Testable scenario for relativity with minimum length

I propose a general class of spacetimes whose structure is governed by observer-independent scales of both velocity (c) and length (Planck length), and I observe that these spacetimes can naturally host a modification of FitzGerald–Lorentz contraction such that lengths which in their inertial rest frame are bigger than a “minimum length” are also bigger than the minimum length in all other inertial frames. With an analysis in leading order in the minimum length, I show that this is the case in a specific illustrative example of postulates for relativity with velocity and length observer-independent scales.     

基于同时的相对性对钟慢尺缩效应的再认识

同时的相对性、钟慢效应和尺缩效应是狭义相对论时空观的主要内容.鉴于同时性是时空测量的基础,本文从同时的相对性出发详述了对钟慢效应和尺缩效应的再认识:钟慢效应是运动时钟走时率变慢和校表问题的综合表现,其实质是同时的相对性在时间量度上的直接反映;尺缩效应的实质是同时的相对性在空间量度上的反映,也是不同观测者对同一客观事实的不同时空描述.     

Specific features of operation of free-electron lasers with a short bunch

The physical specific features of a free-electron laser in the short-wave region in which the bunch length in the proper frame is smaller than the undulator length in the same reference frame are discussed. The regimes of amplification of the external harmonic signal and the induced amplification of proper noise with forming the quasi-coherent radiation, i.e. the self-amplified spontaneous emission (SASE) regime, are considered.     

Space-time in a simple model of a physical system

A model of space-time is worked out starting from the two primitive concepts of preparticle and of membership relation of set theory. We obtain as derivative concepts those of space-time and inertial reference frame, also those of energy, frequency, momentum, and wavelength of a physical system in a given reference frame. Proportionality relations between energy and frequency, and between momentum and (wavelength)^–1 are shown to be satisfied in our model. The same constant of proportionality intervenes in these two relations, and we interpret it as the Planck constant expressed in a particular system of units. Energy and momentum are conserved in the usual sense, provided we consider sufficiently large regions of the space-time diagram associated to the reference frame under consideration. Lorentz transformations and Heisenberg's inequalities are discussed within the framework of our model.     

Another derivation of Weinberg's formula

To investigate how quantum effects might modify special relativity, we will study a Lorentz transformation between classical and quantum reference frames and express it in terms of the four-dimensional (4D) momentum of the quantum reference frame. The transition from the classical expression of the Lorentz transformation to a quantum-mechanical one requires us to symmetrize the expression and replace all its dynamical variables with the corresponding operators, from which we can obtain the same conclusion as that from quantum field theory (given by Weinberg's formula): owing to the Heisenberg's uncertainty relation, a particle (as a quantum reference frame) can propagate over a spacelike interval.     

运动背景下的帧间稳像技术

针对运动背景下帧间稳像技术,提出了一种带运动矢量修正的灰度投影运动估计算法。采用该算法分别对当前帧和参考帧的行、列计算灰度投影序列;将当前帧投影序列局部分块,分别将每一分块与参考帧行、列投影曲线进行互相关计算,得到基于局部投影的行、列运动矢量集合;以分块区域的相关置信度为权系数衡量参数,计算每一分块的像素位移权值,从而计算某一方向帧间的加权运动矢量。实验结果表明:该方法可以使运动目标造成的影响只作用于其中若干个局部分块,而其他分块不受此影响,尽可能保证稳像的准确性。采用该方法稳像后的图像与参考帧图像的均方根误差(RMSE)值明显下降,与参考帧图像更加吻合。     

运动背景下的帧间稳像技术

针对运动背景下帧间稳像技术,提出了一种带运动矢量修正的灰度投影运动估计算法。采用该算法分别对当前帧和参考帧的行、列计算灰度投影序列;将当前帧投影序列局部分块,分别将每一分块与参考帧行、列投影曲线进行互相关计算,得到基于局部投影的行、列运动矢量集合;以分块区域的相关置信度为权系数衡量参数,计算每一分块的像素位移权值,从而计算某一方向帧间的加权运动矢量。实验结果表明：该方法可以使运动目标造成的影响只作用于其中若干个局部分块,而其他分块不受此影响,尽可能保证稳像的准确性。采用该方法稳像后的图像与参考帧图像的均方根误差（RMSE）值明显下降,与参考帧图像更加吻合。     

Transformations between inertial and linearly accelerated frames of reference

Transformation equations between inertial and linearly accelerated frames of reference are derived and these transformation equations are shown to be compatible, where applicable, with those of special relativity. The physical nature of an accelerated frame of reference is unambiguously defined by means of an equation which relates the velocity of all points within the accelerated frame of reference to measurements made in an inertial frame of reference.     

Common time in a four-dimensional symmetry framework

Following the ideas of Poincaré, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, we analyze clock systems and light propagation within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporatingcommon time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of reference. A further consequence is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds and two-way speeds of light signals is considered in detail.Work supported by the NRC, NASA, and the U.S. DOE.     

Equivalence of least-squares estimation of eye aberrations in linearly transformed reference frames

Zernike aberrations, estimated with respect to the wavefront sensor’s reference frame by least-squares, are currently transformed to other frames using algebraic relationships. Obviously, they can also be estimated directly with respect to the transformed frames. In this paper, we demonstrate the equivalence between these two approaches in terms of bias and noise propagation, when the reference frames are related by a linear conformal transformation of coordinates.     

Modulating the amplitude of dark soliton by scattering-length management in Bose-Einstein condensates

We present a family of soliton solutions of the quasi-one-dimensional Bose-Einstein condensates with time-dependent scattering length, by developing multiple-scale method combined with truncated Painlevé expansion. Then, by numerical calculating the solutions, it is shown that there exhibit two types of dark solitons—black soliton (the zero minimum amplitude at its center) and gray soliton (the minimum density does not drop to zero) in a repulsive condensate. Furthermore, we propose experimental protocols to realize the exchange between black and gray solitons by varying the scattering length via the Feshbach resonance in currently experimental conditions.     

