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Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the one-way speed of light in all inertial frames of reference, the special theory of relativity uses the assumption about the Euclidean structure…
The concept of inertial frame of reference in classical physics and special theory of relativity is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is…
The theoretical predictions, derived from the Lorentz and the Tangherlini transformations, for the one-way speed of any physical entity are confronted with the corresponding expressions for the one-way measured speed obtained from a…
Since 1983 the meter is defined to be the "length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second". If there was exactly one single consistent method of synchronizing clocks, or if all…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
A possible way to capture the effects of quantum gravity in spacetime at a mesoscopic scale, for relatively low energies, is through an energy dependent metric, such that particles with different energies probe different spacetimes. In this…
It is shown in this article that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse…
In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of `dark energy', `dark matter', and `dark flow'. Instead of assuming the existence of these theoretical concepts,…
We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric.…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
The clock paradox is analyzed for the case when the onward and return trips cover the same <<distance>> (as observed by the traveling twin) but at unequal velocities. In this case the stationary twin observes the distances covered by her…
The problem of the referring of space and time relationships between physical objects in a curved space-time is discussed. The basic notions of column and weak column that could constitute the basis for consistent general relativistic…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme…
We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the…
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
According to the general theory of relativity, time can flow at different rates depending on the configuration of massive objects, affecting the temporal order of events. Recent research has shown that, combined with quantum theory, this…
The present work aims to search for an implementation of new symmetries in the space-time in order to enable us to find a connection between electrodynamics and gravitation, from where quantum principles naturally emerge. To do that, first…