# Not Understanding Time Dilation - mk 2.

1. Aug 14, 2011

### cmb

Further to the other current thread, I have a different 'don't understand' issue for time dilation. I've thought it over and I might have a slight grasp of 'the answer', but it is still a bit murky for me:

Two space ships of the future pass each other in opposite directions, each travelling at 0.5c relative to some arbitrary point. Each one observes the other to be a space ship going 0.7c away from them [if my presumption that relativistic speeds add up in quadrature?]. Both therefore see the clock of the other ship running slower than their own.

How can both on-board clocks be running slower than each other?

2. Aug 14, 2011

### CDCraig123

Ill take a crazy stab at it this. As this sounds like what if i go back and time and kill grandpa what will happen. As i see it Time Dilation is only relevant to the speed at which you are passing through space time. Not relevant to any other body. Crazy theory of mine, as you move through space-time, space-time applies a force on you the faster you go the greater the force, and the greater this force the faster you will proceed through time. So on your two ships there clocks will be ticking according to there speed through space time, and not according to the speed difference between them. I wish NASA would put a clock into space and give it zero velocity and see what the clock did but this would be pretty hard to do considering we are moving at 580 km/s.

3. Aug 14, 2011

### cmb

As far as I have read, time dilation is an actual issue for ultra-accurate GPS [I think] satellite clocks, and ps corrections need to be fed in.

This is what actually prompted me to think of this in the first place; why does the GPS clock run slower than ground-based ones, when as far as the GPS clock is concerned it is the ground-based clock that's moving!? In this case, I suspect any such effects have more to do with gravity dilation than motional dilation, but I'd value any knowledgeable comments on this.

4. Aug 14, 2011

### CDCraig123

Well if you could find out what the clock says on the voyager spaces crafts said, relative to speed and gravity on the space craft and clocks on earth I bet you would have your answer anyone got a friend at NASA?

5. Aug 14, 2011

### HallsofIvy

Well, actually at $(0.5c+ 0.5c)/(1+ (0.5)^2)= 0.8c$

They don't- none of this is "absolute". Each person sees the other person's clock running slower. A third person, at rest relative to your "arbitrary point", would see the two clocks running at the same speed.

6. Aug 14, 2011

### HallsofIvy

Clocks on satellites and even fast moving jet planes do run slower than on the earth. That has already been verified.

7. Aug 14, 2011

### cmb

OK, so that's how the add up. Thanks,

So, er, do the GPS clocks on the satellites see the clocks running slower on earth, or faster? Maybe I read this wrong, but why this, then:

http://www.metaresearch.org/cosmology/gps-relativity.asp [Broken]

The gravity bit I can see, gravity is what it is at any one point. But the velocity is relative, and if the GPS is running 7,200 ns/day to a ground-based clock watching it because it is moving relative to it, then does the GPS clock 'see' the ground-based clock running faster or slower?

Last edited by a moderator: May 5, 2017
8. Aug 14, 2011

### cmb

Still struggling here. The clock comes back to earth and we find it has lost a few seconds. But if you travelled with the clock, wouldn't the clock on earth (that has been moving relative to you) be the one that's lost the time?

9. Aug 14, 2011

### Staff: Mentor

Are you considering gravitational effects, or just kinematic effects? Both play a role, and near the earth the gravitational effects often dominate and they are often in opposite directions. However, I don't want to go into GR if you are struggling to understand SR.

10. Aug 14, 2011

### cmb

Please see my previous comment. I'm happy with the gravitational issue - according to the article I link to this constitutes 45,900 ns/day. Disregard that, I see that bit.

So now I am talking about the 7,200 ns/day kinematic effect. Which clock runs slower by 7,200 ns/day, the GPS with a guy sitting next to a ground based one, or the ground-based clock as observed by an astronaut floating along with the GPS?

11. Aug 14, 2011

### Staff: Mentor

In which frame? Neglecting the gravitational effects (which can only be done for a very short time), in the ground frame the satellite clock is running slow and in the satellite frame the ground clock is running slow. The satellite frame is not used for GPS navigation in any way, but you certainly could set it up and determine the speed of the ground clocks in that frame.

12. Aug 14, 2011

### cmb

I undertand the question, but there again there is something about that question that makes me hesitate. One clock must be sped up relative to the other so that they stay in sync. I'm finding it tough to fathom that you can slow one OR other, whichever, and still end up with a 'consistent' time frame where both match up.

13. Aug 14, 2011

### Staff: Mentor

Since we are not interested in the gravitational aspect let's not talk about ground and satellite clocks, but just clocks A and B moving inertially in space.

Suppose that A had not just one clock but a whole system of clocks, all synchronized with each other in A's frame. And suppose that B had not just one clock but a whole system of clocks, all synchronized with each other in B's frame.

Now each one says: "My clocks are properly synchronized and running normally, but his clocks are not synchronized and they are running slowly".

Each one also says: "If he wants to make his clock always match the clock that is momentarily next to his then he will have to run his clock faster to counteract the fact that it is running slowly".

