arXiv physics/01100072001-10-02physics.gen-ph

狭义相对论和广义相对论的直观方法

An Intuitive Approach to Special and General Relativity

Charles Francis

备注：: A reformulation with the pedagogical purpose of introducing simplified concepts and techniques for a mathematical treatment, 23 pages, 20 figures

摘要：

赫尔曼·邦迪（Hermann Bondi）提出了k演算，作为仅使用简单代数解释狭义相对论的一种手段（邦迪H.：相对论和常识，伦敦，海涅曼，1964年）。如Bondi所使用的，k是多普勒频移。本文扩展了k-演算，使之包括引力红移，并发展了介绍广义相对论的技术，其中重点是从物理测量过程中进行数学推导。利用几何光学的思想，测地线运动可以从波函数因曲率引起的折射中理解。k演算给出了史瓦西的一个非常简单的推导，表明几何等价于基本粒子之间相互作用的基本最小时间的存在，与静止质量成正比。牛顿近似是从红移直接应用到波函数。最后介绍微分几何，表明k-演算给出了一个等价的治疗广义相对论，并包括爱因斯坦的场方程的一般形式。

英文摘要：

The k-calculus was advanced by Hermann Bondi as a means of explaining special relativity using only simple algebra (Bondi H.: Relativity and Common Sense, London, Heinemann, 1964). As used by Bondi, k is Doppler shift. This paper extends the k-calculus to include gravitational red shift and to develop techniques for an introductory treatment of general relativity in which the emphasis is on mathematical deduction from physical measurement procedure. Using ideas of geometric optics, geodesic motion is understood from the refraction of the wave function due curvature. The k-calculus gives a very simple derivation of Schwarzschild, showing that the geometry is equivalent to the existence of a fundamental minimum time, proportional to rest mass, between the interactions of elementary particles. The Newtonian approximation is seen from direct application of red shift to the wave function. Finally differential geometry is introduced, showing that the k-calculus gives an equivalent treatment of general relativity up to and including the general form of Einstein's field equation.

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