Related papers: On Nonlinear Inertial Transformations
We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is…
In classical mechanics, a procedure for simultaneous synchronization in all inertial frames is consistent with the Galilean transformation. However, if one attempts to achieve such a synchronization utilizing light signals, he will be…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
It is known that action is invariant in special relativity. The goal of this note is to show that the reverse statement is also correct, that special relativity follows from the postulate that action is invariant under the transformation…
It is proved that local Lorentz transformations for different systems cannot derive varying speed of light. Based on the special relativity principle, an invariant speed is necessarily obtained. Therefore, the exact basic principles of the…
Starting from the revelation of the nature of inertial forces, this article discusses the subdivision of the basic physical concept of space-time and raises questions about the metric of standard cosmology. A new form of particle dynamics…
The aim of the article is to find a transformation that links the local affine velocity of a non-rigid body in the laboratory inertial reference frame $ S $ with the centro-affine velocity of motion of this body in the accompanying…
Selleri's paradox, based on an analysis of rotating frames, appears to show that the speed of light in an inertial system is not normally isotropic. This in turn seems at odds with the second postulate of special relativity requiring a…
This work places the invariant $ds^2$ at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension…
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
We consider a scenario of large-scale modification of gravity that does not invoke extra degrees of freedom but includes coupling between baryonic matter and dark matter in the Einstein frame. The total matter energy density follows the…
Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space…
The aim of this article is the formulation of the basic laws of Physics by frames, i.e. quadruples of exterior differential one forms. The basic operator is a modification of the Hodge-de Rham Laplacian d*d*+*d*d, where * is the hyperbolic…
The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the…
Discussed is relationship between nonlinearity and symmetry of dynamical models. The special stress is laid on essential, non-perturbative nonlinearity, when none linear background does exist. This is nonlinearity essentially different from…
This paper presents a generalisation of Sylvester's law of inertia to real non-degenerate quadratic forms on a fixed real vector bundle over a connected locally connected paracompact Hausdorff space. By interpreting the classical inertia as…
Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class.…
We consider the most general Quadratic Metric-Affine Gravity setup in the presence of generic matter sources with non-vanishing hypermomentum. The gravitational action consists of all $17$ quadratic invariants (both parity even and odd) in…
The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…
In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time…