Do GPS Clocks Really Run Slower Than Earth Clocks Due to Time Dilation?

[exmarine]

I had such success with all your answers to my last SRT question here I’ll try another. The LT seems very symmetric. To the observers in each frame, the other’s clocks appear slower, etc. Is that true for out GPS satellites? If we ignore the GRT effect of speeding up their clocks, I think it is agreed that the SRT effect makes their clocks “appear” (?) slower. Don’t their clocks have to really be slower than ours? Do our ground-based clocks appear slower to them – say to an astronaut circling the globe? Thanks in advance for any help.

 

[ghwellsjr]

No, the symmetric effect of moving clocks running slower in an Inertial Reference Frame doesn't apply in non-inertial situations. So, neglecting the effects of gravity, a clock moving in a circle in an IRF will run slower than a clock stationary in that IRF but since there is no IRF in which the circling clock is always at rest, it cannot say that the other clock is running slower than it is.

In fact, this is the very scenario that Einstein predicted in his 1905 paper introducing Special Relativity at the end of section 4.

 

[Agerhell]

I had such success with all your answers to my last SRT question here I’ll try another. The LT seems very symmetric. To the observers in each frame, the other’s clocks appear slower, etc. Is that true for out GPS satellites? If we ignore the GRT effect of speeding up their clocks, I think it is agreed that the SRT effect makes their clocks “appear” (?) slower. Don’t their clocks have to really be slower than ours? Do our ground-based clocks appear slower to them – say to an astronaut circling the globe? Thanks in advance for any help.

The clocks on GPS satellites will tick slower than earthbound clocks if we ignore the fact that they are situated not so deep in the Earth's gravitational field which makes them tick faster, that is correct.

The clocks on board a train going east will tick slower than the clocks on board a train going west, due to the rotation of the earth.

In general if you want to know the rate of time of a moving clock in a near-earth environment you will have to know how fast it is moving in reference to a non-spinning Earth and the gravitational potential at its location.

 

[PeterDonis]

The clocks on GPS satellites will tick slower than earthbound clocks if we ignore the fact that they are situated not so deep in the Earth's gravitational field which makes them tick faster

But, just to be clear, if you take the difference in gravitational potential into account at the altitude of the GPS satellites, it more than offsets the effect of relative velocity; the net effect is that clocks on GPS satellites tick *faster* than clocks at rest on the ground. (The timing signals that come from the GPS satellites are corrected for this.)

 

[Chronos]

Yes, the GPS clocks 'tick' faster than those on Earth due lower gravity [GR effect], which is partially offset by their orbital velocity [SR effect]. The net effect is they would run about 39,000 nanoseconds per day faster than their earthbound counterparts. GPS clocks are precalibrated before launch to cause them to run this much slower, and, voila! Once in orbit they are synchronized with ground clocks. Scientists subsequently tweak the calibration of the GPS clocks to keep them in synch with ground clocks.