1. Mar 19, 2008

### ankitpandey

this question forom a student couldnt be answered by professor in class-
imagine 2 men in two rockets adjuscent to one other.you are one of them. rockets begin to move, say for example, revolve around sun. after few fast revolutions, they stop near each other. now you and the other man meet. both expect the time in their own clocks to be lesser than that in other's. you both compare your wrist watches, and therefore you both now see the same time "together".
WHAT do you think should happen? do you really expect your time to be lesser than his?

2. Mar 19, 2008

### neopolitan

Depends if one is in an orbit or not and then their motion relative to an orbit. You don't provide enough information to provide an answer.

cheers,

neopolitan

3. Mar 19, 2008

### my_wan

What do you mean by stop? The two ships were never in motion relative to each other. No relative motion between them means that wrt each other they were always stopped. No relative motion wrt each other means no relativistic effects wrt each other. Stopping is only more acceleration in the other direction and no different that the acceleration when they started the trip. Stopped in not a definable concept in absolute terms.

4. Mar 19, 2008

### tiny-tim

Hi ankitpandey!

A more interesting example is when they orbit in opposite directions round the earth, so each can genuinely say that the other is moving.

The answer is that an observer on earth will regard both their watches as going slow, but each will regard the other's watch as correct.

There's nothing strange about this, since both are accelerating (their speeds may be constant, but their velocities are changing).

5. Mar 19, 2008

### yuiop

I agree with Tim. If both rockets accelerate in opposite directions and then switch off their engines so that they orbit naturally at the same altitude, then each time they pass each other their clocks will show the same time as each other. Comparing their clock rates to that of an observer on the surface of the Earth is a little difficult, because the surface observer will be deeper in a gravitational well which will cause some time dilation of the surface observer relative to the rockets at higher altitude.

6. Mar 20, 2008

### neopolitan

tiny-tim,

Actually, I think that if they are in natural orbits (not under any acceleration to keep them in orbit), then both would be following a geodesic.

From what I can work out, if their clocks were synchronised on one pass, then the clocks would remain synchronised just as you say. But I think it has more to do with each following a geodesic than their apparent accelerations.

cheers,

neopolitan

7. Mar 20, 2008

### tiny-tim

… gravity is the gradient of positional time dilation …

Hi neopolitan!

Yes, orbits are geodesics.

But time dilation is not zero along a geodesic.

Time dilation depends on velocity and position.

The velocity dependence comes from the Lorentz formula (of special relativity).

The position dependence comes from general relativity.

The gradient of the positional time dilation manifests itself as the "force of gravity", causing an acceleration towards the centre.

For a circular orbit, time dilation will be constant, but it will be different for different radii. For an elliptic orbit, it won't even be constant.

The gradient of positional time dilation will always be towards the centre (or focus), which is the direcction of the gravitational acceleration.

See, for example, the following quote from:
So two spaceships in different orbits have relative time dilation, both due to velocity and to distance from the sun - and these two do not generally cancel.

8. Mar 25, 2008

### ankitpandey

hey.....
thanks for trying to answer, but none werte to the point. i think i didnt frame it properly. let me ask it again...........(takes me time to type)

9. Mar 25, 2008

### ankitpandey

two ships are moving with respect to each other. remove the sun, the earth and everything. now you have an open space, thats all. no orbits. i am a man in one of those rockets, and wish to calculate time in another guys watch, who is in the other. according to relativity, no frame is preffered. so why cant i find time in his clock by knowing his velocity relative to me, which is first away, and then towards, and then using the time diliation formula? when we meet, both of us will expect our time to be lesser than the others, wont we?

Last edited: Mar 25, 2008
10. Mar 25, 2008

### tiny-tim

… nothing to orbit round …

Hi ankitpandey!

You haven't specified how they're moving (it can't be in an orbit (a geodesic), because there's nothing to orbit around)!

At least one of them will have to accelerate and decelerate.

Do you want to specify … ?

11. Mar 25, 2008

### ankitpandey

check this one- i recently found it in a site... it is similiar to my question.... i am not challenging relativity here, i just want to know if there is some point i am missing somewhere...

"Consider two small planets that are moving apart or toward each other at a constant relative velocity, measured by both as being exactly 0.6c. (c represents the speed of light.) There is a baby boy born on each planet, at a moment that we will say is simultaneous, although that is not important here. (We might say that an observer, who is moving at a velocity exactly halfway between their planets' velocities and happened to be exactly equal distance from both planets at that moment, witnessed both births at what he considered the same moment. A critically important factor in this is that the observer was traveling at a velocity that was exactly halfway between.)
When EACH looks at the other, from their own inertial rest-frame, they each have no sensation of motion. Therefore, they see the expected Special Relativity (SR) effect of Time Dilation, due to what they each see as the OTHER planet moving toward or away from them. For this velocity of 0.6c, we can easily calculate that this is a factor of 0.8 regarding time passage. As each grows up, they therefore EACH see the other as aging more slowly (0.8 times as fast) than they age. We are going to momentarily neglect the fact that the two might see each the other as having been born before or after themselves, and ONLY consider the INTERVAL while they constantly watch each other. During an interval when they each live 30 (Earth) years, they each see that the other has only lived 24 (Earth) years!. This is true of BOTH of them! There can be no doubt of this because EACH of them is in a rest-frame coordinate system which is not accelerating, and which each therefore considers to be "stationary", such as we tend to do here on Earth."