Use of the Lorentz Transformations in Noninertial Reference Frames

The Lorentz transformations are used within the model of a noninertial reference frame without infinitely high accelerations arising at instantaneous jumps of an accelerated observer between different inertial reference frames. It is demonstrated that the twin paradox can be explained within this model with the help of the Lorentz transformations. Based on the model of a noninertial reference frame, the acceleration a measured in the noninertial reference frame is related to the acceleration a measured in an inertial reference frame.     

Molecular symmetry as an aid to geometry determination in ligand protein complexes

Dipole-dipole couplings between pairs of spin 12 nuclei, which can be measured from NMR spectra in field-ordered media, offer useful constraints on the orientation of various fragments in molecular systems. However, the orientation of fragments relative to a molecule fixed reference frame is often key to complete structure determination. Here, we demonstrate that the symmetry properties of molecular complexes can aid in the definition of a reference frame. It is shown that a threefold rotational symmetry axis dictates the direction and symmetry of the experimentally determined order tensor for alpha-methyl-mannose in fast exchange among the three symmetry-related binding sites of mannose binding protein. This approach facilitates studies of the geometry of the ligand in the protein-ligand complex and also may provide a novel route to structure determination of a homomultimeric protein.     

Production of tachyons and antiparticles in extended manifolds of general relativity

The extended space-time manifold in a uniformly accelerating reference frame is considered both for positive and negative accelerations. An analogy between the light barrier and a black hole event horizon in the theory of relativity is drawn. It is shown that bradyon-tachyon-antibradyon transformations are possible in the proper reference frame by a constant acceleration, i.e. for the light barrier penetration.     

Rotating Frames in SRT: The Sagnac Effect and Related Issues

After recalling the rigorous mathematical representations in Relativity Theory (RT) of (i) observers, (ii) reference frames fields, (iii) their classifications, (iv) naturally adapted coordinate systems (nacs) to a given reference frame, (v) synchronization procedure and some other key concepts, we analyze three problems concerning experiments on rotating frames which even now (after almost a century after the birth of RT) are sources of misunderstandings and misconceptions. The first problem, which serves to illustrate the power of rigorous mathematical methods in RT, is the explanation of the Sagnac effect (SE). This presentation is opportune because recently there have appeared many non sequitur claims in the literature stating that the SE cannot be explained by SRT, even disproving this theory or claiming that the explanation of the effect requires a new theory of electrodynamics. The second example has to do with the measurement of the one-way velocity of light in rotating reference frames, a problem about which many wrong statements appear in recent literature. The third problem has to do with claims that only Lorentz-like type transformations can be used between the nacs associated with a reference frame mathematically modeling of a rotating platform and the nacs associated with a inertial frame (the laboratory). We show that these claims are equivocal.     

EAMCD: an efficient algorithm based on minimum coupling distance for community identification in complex networks

Community structure is an important feature in many real-world networks, which can help us understand structure and function in complex networks better. In recent years, there have been many algorithms proposed to detect community structure in complex networks. In this paper, we try to detect potential community beams whose link strengths are greater than surrounding links and propose the minimum coupling distance (MCD) between community beams. Based on MCD, we put forward an optimization heuristic algorithm (EAMCD) for modularity density function to welded these community beams into community frames which are seen as a core part of community. Using the principle of random walk, we regard the remaining nodes into the community frame to form a community. At last, we merge several small community frame fragments using local greedy strategy for the modularity density general function. Real-world and synthetic networks are used to demonstrate the effectiveness of our algorithm in detecting communities in complex networks.     

Kinematics in the Special Theory of Ether

The aim of this paper is to show that the Michelson–Morley and Kennedy–Thorndike experiments are not sufficient for justification of the theory of special relativity because these experiments can be explained using another theory in which a universal reference frame exists. In this paper, we derive a novel theory of body kinematics with a universal reference frame. We call this theory the special theory of ether (STE). The reason that the universal reference frame could not be found using the Michelson–Morley and Kennedy–Thorndike experiments is also explained. As well, based on a geometric analysis of the Michelson–Morley and Kennedy–Thorndike experiments, we derive another coordinate and time transformation that differs from the Lorentz transformation. In addition, the transformation law of speed, the formula for the addition of velocities for the absolute velocity, as well as length-contraction and time-dilation formulas are derived. The paper contains only the investigations of the original authors.     

General relativistic analysis of simplest optical gravitational wave detectors

In this article we continue to study the simplest forward trip optical position meter in the frame-work of general relativity. We demonstrate the apparent paradox arising from careless analysis of these system in the laboratory reference frame (corresponding to the transeverse-traceless gauge) and show the way to overcome this problem in the proper reference frame of observer (corresponding to the local Lorentz gauge). Then we show that careful taking into account initial synchronization procedure solves this problem even in transeverse-traceless gauge.     

Locally inertial reference frames in Lorentzian and Riemann‐Cartan spacetimes

In this paper the concept of locally inertial reference frames ( LIRF s) in Lorentzian and Riemann‐Cartan spacetime structures is scrutinized. A rigorous mathematical definition of a LIRF in both structures is given, something that needs preliminary a clear mathematical distinction between the concepts of observers, reference frames, naturally adapted coordinate functions to a given reference frame and which properties may characterize an inertial reference frame (if any) in the Lorentzian and Riemann‐Cartan structures. Hopefully, the paper clarifies some obscure issues associated to the concept of a LIRF appearing in the literature, in particular the relationship between LIRF s in Lorentzian and Riemann‐Cartan spacetimes and Einstein's most happy thought, i.e., the equivalence principle.