相关论文: An omission in Special Relativity
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…
The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of…
Special relativity theory is generalized to two or more ``maximal'' signalling speeds. This framework is discussed in three contexts: (i) as a scenario for superluminal signalling and motion, (ii) as the possibility of two or more ``light''…
This work deals with the questions of absolute space and relativity. In particular, an alternative derivation of the effects described by special relativity is provided, which is based on a description that assumes a privileged reference…
Different formulations of special relativity are theoretically discussed. First an invariant formulation, i.e., the ''true transformations (TT) relativity,'' is exposed. There a physical quantity is represented by a true tensor which…
We compare the results obtained by interpreting some fundamental relativistic experiments from the point of view of two alternative theories: Einstein's special relativity theory and the Lorentz-Poincare theory admitting the existence of a…
We introduce an equivalence relation on the space $W^{1,1}(\Omega;{\mathbb S}^1)$ which classifies maps according to their "topological singularities". We establish sharp bounds for the distances (in the usual sense and in the Hausdorff…
A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…
We show that any two frames in a separable Hilbert space that are dual to each other have the same excess. Some new relations for the analysis resp. synthesis operators of dual frames are also derived. We then prove that pseudo-dual frames…
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…
We investigate the physics of quantum reference frames. Specifically, we study several simple scenarios involving a small number of quantum particles, whereby we promote one of these particles to the role of a quantum observer and ask what…
Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is…
Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…
We introduce an equivalence relation on the global class of morphisms of a category that extends several classical notions of equivalence in mathematics. We show that the standard group-action equivalence is a special case of our framework.…
The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity…
Lorentzian frames may belong to one of the 199 causal classes. Of these numerous causal classes, people are essentially aware only of two of them. Nevertheless, other causal classes are present in some well-known solutions, or present a…
Finite tight frames are interesting in various topics including questions of quantum information. Each complex tight frame leads to a resolution of the identity in the Hilbert space. Symmetric informationally complete measurements are a…
An apparent paradox in Einstein's Special Theory of Relativity, known as a Thomas precession rotation in atomic physics, has been verified experimentally in a number of ways. However, somewhat surprisingly, it has not yet been demonstrated…
A precise formulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity, but…