12. Mar 25, 2008

### ankitpandey

i have mentioned address of above data below. you might preffer to read it completely before answering. its really long, that web page.

"The Twins Paradox of Relativity is Certainly Wrong!Even High School students learn about the Twins Paradox of Relativity, where a rapidly traveling twin arrives back younger than his twin brother!
mb-soft.com/public2/twinspar.html - 49k - Cached - Similar pages "

13. Mar 25, 2008

### my_wan

You say your ship are "first away then towards". What you need to define to answer this question is which ship accelerated so that the away motion became a toward motion. What needs to be understood is that motion may be relative but acceleration is not, except to degree of how much. Acceleration is not just changing speed in the common way of thinking of it. It occurs when you change the direction of motion. When you slow down relative to something you have simply changed the direction of relative motion toward the reference.

If you are both in ships and you keep speeding away then slowing down then less time will pass for you each time you meet. If you speed away and he speeds up to catch you his time will be what passed slower since you were last together.

14. Mar 25, 2008

### tiny-tim

no paradox … therefore nothing to explain … !

Hi ankitpandey!

Twins paradoxes are pointless unless the twins start and finish together (or keep passing each other).

In the example you quote, they never turn round, so they meet only once.

There's no paradox, and therefore nothing to explain!

15. Mar 25, 2008

### ankitpandey

dear..... um...."my_wan"
you are talking in absolute frame..... relatively, two bodies always have same acceleration with respect to one another. with frame of reference of two different bodies, you can never make out which is moving toward and which moing away, as you have written. if you do so, you voilate the basic postulate of relativity, which states that no frame is to be preffered. these statements voilate relativity-
" Acceleration is not just changing speed in the common way of thinking of it. It occurs when you change the direction of motion. When you slow down relative to something you have simply changed the direction of relative motion toward the reference.

If you are both in ships and you keep speeding away then slowing down then less time will pass for you each time you meet. If you speed away and he speeds up to catch you his time will be what passed slower since you were last together."
'speeds away and he speeds towards you' is undefined in relativity. you are considering some frame stationary here... for example, you are considering their motion relative to earth. relatively, all you must use is that they are moving towards each other. please read my last few messages as well before answering.(cont. in page 2)

Last edited: Mar 25, 2008
16. Mar 25, 2008

### ankitpandey

"Twins paradoxes are pointless unless the twins start and finish together (or keep passing each other).

In the example you quote, they never turn round, so they meet only once."
was that meant to be an answer to my question or the other long one from the web?
well.... they do turn around... when did i, or the other question, say that they dont? they still have a definite velocity, and time diliation should definitely still be applicable the same way as before they turned. they do meet again the same way.

Last edited: Mar 25, 2008
17. Mar 25, 2008

### ankitpandey

"Twins paradoxes are pointless unless the twins start and finish together (or keep passing each other).

In the example you quote, they never turn round, so they meet only once."
wasthat supposed to be answer to my question, or to the long one from the web?
well.... they do turn around... when did i, or that question say that they dont? they still have a definite velocity, and time diliation should definitely still be applicable the same way as before.

18. Mar 25, 2008

### tiny-tim

… accelerating, not just speeding …

erm … "less time will pass for you each time you meet" and "his time will be what passed slower since you were last together" … don't make any sense.
I see what you mean … an observer can't tell whether he is speeding … but this problem is about accelerating away and accelerating towards you, and any observer can tell whether he is accelerating!

19. Mar 25, 2008

### tiny-tim

(btw, if you press "edit" you can delete one of the last two almost identical posts)

You didn't say they did. We're not going to read things in unless they're obvious, and that certainly wasn't!
Yes, but only during steady speed … the acceleration cancels out all the time lost during steady speed!

20. Mar 25, 2008

### ankitpandey

i dont agree. if all the bodies, including the man undergo uniform acceleration, you can define or make out only your acceleration with respect to the other body only. for example, if two bodies of some in space move toward each other due to gravitation, (f=gMm/r)your absolute acceleration be "a" from a non relative frame which was unaffected by gravity. but you will, seeing that body, declare that your acceleration ia more than "a", because it is also moving towards you in the relative frame.