A Brief Note on a New Cosmic “Coincidence” and New Physics

The latest results from the Wilkinson Microwave Anisotropy Probe (WMAP) with regard to the Cosmic Microwave Background (CMB) throw up some intriguing results, and the question has been asked “Does this point to new physics?” We point out that indeed all this indicates new physics on the Planck scale.     

Soft Singularity and the Fundamental Length

It is shown that some regular solutions in 5D Kaluza-Klein gravity may have interesting properties if one from the parameters is in the Planck region. In this case the Kretschman metric invariant runs up to a maximal reachable value in nature, i.e. practically the metric becomes singular. This observation allows us to suppose that in this situation the problems with such soft singularity will be much easier resolved in the future quantum gravity then by the situation with the ordinary hard singularity (Reissner-Nordström singularity, for example). It is supposed that the analogous consideration can be applied for the avoiding the hard singularities connected with the gauge charges.     

A Note on Stress-Tensors,Conservation and Equations of Motion

Some unusual relations between stress tensors, conservation and equations of motion are briefly reviewed. This work was supported by the National Science Foundation under grants PHY99-73935:04-01667.     

Vacuum Non Singular Black Hole Solutions in Tetrad Theory of Gravitation

Starting from a spherically symmetric tetrad with three unknown functions of the radial coordinate and assuming a specific form of the vacuum stress-energy momentum tensor, a general solution of Møller's field equations in case of spherically symmetric nonsingular black holes is derived. The general solution is characterized by an arbitrary function and two constants of integration. The previously obtained solutions are verified as special cases of the general solution. The associated metric of the general solution gives no more than the spherically symmetric nonsingular black hole obtained before. The energy content of the general solution depends on the asymptotic behavior of the arbitrary function, and is different from the standard one.     

Equivalence Postulate and Quantum Origin of Gravitation

We suggest that quantum mechanics and gravity are intimately related. In particular, we investigate the quantum Hamilton–Jacobi equation in the case of two free particles and show that the quantum potential, which is attractive, may generate the gravitational potential. The investigation, related to the formulation of quantum mechanics based on the equivalence postulate, is based on the analysis of the reduced action. A consequence of this approach is that the quantum potential is always non-trivial even in the case of the free particle. It plays the role of intrinsic energy and may in fact be at the origin of fundamental interactions. We pursue this idea, by making a preliminary investigation of whether there exists a set of solutions for which the quantum potential can be expressed with a gravitational potential leading term which alone would remain in the limit 0. A number of questions are raised for further investigation.     

A Note on Classification of Teleparallel Conformal Vector Fields in Cylindrically Symmetric Static Space-Times in the Teleparallel Theory of Gravitation

In this paper we explored teleparallel conformal vector fields in cylindrically symmetric static space-times in the teleparallel theory of gravitation by using the direct integration technique. It turns out that the dimension of teleparallel conformal vector fields are 8, 9, 10 or 11. The case VI in which the space-time becomes conformally flat admits eleven independent teleparallel conformal vector fields.     

String theory, scale relativity and the generalized uncertainty principle

Extensions (modifications) of the Heisenberg uncertainty principle are derived within the framework of the theory of special scale-relativity proposed by Nottale. In particular, generalizations of the stringy uncertainty principle are obtained where the size of the strings is bounded by the Planck scale and the size of the universe. Based on the fractal structures inherent with two dimensional quantum gravity, which has attracted considerable interest recently, we conjecture that the underlying fundamental principle behind string theory should be based on an extension of the scale relativity principle whereboth dynamics as well as scales are incorporated in the same footing.     

A Non-geometric Relativistic Theory of Gravitation

A non-geometric relativistic theory of gravitation is developed by defining a semi-metric to replace the metric tensor as gravitational vector potential. The theory show that the energy-momentum tensor of the gravitational field belong to the gravitational source, gravitational radiation is contained in Einstein’s field equations that including the contribution of gravitational field, the real physical singularity in the gravitational field can be eliminated, and the dark matter in the universe is interpreted as the matter of pure gravitational field.     

分子间存在引力实验的改进

“分子引力”实验是初中物理“分子运动论”教学中的一个重要的验证性演示实验.传统的演示实验存在着实验现象不明显,成功率不高,不便于学生观察等缺陷.利用甘油能增加液体膜韧性的特点,利用液体膜拉动吸管运动可以让学生很直观地观察到分子间的引力,降低学生对于微观现象的理解难度.     

微机辅助光电效应实验

本介绍一种借助微机研究光电效应的实验系统，微机作为中心控制单元，完成数据采集和存储，实现大量观测数据的建模和平均。最后给出了普朗克常数的测定结果。     

A Note on the Rarita-Schwinger Equations

Assuming that the background spacetime is a solution of the Einstein vacuum equations without cosmological constant, we analyze how the Rarita-Schwinger equations can be obtained via a particular generalization of the usual spin-3/2 massless free field equations. On the basis of this analysis we speculate on the possibility of finding other generalizations of the Rarita-Schwinger equations.     

A Solution of a Nonsymmetric Theory of Gravitation

The field equations of a proposed nonsymmetrictheory of gravitation are solved exactly for the case ofa static and spherically symmetric point singularity.The physical consequences of the solution are analyzed for the precession of perihelia,deflection of light, red-shift and radar-echodelay.     

A Note on Palindromicity

Two results on palindromicity of bi-infinite words in a finite alphabet are presented. The first is a simple, but efficient criterion to exclude palindromicity of minimal sequences and applies, in particular, to the Rudin–Shapiro sequence. The second provides a constructive method to build palindromic minimal sequences based upon regular, generic model sets with centro-symmetric window. These give rise to diagonal tight-binding models in one dimension with purely singular continuous spectrum.     

Gravitation of the Klein-Gordon scalar field

This paper presents an exact solution of the Einstein-Klein-Gordon equations in the static and spherically symmetric case and points out the differences between it and Yilmaz's solution. In addition, the essential difference between the exact solution and the post-Newtonian approximate solution is also shown.