Related papers: Physics of Non-Inertial Reference Frames
We discuss the non-relativistic limit of quantum field theory in an inertial frame, in the Rindler frame and in the presence of a weak gravitational field, highlighting and clarifying several subtleties. We study the following topics: (a)…
It is generally believed that physical laws, reflecting an inherent order in the universe, are ordained by nature. However, in modern physics the observer plays a central role raising questions about how an observer-centric physics can…
Inertial effects in non-inertial reference frames are compared with quantum properties of tests objects. The real space-time and perfect inertial reference frame can be compared accurate to the uncertainty relation. Complexities if…
In order to test the validity of Mach's principle, we calculate the action of the entire universe on a test mass in its rest frame, which is an acceleration ${\bf g}^*$. We show the dependence of the inertia principle on the lapse and the…
By proper co-ordinates of non-inertial observers (shortly - proper non-inertial co-ordinates) we understand the proper co-ordinates of an arbitrarily moving local observer. After a brief review of the theory of proper non-inertial…
This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
The study of quantum mechanics in non-inertial reference frames, particularly in the context of open systems, introduces several intriguing phenomena and challenges. This paper presents a comprehensive framework for analyzing the quantum…
It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying $\text{Newton's}$ methods in $\textit{Principia}$ is neo-Newtonian or Galilean space-time. I…
We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to re-derive, in the first post-Newtonian approximation, the well known geometric dragging of frames. We…
A relativistic theory of gravity like general relativity produces phenomena differing fundamentally from Newton's theory. An example, analogous to electromagnetic induction, is gravitomagnetism, or the dragging of inertial frames by…
The internal state of a composite particle and its transformation, when changing from the reference frame, where this composite particle is at rest, to a reference frame, where it moves relativistically, have been considered. It is supposed…
In this paper we give a review of the most general approach to description of reference frames, the monad formalism. This approach is explicitly general covariant at each step, permitting to use abstract representation of tensor quantities;…
The solution of time dependent differential equations with neural networks has attracted a lot of attention recently. The central idea is to learn the laws that govern the evolution of the solution from data, which might be polluted with…
Interactions are explored through the observation of the dynamics of particles. On the classical level the basic underlying assumption in that scheme is that Newton's second law holds. Relaxing the validity of this axiom by, e.g., allowing…
This is the fourth in a series of papers on developing 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…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics…
We show that the linearity of an evolution of Quantum Mechanics follows from the definition of kinematics. The same result is obtained for an arbitrary theory with the state space that includes mixtures of different preparations. Next, we…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…