[neilep (OP)]

A lot of seasoned scientists and academic nice peeps know this.

Where you have the case of the twins and one of them buggers off in a space craft at nearly the speed of light and then returns back at some time to find that he (or she) is younger than the twin left at home !

What I want to know is .....exactly how long did the space bound twin go away for then ?

Say the space-bound twin goes away for five years......comes back but is only two years younger than his brother....was he away for five years or two years ?

Is it both ?

Do I need to ingest more fish oils ?

[Soul Surfer]

The answer of course is that both the percieved times for each of the twins are valid  That is 5 years for the traveller and seven years for the one who stayed at home according to your requirement that their age difference is now two years.

The differences in percieved time between the twins are valid but how do you know that one is older than the other unless the difference is a very long time. 

[neilep (OP)]

Yes ..yes of course !!..THANK YOU Ian........

Aren't there ways to detect differences in age at the atomic scale or something ?....or....ahh !!...they would both be in possession of atomic clocks !! ?

[DoctorBeaver]

One's beard would be longer!  []

[neilep (OP)]

One's beard would be longer!  []

LOL......even if they are girlies ?...oooooooooooh !!!..LOL

[syhprum]

The most noticeable effect is upon the Mesons that are created when cosmic rays hit the upper atmosphere, these would normally decay before they reach the ground but when they are created with high energy they travel closer to the speed of light and have an extended life time and reach the ground.

[lightarrow]

A lot of seasoned scientists and academic nice peeps know this.
Where you have the case of the twins and one of them buggers off in a space craft at nearly the speed of light and then returns back at some time to find that he (or she) is younger than the twin left at home !
What I want to know is .....exactly how long did the space bound twin go away for then ?
Say the space-bound twin goes away for five years......comes back but is only two years younger than his brother....was he away for five years or two years ?
Is it both ?

Five years of his time or of the Earth's time?
If it's Earth's time, then the max age difference is 5 years (5 y. on earth - 0 y. on the astronaut's time).
If it's his time, then the max age difference is ∞ (∞ - 5 = ∞).

[Atomic-S]

Things get interestinger when you have triplets, one stays on the ground, one goes off in a spacecraft to the celestial north, the other off to the celestial south, and both later return. What are their relative ages, and why?

[lightarrow]

Things get interestinger when you have triplets, one stays on the ground, one goes off in a spacecraft to the celestial north, the other off to the celestial south, and both later return. What are their relative ages, and why?

I'm not very good in astronomy. How does our solar system move with respect celestial north?
If it moved towards celestial north, then the astronaut moving 1 light year (for example) towards celestial north, will come back home (on earth) before the astronaut moving 1 l.y. towards celestial south, since the solar system would have approached him meanwhile. (I suppose). Is this correct?

[Atomic-S]

Well, with respect to what is the distance being measured?

[lightarrow]

Well, with respect to what is the distance being measured?

I'm not an astronomer. If your question couldn't be answered easily, I imagine it would be difficult to establish stars distances too.

[lyner]

The twins' paradox states that, because all motion is relative, each twin will see the other as traveling at the same speed and, yet, each twin will see his brother as being younger than himself when they get back together again.  There is an implied symmetry in their two situations.
In fact, there is no real paradox involved, or at least, it is easily resolved.
For the twins to see each other again after all those years, at least one of them has to get back with his brother. This will involve acceleration -i.e.  slowing down and then traveling   back to the other twin - more speeding up and slowing down. The conditions for special relativity no longer apply as  this is no longer an inertial frame (constant velocity with no acceleration or gravitational field), so, if one has been stationary or in an inertial frame and the other has been speeding up and slowing down, GENERAL relativity comes into play for one of them, so they will have had experienced  different relativistic effects and one will appear older than the other.   Time slows down  under conditions of acceleration or a gravitational field.
The one who did the return journey will appear, to BOTH of them, to be the younger one.
If they both go away and come back, they will look the same age.
  No paradox.
You can see this effect in the 'flying clock' experiment, which has been done a number of times; Two identical Caesium clocks were synchronised then one of them was taken on a long supersonic flight. - involving acceleration.  When it returned it was  showing a measurably earlier time (i.e. it had been running slower).

[lightarrow]

In fact, there is no real paradox involved, or at least, it is easily resolved.
For the twins to see each other again after all those years, at least one of them has to get back with his brother. This will involve acceleration -i.e.  slowing down and then traveling   back to the other twin - more speeding up and slowing down. The conditions for special relativity no longer apply as  this is no longer an inertial frame (constant velocity with no acceleration or gravitational field), so, if one has been stationary or in an inertial frame and the other has been speeding up and slowing down, GENERAL relativity comes into play for one of them, so they will have had experienced  different relativistic effects and one will appear older than the other.   Time slows down  under conditions of acceleration or a gravitational field.
The one who did the return journey will appear, to BOTH of them, to be the younger one.
If they both go away and come back, they will look the same age.

