华罗庚与爱因斯坦相对论及其扩展——纪念华罗庚诞辰一百周年

华罗庚先生运用矩阵几何与投影几何,研究并简化了爱因斯坦狭义相对论的基本原理,得到惯性运动的对称性,并促进了对德西特不变的狭义相对论的研究.他的深入考察至今仍引领着我们如何面对精确宇宙学的挑战.爱因斯坦相对论作为以宇宙常数Λ>0为特征的宇观物理学的基础面临疑难.相对性原理应该扩充到具有两个不变普适常数c和l,具有24个生成元的惯性运动对称性的相对性原理.于是,存在庞加莱、德西特和反德西特不变的3种相对论,伴随着对偶庞加莱运动学,它们构成相对论三位一体.取……,德西特相对论提供宇观尺度之新运动学,亦可避开相对性的宇宙佯谬.华老不仅是大数学家,而且是大思想家和大教育家,是一位为复兴中华民族而奉献终身的伟大代表.     

Schwarzchild-de Sitter 黑洞的热力学性质

在考虑黑洞视界与宇宙视界具有关联性的基础上,证明de Sitter时空的热力学熵为黑洞视界热力学熵与宇宙视界热力学熵之和.给出了考虑两视界具有关联性后的de Sitter时空的热力学特性.研究表明,de Sitter时空的能量上限为纯de Sitter时空能量,deSitter时空的热容量是负的,de Sitter时空一般是量子力学不稳定的.     

相对论问答录之一

<正>问题一、狭义相对论建立在哪两条公理的基础之上?狭义相对论建立在"相对性原理"和"光速不变原理"这两条公理的基础之上。相对性原理是说,物理规律在所有惯性系中都相同。需要强调,这里所说的相对性原理已经是伽利略相对性原理的推广。伽利略相对性原理只针对     

谈“相对论”教学中遇到的几个问题的处理

根据狭义相对性原理,惯性系是完全等价的,在同一个惯性系中,存在统一的时间,称为同时性,而相对论证明,在不同的惯性系中,却没有统一的同时性,也就是两个事件(时空点)在一个惯性系内同时,在另一个惯性系内就可能不同时,这就是同时的相对性,在惯性系中,同一物理过程的时间进程是完全相同的,如果用同一物理过程来度量时间,就可在整个惯性系中得到统一的时间.非惯性系中,时空是不均匀的,也就是说,在同一非惯性系中,没有统一的时间,因此不能建立统一的同时性.由此从下面几个问题来说明,值得一起商榷. 一.对于人教版3-4课本P109图15.2-3如何解释?     

高维de Sitter时空中宇宙视界处的Fermi子隧穿

运用半经典近似理论,本文研究了来自静态高维de Sitter时空和高维Schwarzschild-de Sitter时空宇宙视界处的Fermi子隧穿辐射.在文中,描述1/2自旋粒子行为的Dirac方程被简化为一个简单的形式,接着运用方程组有非平凡解的条件,可以得到了半经典的Hamilton-Jacobi方程,从而使得问题大大得以简化,最终得到了静态de Sitter时空中宇宙视界处的Fermi子隧穿率和Hawking温度.     

从爱因斯坦火车到洛伦兹变换

爱因斯坦火车是狭义相对论中展示同时性的相对性的经典模型, 爱因斯坦利用该模型证明了“ 同时性 的相对性” . 在狭义相对论中, 空间和时间并不相互独立, 而是一个统一的四维时空整体, 不同惯性参考系之间的时 空坐标变换关系式与洛伦兹变换在数学表达式上是一致的, 通过分析爱因斯坦火车模型中光在不同惯性参考系内 到达车壁的时间, 利用简单的数学变换更加容易地得到了洛伦兹变换, 从而验证了洛伦兹变换在狭义相对论的核 心地位     

狭义相对论的欧氏假定与暗宇宙的启示

本文分析爱因斯坦相对论中关于一类没有相对运动的惯性系中刚性量杆的欧氏假定，以及相对性原理与宇宙学问的不协调。简单介绍我国学者提出的德西特不变的相对论，以及由暗宇宙启示的马赫原理。该相对论提供一个加速膨胀的观测宇宙所渐近趋向的模型。这里，不存在相对性原理与宇宙学问的不协调，存在一类相对于宇宙背景静止的优越惯性系，3维宇宙空间是闭的，宇宙常数起到惯性运动起源的作用。同时，这个模型提供观测宇宙的熵界，与全息原理的猜测一致，当曲率半径趋于无限时，这类优越惯性系仍然存在，不完全是爱因斯坦狭义相对论。     

《从零学相对论》连载(14)

第6讲广义相对论初步§6.1引力的实质是时空的弯曲相对性原理要求物理规律在所有惯性系中有相同的数学表达式,用于狭义相对论,就是要求物理规律的数学表达式具有洛伦兹协变性.这是一个管定律的定律.因此,在建立狭义相对论物理学时,原则     

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.     

