# Asking a simple question about twins paradox

1. Jan 5, 2006

### dreamsfly

imagine that two spaceships are far away from each other,both at rest,then one of them accelerate to nearly C towards the other,assume that after the accelerating process,their clocks are just the same,when their distance is almost 0(no decelerating),they change the infermation,then what will happen?who will be older?

2. Jan 5, 2006

### dicerandom

I'm not quite sure what you're getting at here, when you say that the twins clocks are both zero after the accelerating process do you mean that they are the same age then? Also, whose reference frame would the event of both clocks reading zero be measured in? If the twins are traveling relative to one another and are seperated by a distance and one of them measures the clocks both reading 0 at the same time the other twin will not agree that those events occured at the same time.

3. Jan 5, 2006

### dreamsfly

Thank you for your answer,dicerandom!
I mean that after the accelerating process their age and time are right the same,maybe they don't know,but it's the fact.And when they get closer,not deccelerating.Because in the stage of even velocity,they will both consider the other is older than himself,then when they get near enough and change their infermation,what will happen.what I mean is just to eliminate the effection of accelerating

4. Jan 5, 2006

### pervect

Staff Emeritus
The problem is that simultaneity is relative, as dicerandom tried to explain.

See for instance http://www.bartleby.com/173/9.html which quotes Einstein.

The above link contains a more detailed explanation of this remark, along with the necessary background and some diagrams which explan in detail the ideas of the "train" frame of reference and the "embakment" frame of reference.

5. Jan 5, 2006

### HallsofIvy

Staff Emeritus
There's your difficulty. No, it's not a fact. "age and time" are not fixed quantities- they depend upon the frame of reference in which they are measured. Since the "twins" are not right next to each other to begin with they have no way of comparing their ages that does not bring "simultaneity" problems into play. It makes no sense to ask which is older when they do pass by one another since there is no way of getting a definite answer to that question before.

6. Jan 5, 2006

### dicerandom

You can certainly ask which is older, for instance they could each have a window in their rocket ship and simply hold up a sign. The problem is just that, with the way dreamsfly set the situation up, which is older depends on which frame both clocks reading zero was observed in.

You can lay down a definite answer, though. If, for instance, both their clocks started at 0 while they were in the same refrence frame directly before the one rocket started accelerating it would be the accelerating twin who was younger when they passed.

7. Jan 6, 2006

### Jimmy Snyder

Almost, but no cigar. You are right about one thing. All observers agree on events. That is, when the two space ships meet in time and space, all observers agree that they do and if the travellers hold signs with their ages in the window, all observers will agree upon what the signs say. But the information on the signs will not be comparable. This is because each sign contains a person's age, that is, the difference in time between two events. While the final events are the same for the two ships, the initial events are not and so there is disagreement on whether the initial events are simultaneous.

Last edited: Jan 6, 2006
8. Jan 6, 2006

### dicerandom

jimmy:

I don't agree that the information on the signs will not be comparable, but I think that we're saying the same thing nonetheless. Both signs will display the ammount of proper time which has passed for each observer since some agreed upon zero time, say a birthday, it's just that one observer will think that these events happened simultaneously whereas the other will not. That doesn't make the information written on the signs (i.e. "hi, here's how old I am") any less meaningful though.

9. Jan 16, 2006

### SteyrerBrain

What, if the setting is changed a little: both clocks are at the beginning at the same place. One clock stays at rest (in an inertial frame without forces), the other clock travels on a circle with radius r and constant tangential speed v. Seen from the inertial frame of the first clock, the second clock returns after every 2*r*pi/v time. Can one talk about simultaneity, every time the clocks meet? If yes, how much does the second clock stay back behind the first between each return? A simple exercise in general relativity?

thank you,

Wolfgang

10. Jan 16, 2006

### JesseM

SR can analyze accelerated motion from the point of view of an inertial reference frame--if a clock's speed as a function of time in your inertial frame is v(t), then the time elapsed on the clock between two times $$t_0$$ and $$t_1$$ in that frame will be $$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt$$. For the case of circular motion, the speed is constant, so each time the clock returns to its starting point it will have elapsed $$\sqrt{1 - v^2/c^2}$$ times the amount of time it took to travel the complete circle as seen in the inertial frame of the other clock that it repeatedly returns to. So if this time is 2*r*pi/v as seen in the inertial clock's frame, the clock travelling in the circle will only have elapsed $$(2 \pi r / v) \sqrt{1 - v^2/c^2}$$.

11. Jan 16, 2006

### SteyrerBrain

Thank you for your answer. I thought I might be wrong about simultaneity in that "experiment" and I was not aware of the fact that already SR can compute the time dilatation for accelerated motion.

Can the calculation for time dilatation in this setting also be done (rather easily) in the second clock's reference frame? This should now only be solveable with GR, I guess? Somehow the radial acceleration of v^2/r must know come into play?

thank you,

Wolfgang

12. Jan 16, 2006

### pervect

Staff Emeritus
As far as simultaneity from the rotating particles POV goes, there are indeed concerns. Consider the related case of the relativistic rotating disk.

http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html

Another paper worth reading is http://arxiv.org/abs/gr-qc/9805089

There is a lot (a whole lot) of literature on the relativistic rotating disk, including at least one whole book

http://www.amazon.com/gp/product/14...002-8393802-4805656?n=507846&s=books&v=glance

(if you look at the price you'll see why I dont' own it :-). Other people must feel similarly,as there are no reviews.)

