Related papers: The general form-invariance principle
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…
We describe a completely general and fully non-perturbative framework for constructing dynamical reference frames in generally covariant theories, and for understanding the gauge-invariant observables that they yield. Our approach makes use…
We discuss implications of the cosmological frame principle which states that cosmological effects of modified gravity must be stable as solutions of each of the corresponding sets of dynamical equations holding in the two…
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used.…
We investigate the invariance principle for set-indexed partial sums of a stationary field $(X\_{k})\_{k\in\mathbb{Z}^{d}}$ of martingale-difference or independent random variables under standard-normalization or self-normalization…
A new relativistic transformation in the velocity space (here named the differential Lorentz transformation) is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz…
In general relativity, the use of conformal transformation is ubiquitous and leads to two different frames of reference, known as the Jordan and the Einstein frames. Typically, the transformation from the Jordan frame to the Einstein frame…
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…
We describe the space-time model of a uniformly rotating frame of reference satisfying the Helmholtz free mobility postulate, as we implemented it in a preceding article \cite{Bel1}, and we discuss the implications of this model as it…
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…
We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined…
This work introduces a novel three-fold classification of reference frames in General Relativity, distinguishing between Idealised Reference Frames (IRFs), Dynamical Reference Frames (DRFs), and Real Reference Frames (RRFs). By defining a…
It is proved by means of the dynamical effects of special relativity that velocity caused by accelerating process is not a relative concept. The influence of accelerating process should be considered in space-time theory. Besides the…
Many professional physicists do not fully understand the implications of the Einstein equivalence principle of general relativity. Consequently, many are unaware of the fact that special relativity is fully capable of handling accelerated…
In this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed…
We consider the problem of internal particle state transformation, which is a bound state of several constituents, from the particle's rest frame to the system in which this particle is relativistic. It is assumed that in the rest frame of…
First, we extend the special relativity into the superluminal case and put forward a superluminal theory of kinematics, in which we show that the temporal coordinate need exchanging with one of the spatial coordinates in a superluminal…