洛伦兹破缺的电动力学模型

由于宇宙常数的存在, 时空为渐近de Sitter(dS)的时空. 文中将静态dS度规作为时空的近似刻画, 研究了在此度规下的一个洛伦兹破缺的电动力学模型. 通过张量的标架场分解的方法, 得到了静态dS时空中的电磁场方程. 另外, 分别研究了静态dS时空中点电荷的静电场和圈电流的静磁场, 并且同时讨论了在此模型下的洛伦兹破缺效应.     

From De Sitter Special Relativity and Snyder's Model to Complete Yang Model

The de Sitter special relativity on the Beltrami-de Sitter-spacetime and Snyder's model in the momentum space can be combined together with an IR-UV duality to get the complete Yang model at both classical and quantum levels, which are related by the proposed Killing quantization. It is actually a special relativity based on the principle of relativity of three universal constants (c,l_P,R).     

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.     

Asymptotically anti-de Sitter spaces

Asymptotically anti-de Sitter spaces are defined by boundary conditions on the gravitational field which obey the following criteria: (i) they are O(3, 2) invariant; (ii) they make the O(3, 2) surface integral charges finite; (iii) they include the Kerr-anti-de Sitter metric. An explicit expression of the O(3, 2) charges in terms of the canonical variables is given. These charges are shown to close in the Dirac brackets according to the anti-de Sitter algebra. The results are extended to the case ofN=1 supergravity. The coupling to gravity of a third-rank, completely antisymmetric, abelian gauge field is also considered. That coupling makes it possible to vary the cosmological constant and to compare the various anti-de Sitter spaces which are shown to have the same energy.On leave from Département de Physique, Université Libre de Bruxelles, BelgiumChercheur qualifié du Fonds National Belge de la Recherche Scientifique     

Geometric Simultaneity and the Continuity of Special Relativity

In this note I briefly discuss some aspects of relative geometric simultaneity in special relativity. After saying a few words about the status and nature of Minkowski spacetime in special relativity, I recall a uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth and I prove an extension of it for simultaneity relative to an inertial frame in time-oriented spacetimes. Then I point out that the uniqueness results do not generalise to definitions of simultaneity relative to the rotating disk. Finally, I evaluate some recent claims of Selleri in the light of the results. Whilst some of his claims are supported by the approach taken here, the conclusion he draws from these claims, that special relativity harbours a discontinuity and so stands in need of replacement, does not follow and is rejected.     

From De Sitter Special Relativity and Snyder＇s Model to Complete Yang Model

The de Sitter special relativity on the Beltrami-de Sitter-spacetime and Snyder＇s model in the momentum space can be combined together with an IR-UV duality to get the complete Yang model at both classical and quantum levels, which are related by the proposed Killing quantization. It is actually a special relativity based on the principle of relativity of three universal constants （c, ρp, R）.     

Hamiltonian Formalism of de-Sitter Invariant Special Relativity

The Lagrangian of Einstein's special relativity with universal parameter c (SR_c) is invariant under Poincaré transformation, which preserves Lorentz metric η_μν. The SR_c has been extended to be one which is invariant under de Sitter transformation that preserves so-called Beltrami metric B_μν. There are two universal parameters, c and R, in this Special Relativity (denoted as SR_cR). The Lagrangian-Hamiltonian formulism of SR_cR is formulated in this paper. The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for SR_cR-free particle is performed. The physics related to it is discussed.     

Parametrical embeddings of static spherically symmetric spacetimes

An analysis for a direct calculation of the embeddings in flat spacetimes of static spherically symmetric manifolds with Lorentz metric is worked out. For each manifold with non-constant curvature we arrive at a parametrical embedding which represents an infinite geometrical multiplicity of the embedded surface. The embeddings of manifolds with constant curvature are not parametrical and can be determined univocally. Examples concerning Schwarzschild, Reissner-Weyl, de Sitter and anti-de Sitter spacetimes are considered.     

One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry

The de Sitter invariant Special Relativity (dS-SR) is SR with constant curvature, and a natural extension of usual Einstein SR (E-SR). In this paper, we solve the dS-SR Dirac equation of Hydrogen by means of the adiabatic approach and the quasi-stationary perturbation calculations of QM. Hydrogen atom is located in the light cone of the Universe. FRW metric and ΛCDM cosmological model are used to discuss this issue. To the atom, effects of de Sitter space-time geometry described by Beltrami metric are taken into account. The dS-SR Dirac equation turns out to be a time dependent quantum Hamiltonian system. We reveal that: (i) The fundamental physics constants m_e,h,e variate adiabatically along with cosmologic time in dS-SR QM framework. But the fine-structure constant α≡ e²/(hc) keeps to be invariant; (ii) (2s^1/2-2p^1/2)-splitting due to dS-SR QM effects: By means of perturbation theory, that splitting Δ E(z) are calculated analytically, which belongs to O(1/R²)-physics of dS-SR QM. Numerically, we find that when |R|～{10³Gly, 10⁴Gly, 10⁵Gly}, and z～{1,or 2}, the Δ E(z)>>1 (Lamb shift). This indicates that for these cases the hyperfine structure effects due to QED could be ignored, and the dS-SR fine structure effects are dominant. This effect could be used to determine the universal constant R in dS-SR, and be thought as a new physics beyond E-SR.