相关论文: Two falling-chain demonstrations based on Einstein…
Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we…
We present three natural but distinct formalisations of Einstein's special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made…
The implementation of Einstein's principle of equivalence in Koopman-von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because…
Investigation into the applicability of the equivalence principle in quantum mechanics has taken many forms, with varying conclusions. Here, a dynamical semi-classical description of a wave packet in terms of its center of mass and higher…
We propose a new interpretation of the equivalence principle underlying Einstein's general relativity: a free-falling frame with gravitational force eliminated locally in a small spacetime region shows the existence of a boundary level,…
The principle of equivalence postulating that an acceleration is indistinguishable from gravity by any experiment, is valid within families of particles having the same passive gravitational to inertial mass ratio $m_p/m_i$. Presently…
The conventional nature of synchronisation is discussed in inertial frames, where it is found that theories using different synchronisations are experimentally equivalent to special relativity. In contrary, in accelerated systems only a…
Modern formulations of equivalence principles provide the foundation for an efficient approach to understanding and organizing the structural features of gravitation field theories. Since theories' predictions reflect differences in their…
Point particles fall freely along geodesics; strings do not. In string theory all probes of spacetime structure, including photons, are extended objects and therefore always subject to tidal forces. We illustrate how string theory modifies…
This survey summarizes recent progress on the flat chain conjecture, which asserts the equivalence between metric currents and flat chains with finite mass in the Euclidean space. In particular, we focus on recent work showing that the…
Mach Principle presents the absolute universe. For example, when Einstein stood on the ground and relaxed, his arms fell down naturally. However, if he rotated his body then his arms were lifted up as the rotation was faster and faster.…
We consider a class of condensed matter theories in a Newtonian framework with a Lagrange formalism related in a natural way with the classical conservation laws \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) + \partial_i…
We provide a short proof of the 1-dimensional flat chain conjecture.
This work is divided into two parts. The first examines recent proposals for "witnessing" quantum gravity via entanglement from the point of view of Bronstein's original objection to a quantization of gravity. Using techniques from open…
It is pointed out that at present we only prove that inertial static mass and gravitational static mass are equivalent. We have not proved that inertial moving mass and gravitational moving mass are also equivalent. It is proved by the…
There have been various claims that the Equivalence Principle, as originally formulated by Einstein, presents several difficulties when extended to the quantum domain, even in the regime of weak gravity. Here we point out that by following…
The fascinating and anomalous behaviour of a chain that instead of falling straight down under gravity, first rises and then falls, acquiring a steady shape in space that resembles a fountain's sprinkle, has recently attracted both popular…
Inspired by Einstein's Strong Principle of Equivalence we consider the effects of quantum mechanics to the gravity-like phenomena experienced by an observer in a uniformly accelerating motion in flat spacetime. Among other things, our model…
We give a new, elementary proof of the fact that metric 1-currents in the Euclidean space correspond to Federer-Fleming flat chains.
In many sliding systems consisting of solid object on a solid substrate under dry condition, the friction force does not depend on the apparent contact area and is proportional to the loading force. This behaviour is called Amontons' law…