A lagrangian basis for ashtekar’s reformulation of canonical gravity

A manifestly covariant Lagrangian is presented which leads to the reformulation of canonical general relativity using new variables recently discovered by Ashtekar.     

A laboratory test of Mach's principle and strong-field relativistic gravity

A laboratory experiment that tests the validity of Mach's principle — the relativity and gravitational induction of inertia — and relativistic gravity in strong-field circumstances is described. It consists of looking for a stationary shift in the apparent weight of an object when a transient mass fluctuation is induced in one of its parts, that part then being subjected to a pulsed thrust. The transient mass fluctuation induced is of the order of a few tens of milligrams, and the stationary weight shift observed is several milligrams. Details of the apparatus used (capable of detecting an effect at the level of about a tenth of a milligram) are presented. Procedural protocols are laid out. The results obtained — signals some 10 to 15 times the standard error in magnitude — confirm to better than order of magnitude that the predicted effect is indeed present. The consequences of this confirmation of Mach's principle and relativistic gravity are briefly addressed. In particular, it is pointed out that in light of these results radical timelessness seems to be the correct way to understand reality and, from the practical point-of-view, it may prove possible to make traversable wormholes whenever we choose to devote sufficient resources to that end.     

Relevance of the weak equivalence principle and experiments to test it: Lessons from the past and improvements expected in space

Tests of the Weak Equivalence Principle (WEP) probe the foundations of physics. Ever since Galileo in the early 1600s, WEP tests have attracted some of the best experimentalists of any time. Progress has come in bursts, each stimulated by the introduction of a new technique: the torsion balance, signal modulation by Earth rotation, the rotating torsion balance. Tests for various materials in the field of the Earth and the Sun have found no violation to the level of about 1 part in 10¹³. A different technique, Lunar Laser Ranging (LLR), has reached comparable precision. Today, both laboratory tests and LLR have reached a point when improving by a factor of 10 is extremely hard. The promise of another quantum leap in precision rests on experiments performed in low Earth orbit. The Microscope satellite, launched in April 2016 and currently taking data, aims to test WEP in the field of Earth to ${10}^{?15}$, a 100-fold improvement possible thanks to a driving signal in orbit almost 500 times stronger than for torsion balances on ground. The ‘Galileo Galilei’ (GG) experiment, by combining the advantages of space with those of the rotating torsion balance, aims at a WEP test 100 times more precise than Microscope, to ${10}^{?17}$. A quantitative comparison of the key issues in the two experiments is presented, along with recent experimental measurements relevant for GG. Early results from Microscope, reported at a conference in March 2017, show measurement performance close to the expectations and confirm the key role of rotation with the advantage (unique to space) of rotating the whole spacecraft. Any non-null result from Microscope would be a major discovery and call for urgent confirmation; with 100 times better precision GG could settle the matter and provide a deeper probe of the foundations of physics.     

Observables in a noncommutative approach to the unification of quanta and gravity: a finite model

We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in Gen. Rel. Grav. (36, 111–126 (2004)). Generalized symmetries of the model are defined by a groupoid given by the action of a finite group on a space E. The geometry of the model is constructed in terms of suitable (noncommutative) algebras on . We investigate observables of the model, especially its position and momentum observables. This is not a trivial thing since the model is based on a noncommutative geometry and has strong nonlocal properties. We show that, in the position representation of the model, the position observable is a coderivation of a corresponding coalgebra, coparallelly to the well-known fact that the momentum observable is a derivation of the algebra. We also study the momentum representation of the model. It turns out that, in the case of the algebra of smooth, quickly decreasing functions on , the model in its quantum sector is nonlocal, i.e., there are no nontrivial coderivations of the corresponding coalgebra, whereas in its gravity sector such coderivations do exist. They are investigated.This revised version was published online in April 2005. The publishing date was inserted.     

