# Looking to understand time dilation

1. Oct 27, 2010

### hprog

Hi, I am learning SR and I need help to get the idea of relativity with two clocks.

Yet I can understand that two different frames of reference can each one claim to be at rest, since this is just a logical argument.
But I am not getting the point how they can each claim the other ones clock is the one who slows down, after all this is physical question and it is like two people arguing whether the earth is flat or round in which case only one can be right.

To show an example of what bothers me, lets say that I and another person have synchronized clocks.
Now when it is 12:00 on both of our clocks this person takes off in a linear motion and will never return.
so when my clock will show 5:00, then if the other person is the one who moves then his clock will show 4:00, and if I am the one who moves then the other person's clock will show 6:00.
So the person's clock can be either 4:00 or 6:00 but not both, yet we don't know what it is, but this is like if we don't know if the earth is flat or not and it is a physical question, and can have only one answer, even if we don't know what the answer is.

It is clear to me that I am missing something, so what is it?

2. Oct 27, 2010

### Staff: Mentor

Hi hprog, welcome to PF!

The key point is the last two words you used. "Synchronized clocks". How do you synchronize two distant clocks that are moving wrt each other, are you familiar with the Einstein synchronization convention?

The reason that they can each say that the other is going slow is that they disagree on the synchronization of distant clocks. So when one says "my clock reads 5:00 at the same time yours reads 4:00" the other says "no, those two events did not happen at the same time".

3. Oct 27, 2010

### hprog

So what does it clock actually read?
In other words if they would meet there would be some value on both clcoks, what is this value?
Also can this also hold true when both are at rest?

4. Oct 27, 2010

### kamenjar

This question has been bogging me down too, so I could use some help too.

It is claimed that relativistic velocities "slow aging". It is my understanding that even when motion is not towards or away (say accelerated orbital path), there this "effect" is still present. If the object in such orbital motion is moving with a clock made on earth it will receive signals from earth at higher frequency than it would generate them. If earth could display a clock it is obvious that it would appear to run faster, where if it could display it, it would appear to be slower.

5. Oct 27, 2010

### Staff: Mentor

Do you see how these two scenarios are different scenarios? In the first scenario after 12:00 both observers can be considered inertial and the situation is completely symmetric. In the second scenario at least one of the observers must accelerate after 12:00 in order to re-unite, they cannot both be inertial and the situation is no longer symmetric. The second scenario is the famous twin-paradox: http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SR/TwinParadox/twin_paradox.html

6. Oct 27, 2010

### Staff: Mentor

7. Oct 27, 2010

### kamenjar

But then why does the wikipedia article on time dilation try to imply that "Time dilation due to relative velocity symmetric between observers"? How can it be symmetric when one clock is simply slowed and the subjects "see" them as such. Or do they not?

8. Oct 27, 2010

### ghwellsjr

Actually, you are jumping to a conclusion when you say only one can be right (what if the earth were a cube?) because we could have any number of other defined reference frames and conclude that both of them are wrong.

If we knew how to determine an absolute rest frame where the speed of light is c in all directions, we could legitimately answer the issue of how to assign times to all events and we could determine the apparent timing rate of all moving clocks. But we can't do that. So we do that next best thing which is to arbitrarily pick any reference frame we want and use that to assign times to all events and use its clocks to define the rate of the passage of time. But we are only allowed to do this for the entire scenario for one frame at at time. It is not legitimate to do this for two frames at the same time and complain about apparent discrepancies. But what is important is that no matter which frame we choose, we will get the same answers for comparing clocks when those clocks are brought together. That's all we can know.

9. Oct 27, 2010

### ghwellsjr

If you pick any one frame and define two clocks in relative motion (one can be stationary and one moving or they can both be moving), and you analyze how each clock ticks and how each clock measures the ticks that are transmitted at the speed of light from the other clock, you will see that each of them will measure the tick rate of the other clock to be going slower than their own. Neither one of them has to be at rest in the reference frame for this to happen. They can both be traveling in opposite directions at the same speed and the effect will be the same.

10. Oct 27, 2010

### HallsofIvy

Staff Emeritus
What do you mean by "actually read"? You seem to be asserting that there is some "correct value". If you really are then you are denying that relativity is true and there is no point in continuing this! (And there is pretty strong experimental evidence in favor of relativity.)

What, exactly, do you mean by "meet"? If you mean "are close enough together to read each others clocks, after having, at some point in the past, sychronized their clocks", but still moving relative to one another, the each would observe the others clock as running slower than his own.

Special relativity talks about the situation when two frames of reference are in motion, relative to one another, at a constant speed. That means that this question as to be dealt with in two separate parts:

a) The "constant speed" is 0. The two frames of reference were at rest relative to one another when the clocks were synchronized and still are. The two observer's will observe both clocks to still be reading the same time.

b) At least one of the frames of reference was in motion relative to the other at the time the clocks were synchronized and has since been accelerated (or decelerated) to match the other's speed. In that case, "all bets are off"- you have now moved outside of special relativity.

Last edited: Dec 7, 2010
11. Oct 27, 2010

### Staff: Mentor

The case of uniform circular motion, e.g. in a muon storage ring, is not symmetric. One observer will measure centrifugal and Coriolis forces in their reference frame and the other will not.

This is a very important point. Inertial motion is relative, accelerated motion is not. Do you understand what an inertial reference frame is?

12. Oct 28, 2010

### granpa

time dilation and length contraction are easy.
its relativity of simultaneity (google it) that confuse all beginners.

