# Time dilation

1. Jan 29, 2013

### Ezio3.1415

Two person have a relative velocity... Each one see other ones time slowing down... We know both will die at the age of 70... Each one will see that the other one is alive when he dies???How?

2. Jan 29, 2013

### oli4

Hi EzioPi
There is no need for time dilation for this to be true
It is enough if the two people looking at each other are far enough.
Just look at the sky and you are looking at bright stars that died a long time ago, no relative velocity, no time dilation necessary to explain it.
So if two observers are far enough from each other, since it takes time for light to go from one to the other, suppose they are 10 light years away.
When one observer is about to die at age 70, the only last image he can have from the other one is 10 years before, so he can only see him as he was when 60. And of course the same thing is true for the other observer
Now time dilation does happen too for relative velocities but the 'problems' or apparent paradoxes are different

3. Jan 29, 2013

### Ezio3.1415

What confuses me is that every person sees the others clock slowing down... The question arises whose clock slows down actually... My equation says both persons are right but I am not able to graspe actually what is happening...

Last edited: Jan 29, 2013
4. Jan 29, 2013

### HallsofIvy

You have not understood oli4's response. Yes, each will die, in his frame of reference, before the other person. There is nothing at all "paradoxical" about that, any more than a person watching another person one light year away will die one year before he could see the other person die. (I started to say "before he sees the other person die" then realized if he is already dead, he can't see it!)

5. Jan 29, 2013

### ghwellsjr

Your question can be interpreted in a lot of different ways and so can have a lot of different answers.

For example, you probably meant that they started off together at the same age and then one or both accelerated to create a relative velocity and then when they look at each other, they each see the other progressing in age more slowly than them self, and so on their deathbed at the age of 70, they see the other one still walking around and in good health. In fact, each one will see the other one younger by exactly the same amount. We can conclude this strictly from the Principle of Relativity, Einstein's first postulate. That says, among other things, that in a symmetrical scenario, what each person sees of the other one will be affected in the same way.

So if this is the way in which you meant for your scenario to be interpreted, then you can analyze it using the Relativistic Doppler formula. You take their relative velocity as a fraction of the speed of light which we call beta and represent with the Greek letter β and you plug it into this formula:

√((1-β)/(1+β))

This will give you a number less than one. Then you take whatever time each person has aged during the scenario and multiply it by that number and that tells you how much they see the other one to have aged.

Can you do that?

Now if you meant to describe a different scenario, then please fill in more details.

6. Jan 29, 2013

### Ezio3.1415

Yeah ghwellsjr I meant this scenerio... Why else post in the relativity section... :p
But ur equation also says that everyone ages less than the other in the other frame...
My ques is why I get this... what is the thing that decides who will age less?

7. Jan 29, 2013

### Ezio3.1415

or is invoking this question brings a third frame? What's the prob with that?

8. Jan 29, 2013

### Staff: Mentor

In this scenario, no such decision is needed/can exist. If the paths are symmetrical, they are symmetrical. Either can be older/younger depending on what reference the question is asked from.

In this scenario, the difference in "aging" does not need to involve time dilation: it can simply be a perception based on signal delay.

9. Jan 29, 2013

### Ezio3.1415

Time dilation does not depend on anything such as signal delay... I don't understand what u said...
Just to clear my ques,forget abt the example... What bothers me is that both think the others time is slowing down at a same rate... I can't grasp this part of time dilation... What governs the thing that whose clock is going to show less time...

10. Jan 29, 2013

### Staff: Mentor

Again: there isn't necessarily any time dilation here.

You are asking a question that you think is about time dilation, but it isn't. You can replace the light signals with sound signals and it works pretty much the same way.

Cases involving a resolved time dilation where one "twin" really is older than the other require them to come back together in a non-symmetrical way. The particulars of the asymmetry (which twin did more accelerating) determines which twin is younger when they are brought back together.

11. Jan 29, 2013

### phinds

What you are missing is that you think there is an ABSOLUTE answer. That is, you think it is REALLY the case that either one or the other of them died first or that they died at exactly the same time. As has already been point out, this is not the case. Neither of those thing is the case. In order for there to be an absolute answer like that, you have to have an absolute frame of reference and there is no such thing.

12. Jan 29, 2013

### Ezio3.1415

Yeah relativity of simultaneity explains this...
Thank you guys...

13. Jan 29, 2013

### robphy

If this problem is truly about time-dilation,
then it's best NOT to use the word SEE (or anything suggesting a signal).
That invokes Doppler and signal-propagation time... (Lightlike related events between the death and SEEING/LEARNING of the death.)

What you probably mean is that:

"when you die 70 years later", according to you, "your traveling friend has not yet aged 70 more years (say she only aged 50)"
or
more precisely, assuming your both start off at the same age of zero,
the event D (your death here at age 70) is simultaneous-according-to-you with event F (when she is there at age 50).

In addition, event G (when she dies there at age 70) is simultaneous-according-to-her with event C (when you are here at age 50).

(Here the events are spacelike-related.)
That's the symmetry between the observers for time-dilation.

Here's a spacetime diagram explanation of the situation.

... but first a Euclidean analogue.
Take a circle (points equidistant from a common point) and draw two radii.
At the tip of each radius, construct its tangent line to the circle.
Each tangent meets the other radial direction beyond the circle.

Now for the Spacetime diagram explanation....
Take a hyperbola (events equal intervals in time from a common meeting event).
Imagine a field of runners with a wristwatch... running from a given starting event with all possible velocities in the x-direction. Ask each runner to mark with firecracker when his watch reads 1 sec. On a position-vs-time graph, you get a hyperbola [in special relativity]... (but a vertical line in Galilean relativity). Let say you do this again when your watches read 70 years, to obtain a similar larger hyperbola.

Draw two radii (These represent each of your worldlines corresponding to equal elapsed times according the respective wristwatches.) to the hyperbola.
At the tip of each radius, construct the tangent line to this hyperbola (the analogue of the circle in spacetime).
Note that each tangent meets the other radial direction before the hyperbola.
Each tangent represents events simultaneous with the tip of its radii according to that observer.
In other words, when you reach your 70th birthday on your worldline, the event on your friend's worldline that you say is simultaneous with your 70th birthday is her 50th birthday.
...and she will say the same thing about your 50th birthday on your worldline being simultaneous with her 70th birthday on her worldline.

As I mentioned earlier, if we did this experiment in Galilean physics, we would get a vertical line [as we might expect] of "my watch reads 1 sec" events. More accurately, we have not-so-precise clocks and we travel at not so large speeds that we extrapolate our limited experiment to a vertical line. If we proceed to draw the tangents to this "circle" [the vertical line], we would see that our sets of events simultaneous with our 70th birthdays coincide. This is absolute simultaneity in ordinary Galilean physics.

Does that help?

14. Jan 29, 2013

### Ezio3.1415

Thank you... I am gonna learn drawing space time diagram... Should have before...