their own relativistically different units. The new interpretation is covered by the two postulates of Einstein. This is a sensational result too in view of all dramatic and romantic history as there is really a failure discovered. The Lorentz transformations remain being in use with another method. The new theory and the discovered problems of logical failures are explained vividly in the same manner as Special Relativity was using easy be thought samples. Reader do not need a high level of mathematics to be fit for as it is a more qualitatively thematic for every one who is interested in relativity matters.

Lyapunov exponents for the Lorentz transformations

We calculate the Lyapunov exponents of the stretch factor $f^-(x)=(1-x^2)^{-1/2}$ from the Lorentz transformations and of its reciprocal $f^+(x)=(1-x^2)^{+1/2}$ as well.