Sorry to contradict your quite good analysis, sophie, but there is no need of General Relativity to solve the paradox: the asymmetry can be understood and calculated precisely even with SR, for example using space-time diagrams. I cannot actually say to have completely understood the subject, but I'm pretty sure of this, because I have read threads on other forums about it.

I myself proposed a different (but equivalent) way of solving the paradox, simply noticing that the two twins measure different distances of the travel: if the twin on earth sees 4 light years as distance from earth to Proxima Centaury, the travelling twin sees less, because of Lorentz contraction. It's possible to show how the difference in time travels can be seen as coming from this fact only.

Actually (even if it's not obvious at all, even for me) they say the acceleration-deceleration of the starship can last so little time that, even if it's very large in intensity, its effects on the time differences becomes negligible.

[lyner]

Surely their must be a paradox if you look at the problem from the point of view of each twin in turn and only consider SR.
Treat one twin (A) as 'stationary' and he will see his returning brother (B) (the one who did all the traveling) as younger.
Now treat the other one (B) as 'stationary'. He will see his brother (A) as the one who did the traveling and, so, will see  A as younger.
Neither of the twins is 'actually stationary' it is all relative.
That is the paradox (the fact that each twin will see the same effect - which is impossible; they can't BOTH be younger than the other one).
The only difference in the two situations, above, is that only A, in the first case and B in the second case are in inertial frames. The other twin is in a non inertial frame and, therefore, can't be subject to simple SR calculations.
The reality will be that the non-inertial twin, in each case, will  age slower    and appear younger.
It's only if you insist on SR calculations for both twins under both circumstances that the paradox is unresolved.

Actually (even if it's not obvious at all, even for me) they say the acceleration-deceleration of the starship can last so little time that, even if it's very large in intensity, its effects on the time differences becomes negligible.

I must say, this statement seems reasonable and I don't have an answer (with sums) to counter it. The only thing I can say is that, without introducing the ideas of non-inertial behavior, you still have your paradox and that needs resolving. I seem to remember that the argument (which I am only repeating from memory) goes that the GR effects are 'just enough' to explain the effect.
I will try to look out my original source when I have time.
Perhaps someone else can resolve our problem?

[lightarrow]

Surely their must be a paradox if you look at the problem from the point of view of each twin in turn and only consider SR.
Treat one twin (A) as 'stationary' and he will see his returning brother (B) (the one who did all the traveling) as younger.
Now treat the other one (B) as 'stationary'. He will see his brother (A) as the one who did the traveling and, so, will see  A as younger.

Not exactly. If you make the calculation you notice than twin B (the one in the starship) doesn't see A as younger, but older. The paradox comes from the *idea* that B should see A as younger (as well); but it's not, actually, just because B comes back.

Neither of the twins is 'actually stationary' it is all relative.
That is the paradox.
The only difference in the two situations, above, is that only A, in the first case and B in the second case are in inertial frames. The other twin is in a non inertial frame and, therefore, can't be subject to simple SR calculations.

It's true, as I said too, that the paradox comes from the fact they are not in inertial ref. frame one respect to the other, but GR is not necessary to solve the paradox. They are two different things.

Let's say A is on earth and B goes to Proxima Centaury (P.C.) at 4 light yars (l.y.) of distance (as measured from earth). B goes at an average speed of 0.8c and comes back.
The following computation can be done by *both* A and B:

In A ref. frame, earth-P.C. distance is S = 4 l.y., but in B ref. frame, earth-P.C. distance is 4*√(1 - 0.8²) = 4*√(1 - 0.64) = 4*√0.36 = 4*0.6 = 2.4 l.y. because of Lorentz contraction.

Time that A have to wait for the entire B journey: S/V = (4 + 4)l.y./0.8c = 10 years.
Time that B have to wait for his journey: S'/V = (2.4 + 2.4)l.y./0.8c = 6 years.
End of paradox.

[lyner]

It's true, as I said too, that the paradox comes from the fact they are not in inertial ref. frame one respect to the other, but GR is not necessary to solve the paradox. They are two different things.

But, as you say here - they are not both in inertial frames so you can't just use SR. The basis of SR is inertial frames so you can't go any further in any argument using SR, alone. (Surely?)

[lyner]

The only way there would be no paradox would be if there were NO apparent different in the ages of the twins when they got together again.
This seems to be our main issue.
In your thought experiment, the twins  can both see that one has gone  faster than the other because one will arrive first  (to punch the time clock, put there by another person, at the other end) - one of them will expect to age differently than the other and, as you say, there would be no paradox here.
The paradox arises when they both end up at the same place and the same time (from a third observer's point of view).
We know that (have measured, in fact, that) there is a difference (even if only using atomic clocks and supersonic speeds). This time difference is easily observed and affects the non - inertial twin / clock.

