Related papers: A New Kind of Uniformly Accelerated Reference Fram…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of…
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 discuss two effects predicted by the general theory of relativity in the context of Rindler accelerated observers: the gravitational spectral shift and the time delay of light. We show that these effects also appear in a Rindler frame in…
The Rindler spacetime describing a series of accelerating observers is Ricci flat, but it still has novel optical effects. In the case of WKB approximation, we derive the light geodesics in the Rindler frame based on the covariant wave…
To generate the standard microlensing light curve one assumes that the relative motion of the source, the lens, and the observer is linear. In reality, the relative motion is likely to be more complicated due to accelerations of the…
The particle detector model consisting of a harmonic oscillator coupled to a scalar field in $1+1$ dimensions is investigated in the inertial case. The same approach is then used in the accelerating case. The absence of radiation from a…
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…
A new derivation of the acceleration of a particle in a non-inertial reference frame, including the Coriolis effect, is developed using the geometry of complex numbers in the complex plane.
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the…
Let $(M,g,J)$ be a closed K\"ahler manifold with negative sectional curvature and complex dimension $m := \dim_{\mathbb{C}} M \geq 2$. In this article, we study the unitary frame flow, that is, the restriction of the frame flow to the…
In highly conducting astrophysical plasmas, charged particles are generically accelerated through Fermi-type processes involving repeated interactions with moving magnetized scattering centers. The present paper proposes a generalized…
In this work, we use real quaternions and the basic concept of the final speed of light in an attempt to enhance the standard description of special relativity. First, we demonstrate that it is possible to introduce a quaternion time domain…
The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising…
Whenever an experiment can be described classically, quantum physics must predict the same outcome. Intuitively, there is nothing quantum about an accelerating observer travelling through a vacuum. It is therefore not surprising that many…
Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the…
The standard relativistic theory of accelerated reference frames in Minkowski spacetime is described. The measurements of accelerated observers are considered and the limitations of the standard theory, based on the hypothesis of locality,…
The coordinate conditions for three exact solutions for the metric components of a coordinate system with constant acceleration or of a static plane symmetric gravitational field are presented. First, the coordinate condition that the…
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and…