标题： 关于物质波的引力能量位移 显示英文标题

标题： On the Gravitational Energy Shift for matter waves

摘要： 光子的引力能移被推广到所有质量等效能量 $E = mc^2$，满足量子条件 $E = h\nu$。在一个相对论双星系统示例中，表明与牛顿引力不同的是，引力能移意味着质量等效能量之间的引力吸引。相应的时空度规变为指数形式。广义相对论弱场测试的所有结果都得到了很好的吻合。二元系统的强场效应可以很容易地研究。还讨论了先驱者号及其他飞越异常问题，这些问题是由于总能量守恒定律的破坏引起的。研究表明，在轨道类型变化过程中相对较小的能量不守恒可以解释这些持续存在的异常现象。 显示英文摘要

摘要： The gravitational energy shift for photons is extended to all mass-equivalent energies $E = mc^2$, obeying the quantum condition $E = h\nu$.On an example of a relativistic binary system, it was shown that the gravitational energy shift would imply,in contrast to Newtonian gravity, the gravitational attraction between full mass-equivalent energies. The corresponding space-time metric becomes exponential. A good agreement was found with all results of weak field tests of General relativity. The strong field effects in a binary system can be easily studied. A long standing problems of Pioneer and other flyby anomalies were also discussed in connection with the violation of total energy conservation. It was shown that relatively small energy non-conservation during the change of the orbit type could explain these persistent anomalies.