# Do I have time dilation right?

by Wakefulpanda
Tags: dilation, time
 Sci Advisor P: 3,456 As with all versions of the twin paradox, it's the landing and taking off again that makes things unsymmetrical. Somebody has to do it, and there is no doubt who has accelerated in this case: the gps guy. His clock is the one that winds up being slower. The ground observer can say, "I've been right here in my inertial frame the whole time." The gps guy cannot say that.
 P: 4 I hoped to not make my question sound to much like the twin paradox. I apologize for my elementary knowledge of the issue. After reading about GPS satellites adjusting for SR my confusion mounted. Is it really as simple as "well the satellite is moving faster relative to us and our computers see the clock as running slower so we have to speed it up?"
P: 18

## Do I have time dilation right?

I think it is that simple. The GPS system is simply the twin paradox. It is the fact that we are utilising data from the speeding satellite in our stationary reference frame that dictates we must take account of the time dilation on the satellite when manipulating the received data in our reference frame.

Imagine a simple scenario where the GPS satellite has a clock on board and we use that to time a 100 meter race.

The athletes line up on the start line and a signal is sent to the satellite to tell it they are ready to race.

The satellite then sends a signal to the starter gun, which fires.

The winning athletes breaks a tape at the finishing line, which sends a signal to the satellite and the satellite uses this to calculate the winner's race time.

We can assume that all signal transit times between the race and satellite are taken into account.

In what time did the athlete win the race?

If we rely on the satellite for the answer, then we must adjust its result for time dilation.

Now replace the athlete with your car, travelling to visit aunt Ethel and you will see the problem, and solution, are the same.
P: 3,180
 Quote by Wakefulpanda I hoped to not make my question sound to much like the twin paradox. I apologize for my elementary knowledge of the issue. After reading about GPS satellites adjusting for SR my confusion mounted. Is it really as simple as "well the satellite is moving faster relative to us and our computers see the clock as running slower so we have to speed it up?"
Hi Wakefulpanda.

Yes, and in addition to Huttate:

The simplest approach is to choose the Earth Centered Inertial frame as "rest system", and that is just what GPS uses. In that frame all satellites are moving fast (even geostationary ones), so that from that perspective the clock frequencies of the satellites are reduced due to their speed.

That effect on clock frequency was already predicted* by Einstein in his famous article of 1905, from logical reasoning based on the Lorentz transformations.

Cheers,
Harald

*his prediction of that time failed to account for the difference in gravitational potential - for obvious reasons!
 P: 18 I would also add: "What I don't understand is if no adjustments were made would person A run out of water first? Since B is dripping at a slower rate as observed by A than this would seem logical. If no adjustments were made what would happen if B were to land and water bottles were compared? OR if each device had an alarm with a flashing light that triggered when the other persons water bottle ran out which persons alarm would trigger first? If person A ran out of water would he see his alarm going off on person B's device? Would the opposite be true if person B was looking at person A's device?" These questions are all [I think] answered by the issue of relativity of simultaneity. What one sees is dependent upon one's frame of reference. The issue of a final side by side comparison is covered by the time dilation during seperation.
PF Patron
P: 193
 Quote by Wakefulpanda 4) Person B flies off at the speed of light,
I think you mean near lightspeed, not exactly lightspeed.

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