Related papers: Using Isabelle to verify special relativity, with …
The special theory of relativity is constructed demanding the retention of the rectilinear form of a trajectory and invariance of the wave equation under linear transformations of space and time coordinates. The usual approach to relativity…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
Searches for anisotropies due to Earth's motion relative to a preferred frame -- modern versions of the Michelson-Morley experiment -- provide precise verifications of special relativity. We describe other tests, independent of this motion,…
It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are…
The light speed anisotropy, i.e., the variation of the light speed with respect to the direction in an "absolute" reference frame, is a profound issue in physics. The one-way experiment, performed at the GRAAL facility of the European…
We propose a relativistic version of the cosmological principle and confront it to the Hubble diagram of supernovae and other probes.
According to this principle, the relativistic changes occurring to the bodies, after velocity changes, cannot be detected by observers moving with them because bodies and stationary radiations change in identical proportion after identical…
In an isotropic and homogeneous Hubble expansion, all transverse motion is peculiar. Like the radial peculiar velocities of galaxies, transverse peculiar velocities are a means to trace the density of matter that does not rely on light…
It is pointed out that at present we only prove that inertial static mass and gravitational static mass are equivalent. We have not proved that inertial moving mass and gravitational moving mass are also equivalent. It is proved by the…
The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The…
Ever since the work of von Ignatowsky circa 1910 it has been known (if not always widely appreciated) that the relativity principle, combined with the basic and fundamental physical assumptions of locality, linearity, and isotropy, leads…
Gravitational lensing - the deflection of light rays by gravitating matter - has become a major tool in the armoury of the modern cosmologist. Proposed nearly a hundred years ago as a key feature of Einstein's theory of General Relativity,…
The special theory of relativity teaches us that, although distinct inertial frames perceive the same dynamical laws, space and time intervals differ in value. We revisit the problem of time contraction using the paradigmatic model of a…
We have formalised Szemer\'edi's Regularity Lemma and Roth's Theorem on Arithmetic Progressions, two major results in extremal graph theory and additive combinatorics, using the proof assistant Isabelle/HOL. For the latter formalisation, we…
Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have been studied in great detail. When considered as complete theories of gravity they…
Special theory of relativity has been formulated in a vacuum momentum-energy representation which is equivalent to Einstein special relativity and predicts just the same results as it. Although in this sense such a formulation would be at…
Some conceptual issues concerning general invariant theories, with special emphasis on general relativity, are analyzed. The common assertion that observables must be required to be gauge invariant is examined in the light of the role…
Inferring universal laws of the environment is an important ability of human intelligence as well as a symbol of general AI. In this paper, we take a step toward this goal such that we introduce a new challenging problem of inferring…
Within the low-energy effective field theories of QED and gravity, the low-energy speed of light or that of gravitational waves can typically be mildly superluminal in curved spacetimes. Related to this, small scattering time advances…
The modern view, that there exists a preferred frame of reference related to the cosmic microwave background (CMB), is in apparent contradiction with the principles of special relativity. The purpose of the present study is to develop a…