Finally, each one says: "If I want to make my clock always match the clock that is momentarily next to mine then I will have to run my clock faster to counteract the fact that his clocks are not synchronized".

14. Aug 14, 2011

### Makep

taking into consideration the directions of the ships relative to each other, we can say that each will be travelling towards the past of the other. this means that:

1. As the ships approach each other, time relative to each other will dilate
2. At the point of passing, time relative to each other will be equal and
3. After passing, time relative to each other will contract

these are always true for relativity. the effect will be the same for two ships with different speeds travelling in the same direction. only this time, the faster ship will be travelling towards the future of the slower ship and the slower laging in the past of the faster ship.

15. Aug 14, 2011

### Staff: Mentor

Makep, almost none of that is correct.

16. Aug 14, 2011

### cmb

I was with you up to the line;

Sorry, I've read it 5 times slowly, and I still don't understand what you are saying here.

17. Aug 14, 2011

### pervect

Staff Emeritus
Have you ever heard of space-time diagrams, cmb? I think they will answer your question.

Here is a space-time diagram for the case where one observer is stationary. The stationary observer concludes that the moving observer is slow, because he uses the green lines to compare his clock to the moving observer.

The moving observer concludes the stationary observer's clock is slow, because she uses the red lines to compare clocks, not the green ones.

This is strange, but not paradoxical. We haven't gotten yet into why the moving obserer uses the green lines, but once you accept that they do, I hope you can see how it resolves the apparent paradox.

We can get into the why of it in another post, or perhaps you have some other questions or issues...

18. Aug 14, 2011

### CDCraig123

Considering I don't no what role gravity plays in time dilation, I thought of a man made object with a clock that would be under the smallest amount of gravity influences. Hence the voyager space crafts.

19. Aug 14, 2011

### cmb

Sorry, I don't understand that diagram. (What are the dots meant to represent, a clock tick? Why are they at different gap lengths on the lines, what is the significance of the angle chosen for the red line? I'd have thought the way to draw it would be dots of equal separation along each path, then the 'observation' line is one that intersects the other path at 90deg, no?)

1) OK, let's deal with the 'real world' example above. So a satellite is launched with clock correction factors of 45,900 ns/day retardation, to counter the gravitational field effect, and 7,200 ns/day advance to account for the kinematic effects. It is launched into space and after 10 years an observer on the ground is still receiving time-stamped messages (inclusive of time-of-flight correction) from it that match the ground-based clocks, because the correct correction factor was fed in at launch. This appears to be what actually happens today, in real life. So, firstly, is my understanding of any of that incorrect?

2) But now for the thought experiment; a satellite is launched tomorrow with an astronaut on board with a life-support capsule sufficient for a 10 year mission, and he stays there for 10 years. He has no audio connection with the ground, he is a space-hermit! Each and every day, as far as he is concerned, he checks the signal from the ground based clock (inclusive of tof correction). He notes that it is losing 14,400ns/day relative to his clock, because the ground based one is running 7,200 ns/day slower, plus his clock has already been set to run 7,200 ns/day faster as well.

3) At the end of his 10 year mission he comes back to earth and says to his flight director "over the 10 years, I observed the ground based clock gradually fall behind mine by 14,400ns/day, and the signal I got from it before I left orbit was 52 milliseconds behind mine" and the flight director says "that's funny, your clock matched ours for all of the 10 years". They compare clocks and find ......???? What do they find? Did the astronaut's clock correct itself during the descent back to earth, or are the clocks at different times?

I presume paragraph 2 is where there must be an error, but I cannot see it? You might argue paragraph 3 but, obviously, we could do the thought experiment for a million years and end up with an hour's difference before he came back down to ground. The act of coming back down surely can't have a 'variable' effect on the astronaut's clock, according to how long he's been up, can it!?

So, my question boils down to: When the astronaut and flight director compared clocks, what did they find?

20. Aug 14, 2011

### Staff: Mentor

Here is a diagram that may help:

Suppose that I am the clock at rest at x=2 (black vertical line). There are a bunch of clocks (white nearly vertical lines) passing by me at .6 c. These clocks are synchronized in their rest frame, but in my frame they are not correctly synchronized. In fact, at t=0 I look and I see that the t'=2 clock reads -1.5, the t'=0 clock reads 0, and the t'=-2 clock reads 1.5. So the closest clock is set behind, the next clock is set OK, and the clock after that is set ahead. If I want to adjust my clock so that it always reads the same as the clock passing me then when the x' clock passes me, my clock reads .66 and his reads -.66, so I set mine back to match his. But then, because I had to set mine back to match the first one, by the time the next clock (x'=0) reaches me my clock reads 2. and this next one reads 2.66. So I have to run my clock faster in order to catch up. The clock after that was set ahead, so I also have to run my clock faster in order to catch up with that one. I have to run my clock fast, not because his clocks are fast, but because they are not synchronized.