Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M=10⁸ ÷10⁹ in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.     

光放大方法及其应用

介绍了光放大的实验原理，阐述了光放大原理在万有引力实验和扫描探针显微镜中的应用。     

密立根油滴实验中一个不能忽视的小问题

本文分析了油滴从静止到匀速的过程,讨论了密立根油滴实验中油滴从静止开始下落到匀速直线运动状态所用的时间.在实验课的教学中给了学生关于加速弛豫过程时间量的概念,排除了测量过程中困扰学生的一个重要因素.     

利用爱因斯坦转盘推求中心引力场中的光频红移--在普通物理教学中讲解等效原理的一种尝试

通过球对称引力场与爱因斯坦转盘上的惯性离心力场的对比，利用强等效原理导出光频的引力红移。     

Higgs bosons inE 6 and intermediate mass scales

Considering the importance ofE ₆ as the grand unification group in superstring theories, several breakdown patterns ofE ₆ through maximal subgroups are studied. The Higgs which break the low energy group and give masses to the fermions are determined in each case. At each scale we consider minimal Higgs and apply extended survival hypothesis to determine the limits on the mass scales. The combination of intermediate mass scales that give rise to acceptable electroweak mixing angle and unification mass is determined. Proton decay rate is found to be acceptable in all cases except one.     

Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.     

Graded differential lie algebras and model building

We develop a mathematical concept towards gauge field theories based upon a Hilbert space endowed with a representation of a skew-adjoint Lie algebra and an action of a generalized Dirac operator. This concept shares common features with the non-commutative geometry à la Connes/Lott, differs from that, however, by the implementation of skew-adjoint Lie algebras instead of unital associative *-algebras. We present the physical motivation for our approach and sketch its mathematical strategy. Moreover, we comment on the application of our method to the standard model and the flipped SU(5)×U(1)-grand unification model.     

A stationary apparent weight shift from a transient Machian mass fluctuation

A transient mass fluctuation, predicted by Lorentz-invariant theories of gravitation wherein inertia is gravitationally induced, can be combined with a synchronous thrust to produce a stationary change in the apparent weight of an object. A substantial effect of this sort—on the order of tenths of a gram or more—should be achievable in laboratory scale apparatus. A detailed derivation of the predicted transient mass fluctuation is given in an appendix.1. This does not mean, however, that it is impossible to directly detect the expected weight fluctuations at higher than low audio frequencies. In fact, in preliminary work toward the experiment described below, L. Shen, K. Wanser, and I have detected evidence of the effect at ultrasonic frequencies employing very unusual capacitors (high energy density ceramic multiplate chip capacitors with strongly suppressed first- and second-order electromechanical effects) mounted on an aluminum pedestal which acts as the spring in the system. The minute displacements produced are detected with a laser interferometer. This work will be described fully in a separate paper.2. Such a transformer can be made with, for example, an Amidon T 300A-26 powdered iron torus. Powdered iron is preferable to ferrite because of its superior flux saturation and energy loss characteristics at the frequencies in question.3. Einstein[7] was the first to point out (in 1912) that the simplest formalism for the gravitational field that incorporates Machian gravitational induction of inertia is that based on the analogy with the electromagnetic field, that is, a Lorentz-invariant four-vector potential theory. Many years later, Sciama[5] showed explicitly how such a theory could account for well-known inertial reaction effects, provided that the mean matter density of the universe were the right value (in fact, just cosmologically critical density). Later he showed that a general relativistic tensor formalism yielded the same conclusions[8]. And, as I have pointed out elsewhere[1–3], Nordtvedt's PPN formalism with GRT parameters chosen yields the same result when the effect of cosmic matter is included.4. Contributions from the Hubble flow tov and thusj are ignored here, since upon integration they vanish by symmetry. Hubble flow does, however, make _c a function ofr. 5. The advanced solutions of the wave equation required to account for inertia in the Lorentz gauge can be avoided if one chooses by using the Coulomb gauge with its action-at-a-distance characteristic. Asserting the equivalent of the Coulomb gauge to get instantaneous inertial reaction forces, as Trederet al.[9] point out, suggests an interesting generalization of GRT.6. This procedure for going from a particle to a continuous media representation is not in general valid, since in all frames, except the rest frame, will involve elements of the stress tensor. Those contributions, however, are of orderv ² /c ² and are here ignored.7. One may find this result troublesome, for one may think thatø is only fixed up to an additive constant. While this is true in linear theories, as discussed below, it is not true in nonlinear theories. Let me also point out here the similarity of Eq. (A12) and the field equations obtained by Trederet al.[9, pp. 70-73] in a higher-derivative manifestly Machian Einstein-Cartan theory of gravitation where the same potential-like coupling of gravity and matter occurs.8. Equation (A13) only applies in the instantaneous rest frame of the test particle. In all other frames of reference one obtains a term involving the time derivative of the acceleration. Terms of this sort, of course, are not normally allowed in dynamics. They are the signature of self-forces and radiation reaction effects. But this should come as no surprise, for the effect arises from the gravitational self-energy interaction when inertial reaction forces are stimulated.     

Unification and infinite series

Some infinite series are analysed on the basis of the hypergeometric function and integer structure and modular rings. The resulting generalized functions are compared with differentiation of the ‘mother’ series.