Related papers: Spacetime Transformations from a Uniformly Acceler…
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…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
Inspired by the covering-space method in path integral on multiply connected spaces, we here present a universal formula of time-evolution kernels for continuous- and discrete-time quantum walks on orbit spaces. In this note, we focus on…
It is generally expected from intuition that the electromagnetic force exerted on a charged particle should remain unchanged when observed in different reference frames in uniform translational motion. In the special relativity, this…
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…
We present a unified framework for the study of late time cosmic acceleration. Using methods of effective field theory, we show that existing proposals for late time acceleration can be subsumed in a single framework, rather than many…
It is shown that the Fermi-Walker gauge allows the general solution of determining the metric given the sources, in terms of simple quadratures. We treat the general stationary problem providing explicit solving formulas for the metric and…
We show that a system is uniformly accelerated if and only if all of the clocks in the system can be synchronized to each other, and the clocks will remain synchronized as long as the acceleration remains uniform. In particular, it is…
We give a closed expression for the Minkowski (1+1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform…
The model of a stationary universe and the notion of local times presented in [10] are reviewed with some alternative formulation of the consistent unification of the Riemannian and Euclidean geometries of general relativity and quantum…
We derive rotation free Lorentz Transformation (LT) between two inertial reference frames without using the second postulate of Einstein, i.e., we do not assume the invariant speed of light (in vacuum) under LT. We find a general…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…
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…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
A locally Lorentz-covariant theory of gravity that is equivalent to general relativity in weak gravitational field is suggested. The space-time standards in local gravitational field are modified in terms of equivalence principle to keep…
Although there is no relative motion among different points on a rotating disc, each point belongs to a different noninertial frame. This fact, not recognized in previous approaches to the Ehrenfest paradox and related problems, is…
The physical equivalence of Einstein and Jordan frame in Scalar Tensor theories has been explained by Dicke in 1962: they are related by a local transformation of units. We discuss this point in a cosmological framework. Our main result is…
Aharonov-Kaufherr model of quantum space-time which accounts Reference Frames (RF) quantum effects is considered in Relativistic Quantum Mechanics framework. For RF connected with some macroscopic object its free quantum motion - wave…
The transformation formulas between two inertial frames for the minimum phase velocity and the phase velocity in an arbitrary direction are given. The derived transformation formula for the reciprocal of the phase velocity along the…
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…