爱因斯坦光速可变理论的马赫主义版本
A Machian Version of Einstein's Variable Speed of Light Theory
摘要：
这是一个鲜为人知的事实，而他是发展他的理论广义相对论，爱因斯坦的最初想法是一个可变的光速理论。事实上，时空曲率可以用光速$c(r)$来模拟，而光速取决于质量的分布。1957年，罗伯特·迪克（Robert Dicke）对爱因斯坦1911年的理论进行了相当大的改进，但直到最近才证明了可变光速方法与传统形式主义的等价性（Broekaert，2008）。使用格林函数，我们表明，爱因斯坦的1911年的想法可以表示在一个分析的形式，类似于泊松方程。使用启发式参数，我们推导出一个简单的公式，直接涉及曲率$w$的本地光速，$w= -c^2 Δ\frac{1}{c^2}$。与传统的公式相反，这允许对广义相对论和引力常数$G$进行马赫解释。引力虽然是用局部方程描述的，但它起源于宇宙中所有其他的质量。
英文摘要：
It is a little known fact that while he was developing his theory of general relativity, Einstein's initial idea was a variable speed of light theory. Indeed space-time curvature can be mimicked by a speed of light $c(r)$ that depends on the distribution of masses. Einstein's 1911 theory was considerably improved by Robert Dicke in 1957, but only recently has the equivalence of the variable speed of light approach to the conventional formalism been demonstrated (Broekaert, 2008). Using Green's functions, we show that Einstein's 1911 idea can be expressed in an analytic form, similar to the Poisson equation. Using heuristic arguments, we derive a simple formula that directly relates curvature $w$ to the local speed of light, $w= -c^2 Δ\frac{1}{c^2}$. In contrast to the conventional formulation, this allows for a Machian interpretation of general relativity and the gravitational constant $G$. Gravity, though described by local equations, has its origin in all other masses in the universe.
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