Do I have time dilation right?

[Wakefulpanda]

Hello all,

First let me say that I have been battling with time dilation for years, all the videos seem to drive me more into confusion and reading does the same. The past few weeks I have been really trying to get a grasp on it better. I understand the concepts, theories, and postulates but I guess I am having trouble putting them into practice. So I created an example that I hope someone could look at.

I recently discovered that GPS satellites have times adjusted due to SR and GR. Now GR I can understand and I think I have a safe understanding of. It is the special relativity that I have a hard time grasping.

Ok here is my example: This is what I imagine mimics the GPS operation.

1) Person A (the ground observer) and Person B (the gps satellite) both have light clocks. Each clock allows light to bounce on plates (your regular light clock I suppose)

2) Person A and person B also have a device that is attached to their light clocks. This device registers each tick of a light clock. Upon that tick it drops a specific amount of water from a bottle (both person A and person B have bottles with the same amount of water. So tick, drop, tock drop.

3) Person A sets his device on a platform here on Earth and person B enters his spacecraft . Each person then starts their device at the exact same moment in time.

4) Person B flies off at the speed of light, person A sees B's water dropping at a slower rate, and person B sees person A's water dropping at a slower rate.

5) Person B lands and person A says "B your water is dropping slower than mine and making it difficult to stay in sync with you, so before you take off again I am going to speed up your water drops so we can stay in sync." B says "you're the boss, adjust my device to match yours since your water drop rate is what matters"

6) Person B takes off again with his sped up device, now person A sees that both devices are dropping water at the same rate.

That is my basic thought which is my understanding of special relativity as the GPS is concerned. I understand this in theory and this basically for me explains how satellites communicate with precision to earth.

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?

It seems to me that if this example were real and I was person A I could only come to one conclusion. I would state "While person B's water seems to be dripping more slowly than mine I understand that our devices are in sync, therefore I can only conclude that person B is in motion relative to me and that light is playing a trick on me.

I know this was very long but I would truly appreciate any insight on this personal struggle of mine. Know that any information or insight given will not be wasted.

Thanks!

 

[Bill_K]

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.

 

[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?"

 

[Huttate]

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, traveling to visit aunt Ethel and you will see the problem, and solution, are the same.

 

[harrylin]

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!

 

[Huttate]

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 separation.

 

[FtlIsAwesome]

4) Person B flies off at the speed of light,

I think you mean near lightspeed, not exactly lightspeed.