13. Oct 28, 2010

### kamenjar

Maybe your pulses at "clock rate" and "the clock" is not the same thing.
A clock is a big fat blueshifted earth doing 5 revolutions around the sun for every second of my clock and a big bluieshifted lightshow above it UTC display spinning days like nuts while I fly by it (or even perpendicularly far away) at .9999 light speed -- and my nice redshifted light show display and showing "barely moving" while you are looking at it when I am redshifted "frozen in time"? What part of clocks appearing to be slowed don't I understand? Is this, rather colorful, statement wrong?

Simplified/Edited:
I understand that while looking at slow moving (static/earth) objects, and moving near light speed, those objects age faster.
I understand that while looking at fast moving objects, subjects in a slow moving (static/earth) reference frames observe those faster objects to be "slowed".
I understand that if I was inside a fast moving ship, and I wave to an "earthling" though a window of a that ship, the earthling would see my hand move slow.
I understand that if I was inside a fast moving ship, and an "earthling" waves to me, his waving would appear to be fast.
One of the ways to observe the aging is to observe earth rotations.
I understand that while I am in a fast moving spaceship, earth performs X rotations around the sun while I blink.
For the above cases, assume that the motion is perpendicular to the line of sight to avoid the effects of speed of propagation of light. Imagine me looking at the "earthling" thru the side window.

Which of these statements are wrong?
Am I thinking in terms of "thermodynamic time"?
Am I thinking in terms of "mechanical clocks"?

I belive there is some discrepancy in thinking and it could be related to atomic clock time vs two kinds of clocks mentioned above.

Last edited: Oct 28, 2010
14. Oct 28, 2010

### ghwellsjr

OK, so I forgot to mention that the two clock have to be identical. Com'on now, can't anything be obvious?

I can't tell if your statement is wrong because it is so full of typos and grammar errors (or whatever) I can't figure out what you are asking about. When you read it, does it confuse you? Why don't you edit it so it makes sense and then I will tell you if it is wrong.

15. Oct 28, 2010

### Hellabyte

I believe the misunderstanding you have is from your assumption that when the first clock shows 4:00, you can somehow instantly know what the other guys clock will read. When you look out into space when your clock reads 4:00, the light from when his clock was 5:00 will now be reaching you. His clock must actually be at some later time (Such as 6:00) when this "5:00" light reaches you. It's like looking out at the stars and realizing that we are seeing very old images of them. Those stars could actually have burnt out in exactly the same way that the moving guys clock could actually be at 6:00 when we see the light from when his clock was at 5:00. Also, when his clock reads 6:00 or whatever the light from when your clock read 4:00 will just be reaching him. Please correct me if my understanding is wrong. I am trying to learn this stuff too.

16. Oct 28, 2010

### ghwellsjr

It's not just that it takes time for information to travel to you from a distant clock and so there is a sense in which the information is old but in addition the traveling clock will appear to be ticking at a slower rate. Consider a clock that is traveling toward you at a very high speed. Let's envision a clock that flashes a bright light once a second. As it is moving toward you, you will see the flashed more often than once per second but as you take into account the time it takes for those flashes to get to you, the actual tick rate will be less than once per second. Then as the clock suddenly passes by you and starts moving away from you, the flashes will be less than once per second, but again, when you take into account the travel time, you will conclude that the clock is ticking more slowly by the same amount as when it was traveling toward you. So the moving clock is ticking at a slower rate than your stationary clock. This means that if while your clock read 4:00 his clock read 5:00, then later when your clock reads 5:00 his clock will not be up to 6:00 yet, it will be running slower.

17. Oct 28, 2010

### kamenjar

I feel that I am hijacking the thread so I should post a separate thread...I do understand the effect of approaching and "leaving". I do understand the perception of relative speeds for moving objects. For that purpose I will try to come up with an example where these "effects" will be minimal.

18. Oct 28, 2010

### jbar18

First of all, I'm new to these forums as well. So I don't have much experience answering these questions, but I'm pretty sure I'm right here, and I think I understand what you are getting confused about. It seems you are wondering about how both people can see the other person with a slower clock, instead of one person having a slower clock and the other having a faster clock.

The way I think about it is to imagine that you are in space, with your clock, and your friend has their clock some distance away from you. Apart from you two with your clocks, there is literally nothing else around. It might also help if you think of the actual rate of ticking, instead of the actual time shown on the clocks.

So let's pretend that you are passing each other, neither of you know which of you is actually moving. You could both be moving a fraction of the total speed, or one of you could be moving the whole speed and the other could be stationary. You will both agree on the total speed. You've said that you understand that in your question.

Well I think that's your answer - if you pass each other with a given velocity v, you could each argue that you are stationary, which means that you are both arguing that the other person is doing all of the moving. So if you were to pass your friend, you would see him moving at speed v, and his clock would be ticking 1/1-(v^2/c^2) times slower. But then, he also observes you moving at this speed v (since both of you appear stationary to yourselves) and so he would also see your clock ticking 1/1-(v^2/c^2) times slower. You both observe each other's clocks moving slower because as far as you are concerned, you are never moving, everything else is.

Last edited: Oct 28, 2010
19. Oct 28, 2010

### Staff: Mentor

hprog, are you comfortable with the concept now or are you still confused?

20. Oct 28, 2010

### Grimble

You have the explanation in a nut shell there.

And if you take it a step further, with each person slowing an equal amount with respect to the other (to get rid of any arguments about the acceleration) then when they have slowed to be at rest with one another their relative velocity will be zero and their clocks slowing, as shewn by your formula above, will also be zero.

The clocks slowing is due to the relative speeds.
Neither clock will appear to be slowed by the person adjacent to that clock.
So does either clock actually slow, or is the slowing merely an effect of measuring a moving object?