Infinitely many nonlocal symmetries and nonlocal conservation laws of the integrable modified KdV-sine-Gordon equation

Nonlocal symmetries related to the Bäcklund transformation (BT) for the modified KdV-sine-Gordon (mKdV-SG) equation are obtained by requiring the mKdV-SG equation and its BT form invariant under the infinitesimal transformations. Then through the parameter expansion procedure, an infinite number of new nonlocal symmetries and new nonlocal conservation laws related to the nonlocal symmetries are derived. Finally, several new finite and infinite dimensional nonlinear systems are presented by applying the nonlocal symmetries as symmetry constraint conditions on the BT.     

Exact classical and quantum solutions for a covariant oscillator near the black hole horizon in Stueckelberg-Horwitz-Piron theory

We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.     

The principle of equivalence and theories of gravity

We construct classical theories of gravity on the basis of special relativity and the Einstein-Infeld accelerating-elevator thought experiment. The resulting theories share most of the main features of general relativity, namely the nonlinear character of the theory, the metrical significance of the gravitational potentials and the geodesic equation of particle motion. They differ from general relativity in at most nonlinear terms in the gravitational constant G in their equations of particle motion and field equations.     

On a Framework for Generating Nonstatic Solutions of the Einstein Field Equations

In this paper we present a simple generalisation of all spherically symmetric static solutions. We present a framework to obtain both anisotropic and isotropic models with and without a barotropic equation of state of the form p = . The nonstaticity in some models necessarily requires a nonzero heat flux which dictates the thermodynamics of our models.     

An improved Hirota bilinear method and new application for a nonlocal integrable complex modified Korteweg-de Vries (MKdV) equation

The Hirota bilinear method has been studied in a lot of local equations, but there are few of works to solve nonlocal equations by Hirota bilinear method. In this letter, we show that the nonlocal integrable complex modified Korteweg-de Vries (MKdV) equation admits multiple complex soliton solutions. A variety of exact solutions including the single bright soliton solutions and two bright soliton solutions are derived via constructing an improved Hirota bilinear method for nonlocal complex MKdV equation. From the gauge equivalence, we can see the difference between the solution of nonlocal integrable complex MKdV equation and the solution of local complex MKdV equation.     

Space tests of relativistic gravity with precision clocks and atom interferometers

Precision clocks and interferometers in space can test relativistic gravity with extremely high sensitivity. Yet, only a single such test has been performed, namely the celebrated flight of a hydrogen maser in a sub-orbital trajectory in 1976 (GP-A mission). This paper suggests some of the obstacles to space flight of precision instruments, and describes how the emergence of new technology might offer a pathway for removing those obstacles. A brief review of emerging technologies is made, and new mission concepts based on them are described. Some of the technologies that can impact more tests of relativistic gravity in space at a more distant future are also described.     

On the nonlocal symmetries of certain nonlinear oscillators and their general solution

In this Letter we establish the integrability of two nonlinear oscillators through group theoretical method. We utilize the algorithm given in [M.L. Gandarias, M.S. Bruzon, J. Nonlinear Math. Phys. 18 (2011) 123] and construct nonlocal symmetries for these two oscillators. From the knowledge of the latter we derive first integral and general solution for these two nonlinear nonpolynomial oscillator equations.     

A new formulation of the initial value problem for nonlocal theories

There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of nonlocality leads to improved UV behavior, novel cosmological dynamics and is a generic prediction of string theory. On the other hand, fundamentally nonlocal models are fraught with complications, including instabilities and complications in setting up the initial value problem. We study the structure of the initial value problem in an interesting class of nonlocal models. We advocate a novel new formulation wherein the Cauchy surface is “smeared out” over the underlying scale of nonlocality, so that the usual notion of initial data at t=0$t=0$ is replaced with an “initial function” defined over −M−1?t?0$-M^{-1}?t?0$ where M is the underlying scale of nonlocality. Focusing on some specific examples from string theory and cosmology, we show that this mathematical re-formulation has surprising implications for the well-known stability problem. For D-brane decay in a linear dilaton background, we are able to show that the unstable directions in phase space cannot be accessed starting from a physically sensible initial function. Previous examples of unstable solutions in this model therefore correspond to unphysical initial conditions, an observation which is obfuscated in the old formulation of the initial value problem. We also discuss implication of this approach for nonlocal cosmological models.     

