- #1
OS Richert
- 35
- 0
I am looking over the Project A: Global Positioning System is Exploring Black Holes; introduction to General Relativity by Taylor and Wheeler. At first, they convincingly suggest that the time dilation caused by the differences in radius from Earth clocks to the satelight clocks will cause the satalight clocks to run fast on the order of 50000 nanoseconds. Makes sense. But then they say this.
Here we go again! Why does the satellite which moves faster have a clock that actually runs slower. Faster according to whose frame of reference? Can't the satellight clock simply claim that it is the Earth's clock that is in motion according to the satellight's frame of reference. It seems that in this sentence that are indeed defining a preferred frame of reference. The Earth clock must actually be moving slower in space the the satellight clock (since it actually expereinces time dilation when you compare the two).
OR is the trick here that we consider the Earth clock to be the frame of reference because it is the one receiving the signal and doing the GPS calculations. So anything in motion with repsect to it seems to have a clock that runs slow, even though they would say the same about you. In other words, if the ground clock sent a signal to the satellight clock, it likewise would think the Earth clock was running slow. And somehow this is all accounted for by time simaltaneounity
In addition to effects of position, we must include effects due to motion of satellite and Earth observer. In which direction will these effects influence the result? The satellite clock moves faster than the clock revolving with Earth's surface. But Special relativity tells us that (in an imprecise summary) "moving clocks runs slow"
Therefor we expect the effect of motion to reduce the amount by which the satellite clock runs fast compared to the Earth Clock. In brief, when velocity effects are taken into account, we expect the satellite clock to run faster then Earth clock by less than the estimated 50000 nanoseconds per day
Here we go again! Why does the satellite which moves faster have a clock that actually runs slower. Faster according to whose frame of reference? Can't the satellight clock simply claim that it is the Earth's clock that is in motion according to the satellight's frame of reference. It seems that in this sentence that are indeed defining a preferred frame of reference. The Earth clock must actually be moving slower in space the the satellight clock (since it actually expereinces time dilation when you compare the two).
OR is the trick here that we consider the Earth clock to be the frame of reference because it is the one receiving the signal and doing the GPS calculations. So anything in motion with repsect to it seems to have a clock that runs slow, even though they would say the same about you. In other words, if the ground clock sent a signal to the satellight clock, it likewise would think the Earth clock was running slow. And somehow this is all accounted for by time simaltaneounity