While everyone agrees on the results of measurements (when the process of measurement is defined exactly enough), the philosophical interpretation and choice of measurement methods (i.e. coordinate systems) tends to vary widely, often leading to a lot of confusion :-(. I find the philosophical POV in the sci.physics FAQ and the Tartaglia paper I cited above to be the simlest and clearest.

Someone interested in a long argument can probably look up some of the long arguments we've had on the board here in the past on the topic (look for rotating disk).

13. Jan 17, 2006

### SteyrerBrain

I see the relation of the rotating disk to the above described setting (one clock resting, the second clock moving on a circle), but isn't the setting with the two clocks *much* simpler? Therefore I would expect that a computation in the reference frame of the second clock moving on a circle is rather simple!? Ofcourse the clocks should be assumed mass-less, etc. Shouldn't it be possible to set out with the equivalence principle? I'll try to work this out myself. Hints are welcome.

Wolfgang

14. Jan 17, 2006

### JesseM

For an object moving inertially in flat spacetime, there is a single standard way to define a coordinate system that qualifies as "the reference frame" of that object. But for a non-inertial object, I'm not sure this is true--there might be multiple possible ways to define a global coordinate system where the object is at rest at all times, with no standard procedure for choosing which should be termed "the object's reference frame". And these different coordinate systems could have different definitions of simultaneity.

15. Jan 17, 2006

### pervect

Staff Emeritus
Well, you might try starting out with the arbitrarily accelrated observer, MTW pg 170.

The arguments which suggest that this coordinate system is going to be strictly limited in size for self consistency should still apply, though, making "the" coordinate system not generally applicalble for arbitrarily distant objects.

There will also be some interesting issues arising from Thomas precession of your basis vectors, I think.

16. Jan 19, 2006

### SteyrerBrain

I guess I understand too little about GR to see the reason for different coordinate systems for a non-inertial object. It can't be the directions of the coordinate axes - these are also not uniquely determined in an inertial frame. Can you give me a hint, where the problem arises?

But still: since the clocks periodically meet at one point (always the starting point), all computations - even based on different coordinate systems - should agree on the time offset between the clocks at this meeting point!? Different definitions of simultaneity can only occur for objects/events, that are apart (as far as I understand).

Wolfgang

17. Jan 19, 2006

### SteyrerBrain

I guess I need some insider-background-info:
* What does POV mean?
* MTW references a book?

Concerning "limited coordinate system" and "Thomas precession": I see that the seamingly easy problem might turn out a lot harder than expected. (And I must admit that I am not familiar with these terms.) I will still try to start out with the equivalence principle.

Wolfgang

18. Jan 19, 2006

### JesseM

I don't understand much about GR either, but as I understand it GR does allow you to use any coordinate system you can dream up, and intuitively it's not hard to see some problems with defining the coordinate system of an accelerating observer--for example, how do you want simultaneity to work at each point during the acceleration? At each moment along the object's worldline, should its definition of simultaneity match that of the inertial frame where it's at rest at that moment? If you try to do it this way, you can have problems with planes of simultaneity at different points along the wordline intersecting each other, so that the same event is sometimes assigned multiple time coordinates, and distant clocks can run backwards as coordinate time runs forwards. For instance, suppose I am approaching the earth at high velocity and then when I get within a certain distance I accelerate rapidly until I am moving away from the earth at high velocity; if you draw the planes of simultaneity for my instantaneous inertial rest frame shortly before and after I accelerate, you may find that the date on earth before I accelerate is actually later than the date on earth after I accelerate, according to the definition of simultaneity in my instantaneous inertial rest frame at each moment.

And how can your coordinate system be defined physically? For an inertial observer, you can define the coordinates of different events in terms of local readings on a network of rulers and clocks which are at rest relative to the observer, and which are synchronized according to the Einstein convention (assume the speed of light is constant in your own rest frame, so that if you turn on a light at the midpoint of two clocks, they should both read the same time when the light hits them). In this situation, all other inertial frames will agree that the rulers and clocks have the same (constant) velocity as the observer at every moment. But for an accelerating observer, if he has his own network of accelerating rulers and clocks I don't think it's possible that all inertial frames would see the rulers and clocks having the same velocity as the observer at all moments, which would also mean that all inertial frames would not see all the clocks ticking at the same rate or all the rulers being the same length at a given moment. Given this, there doesn't seem to be any one "natural" way of having the rulers and clocks accelerate, since if there is one frame where all the rulers and clocks are matching the observer's velocity at each moment, this won't be true in other frames, and there's no reason to set it up so this happens in one frame as opposed to another (again, I guess you could try to set it up so that in the instantaneous inertial rest frame of the accelerating observer, all the rulers and clocks were at rest as well, but past a certain distance this might not work because it would require rulers and clocks to move in impossible ways like going backwards in time or faster than light).
Yes, that's definitely true, as long as you are using the correct laws of physics in each coordinate system (you can't assume that the usual rules of SR will work in a non-inertial coordinate system). Like I said, my understanding is that the rules of GR work in any arbitrary coordinate system, although for each new coordinate system I'm guessing you have to first find the correct form of the metric when expressed in that system.

Last edited: Jan 19, 2006
19. Jan 30, 2006

### pervect

Staff Emeritus
Somehow I missed this

MTW is Misner, Thorne, & Wheeler's book titled "Gravitation".

See also this post of mine:

https://www.physicsforums.com/showpost.php?p=887032&postcount=91

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