Towards a gravity dual for the large scale structure of the universe

The dynamics of the large‐scale structure of the universe enjoys at all scales, even in the highly non‐linear regime, a Lifshitz symmetry during the matter‐dominated period. In this paper we propose a general class of six‐dimensional spacetimes which could be a gravity dual to the four‐dimensional large‐scale structure of the universe. In this set‐up, the Lifshitz symmetry manifests itself as an isometry in the bulk and our universe is a four‐dimensional brane moving in such six‐dimensional bulk. After finding the correspondence between the bulk and the brane dynamical Lifshitz exponents, we find the intriguing result that the preferred value of the dynamical Lifshitz exponent of our observed universe, at both linear and non‐linear scales, corresponds to a fixed point of the RGE flow of the dynamical Lifshitz exponent in the dual system where the symmetry is enhanced to the Schrödinger group containing a non‐relativistic conformal symmetry. We also investigate the RGE flow between fixed points of the Lifshitz dynamical exponent in the bulk and observe that this flow is reflected in a growth rate of the large‐scale structure, which seems to be in qualitative agreement with what is observed in current data. Our set‐up might provide an interesting new arena for testing the ideas of holography and gravitational duals.     

A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment

This article presents a simplified three-unknown shear and normal deformations nonlocal beam theory for the bending analysis of nanobeams in thermal environment. Eringen's nonlocal constitutive equations are considered in the analysis. Governing equations are derived according to the present refined theory using Hamilton's principle. Central deflections of nanobeams under uniform and point loads are given and compared with the available ones in the literature. Additional results of displacement and stresses are presented for future comparison. The effects of nonlocality, temperature parameters, length of beam, length-to-depth ratio as well as shear and normal strains are all investigated.     

Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model

We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group on a space E. We define the algebra of smooth complex valued functions on , with convolution as multiplication, in terms of which the groupoid geometry is developed. Owing to the fact that the group G is finite the model can be computed in full details. We show that by suitable averaging of noncommutative geometric quantities one recovers the standard space-time geometry. The quantum sector of the model is explored in terms of the regular representation of the algebra , and its correspondence with the standard quantum mechanics is established.     

ITER纵场磁体支撑屈曲分析与半原型测试件初步设计

针对新设计的ITER纵场重力支撑结构特点,用ANSYS有限元软件对它建立了有限元模型。采用Block Lanczos方法求出了ITER重力支撑的屈曲特征值。分析结果表明ITER重力支撑不会发生屈曲。为了确保新设计结构的可靠性,初步设计了全尺寸支撑的半原型件拟用来对支撑进行工程受力测试。     

Generation of quantum switch and nonlocal fields with an external field in a high quality dispersive cavity

We present a scheme to prepare an optical “quantum switch”, a superposition of “open” and “closed” states. The scheme is based on the interaction of an Λ-type three-level atom with a single-mode of quantized cavity field and an external classical driving field, in the regime where the atom and fields are highly detuned. We show how this interaction can be used to generate coherent states of the cavity field in contrast to the usual method used in microwave cavity QED of injecting a coherent state into a cavity. A combination of switches could be used to prepare a quantum superposition of coherent field states located simultaneously in two cavities. Compared with previous proposals, our scheme is simplified due to economizes the Ramsey zone and the time required for the state generation is short.     

力学综合课程建设的研究和实践

简述了我校物理系进行力学综合课程建设的基本思想和措施，以及建立将普通物理力学、理论力学和量子力学基础综合成一门课程的新的教学内容结构体系的具体做法．这样做，不但大大减少了重复内容和课时。而且有助于学生从整体上把握力学理论的基本框架，有助于培养学生的综合研究能力和创新能力。     

重力加速度测量仪的设计与制作

对重力加速度测量仪进行了重新设计,用条形重物块作为自由落体避免了用小球作重物时经过光电门因偏心带来的测量误差,用弹簧夹物装置代替电磁铁释放重物,消除了电磁铁剩磁对重物的吸引作用,提高了测量精度.