具有特殊参考系的引力试探理论中的能量和运动方程
Energy and equations of motion in a tentative theory of gravity with a privileged reference frame
摘要：
基于对引力作为压力的尝试性解释，引力的标量理论以前被研究过。它假定了空间（时间）的引力收缩（膨胀）标准。在静态情况下，与狭义相对论中的牛顿定律相同的牛顿定律也是用这些扭曲的局部标准来表示的，并且发现它隐含着测地线运动。在这里，我们在最一般的情况下重新考察运动的表述。一个相容的牛顿定律仍然可以被定义，它解释了空间度规的时间变化，但它与含时场的测地线运动不相容。测试粒子的能量被定义为：在静态情况下它是常数。从“尘埃”出发，推导出物质能量的平衡方程。如果假设牛顿定律，理论的场方程允许将其重写为真正的守恒方程，包括引力能。后者包含一个牛顿项，加上引力波（或光）的局部速度的相对速率的平方，速度用绝对标准表示。
英文摘要：
Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law as in special relativity was expressed in terms of these distorted local standards, and was found to imply geodesic motion. Here, the formulation of motion is reexamined in the most general situation. A consistent Newton law can still be defined, which accounts for the time variation of the space metric, but it is not compatible with geodesic motion for a time-dependent field. The energy of a test particle is defined: it is constant in the static case. Starting from 'dust', a balance equation is then derived for the energy of matter. If the Newton law is assumed, the field equation of the theory allows to rewrite this as a true conservation equation, including the gravitational energy. The latter contains a Newtonian term, plus the square of the relative rate of the local velocity of gravitation waves (or that of light), the velocity being expressed in terms of absolute standards.
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