Getting Signs Right!

摘要

In [1] V.N. Strel'tsov has pointed out an apparent failure of Gen- eral Relativity Theory (GRT) to get the right sign of the gravity effect on clock running rates. However, it has been said that signs are the most difficult part of physics, and I suggest that this is a case in point. He gives as the ratio of proper time to frame time increments dτ / dts, based on the Schwarzschild metric, the expression f = 1- 2|Φ|/c2 -v2 /c2~(1/2), where f is the multiplier (correction fac- tor) that must be applied to the definition of the number of atomic oscillations per "second" for clocks placed in orbit to cause them to run synchronously with surface clocks, for instance, as part of the Global Positioning System (GPS). The corresponding expression given by Moeller [2], as cited by Strel'tsov, is f = 1 + 2χ/ c2 - v2 / c2~(1/2). As it happens, fault can be found with both of these expressions, in that they fail to specify a useful gauge for the gravity potential functions denoted by Φ or χ.