Haar波与引力惯性的起源
Haar Wavelets and the Origin of Gravitational Inertia
摘要：
除了能量信号波与引力场相互作用的地方，时空被认为是闵可夫斯基无处不在的地方。适当地选择共形度量f[k（x-vt）]Nuv来表示这种相互作用，其中f[k（x-vt）]是广义波或信号函数。参数化和泰勒展开为零，时空度量被转换成一个哈尔小波参数宽度τ。将Haar度规应用于广义相对论波动方程的时间分量，将其从二阶协变微分方程简化为一阶偏微分方程，使得爱因斯坦张量可以很容易地以常见的泊松引力形式表示。通过与这个方程的物质密度的比较，哈尔-爱因斯坦的结果表明，引力子的波长成为引力的基本来源。由于信号波是单向的，它强烈支持马赫的假设，即惯性来自宇宙中的所有物质。此外，由于Haar度量是共形的，信号度量被精确求解。
英文摘要：
Spacetime is considered to be everywhere Minkowski except at the location where a signal wave of energy interacts with the gravitational field. The conformal metric f[k(x-vt)]Nuv is suitably chosen to represent this interaction, where f[k(x-vt)]is a generalized wave or signal function. Parametrized and Taylor expanded at zero, the spacetime metric is transformed into a Haar wavelet having parameter width tau. Applying the Haar metric to the time component of General Relativistic wave equation reduces it from a second ordered covariant differential equation to a first ordered partial differential equation that allows the Einstein Tensor to be easily be expressed in the familiar Poisson form for gravitation. By comparison with the matter density of this equation, to the Haar-Einstein result, shows that the wavelength of a graviton becomes the fundamental source for gravitational attraction. Since the signal wave is unidirectional, it strongly supports Machs assumption that inertia arises from all the matter in the universe. Furthermore, because the Haar metric is conformal, the signal metric is solved for exactly.
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