 After some more thought:

Actually (even if it's not obvious at all, even for me) they say the acceleration-deceleration of the starship can last so little time that, even if it's very large in intensity, its effects on the time differences becomes negligible.

To accelerate to significant speeds would actually take considerable time and the  energy involved to account for the relativistic mass increase (ΔΕ= Δm csquared is relevant)  would be non-negligible  and there is plenty of scope for the 'time factor' to be distorted a significant amount, too.
The Mossbauer effect, for example, relies on very  narrow resonances  in  metal atoms and  detects time dilation  by using the effect on the absorption  of RF waves by tightly bound atoms. It is sufficiently sensitive to detect the difference in gravitational field  (an acceleration) on the rate time progresses  between two different floors in a laboratory building.  So it is quite easy to disturb time  a measurable amount in non-inertial frames.

[socratus]

“Twin paradox” and  “ twins brothers”.
Einstein's Special Relativity Theory / Twin paradox
(time  travel with speed c=1 )
does not have any relation to a astronaut.
Special Relativity Theory only examines the behaviour
of a quantum of light / electron.
Twin Paradox (time travel ) has relation only to
a light quantum / electron.
SRT/ Twin Paradox has grown from Maxwell's theory.
And only an electron/ quantum of light is a main
and single hero in the Maxwell's theory and SRT.
=========== 
http://www.socratus.com

[lightarrow]

The only way there would be no paradox would be if there were NO apparent different in the ages of the twins when they got together again.
This seems to be our main issue.
In your thought experiment, the twins  can both see that one has gone  faster than the other because one will arrive first  (to punch the time clock, put there by another person, at the other end) - one of them will expect to age differently than the other and, as you say, there would be no paradox here.

I'm not sure to have understood what you want to say. Anyway, the experiment is very simple. The first event is: the twins say goodbye to each other, and a green lamp flashes (for example). The second event: they hug together at the end of the journey and a blu lamp flashes. Then they look better at each other and discover (also testified by their whatches) that B is 4 years younger than A. What does "one will arrive first" mean?

The paradox arises when they both end up at the same place and the same time (from a third observer's point of view).

A has never moved from earth, how could they have ended up in a different place?
In relativity we have to specify events, not simply places and times. An event is a space-time 4-vector: (ct,x,y,z). The utility is that the space-time interval between two events is invariant, that is, doesn't change from a ref. frame to another. The interval ds is defined in this way:
ds² = (ct)² - (dx²+dy²+dz²).
So, the total interval Δs between two events is:
Δs = ∫ds = ∫Sqrt[(ct)² - (dx²+dy²+dz²)]
and this (scalar) quantity Δs is invariant.

After some more thought:

Actually (even if it's not obvious at all, even for me) they say the acceleration-deceleration of the starship can last so little time that, even if it's very large in intensity, its effects on the time differences becomes negligible.

To accelerate to significant speeds would actually take considerable time and the  energy involved to account for the relativistic mass increase (ΔΕ= Δm csquared is relevant)  would be non-negligible  and there is plenty of scope for the 'time factor' to be distorted a significant amount, too.
The Mossbauer effect, for example, relies on very  narrow resonances  in  metal atoms and  detects time dilation  by using the effect on the absorption  of RF waves by tightly bound atoms. It is sufficiently sensitive to detect the difference in gravitational field  (an acceleration) on the rate time progresses  between two different floors in a laboratory building.  So it is quite easy to disturb time  a measurable amount in non-inertial frames.

Ok, now consider this: Instead of a 4 l.y. distant star, the travel is to a 40 l.y. star. Accelerations and decelerations of B can last exactly the same as in the previous 4 l.y. travel, but, now, they end up with an age difference of 100years - 60years = 40 years, not 4. So, how can accelerations and decelerations have to do with it?

[lyner]

Ok, now consider this: Instead of a 4 l.y. distant star, the travel is to a 40 l.y. star. Accelerations and decelerations of B can last exactly the same as in the previous 4 l.y. travel, but, now, they end up with an age difference of 100years - 60years = 40 years, not 4. So, how can accelerations and decelerations have to do with it?

I thought you'd got me on that one!  But . . . .

As far as each twin is concerned, in my very simple model, there is no 'fixed ' earth or distant star. In fact we have no fixed grid in space for our measurements, at all.
They are both in a deserted part of deep space. I am not allowing you to have any more in your experiment than this.
They could both be going at any speed you like at the start of the experiment. The only things they can see or measure are each other and their ships and their relative motion.
Apart from the fact that one has used his engines (which must play a part in resolving the paradox), when they start to move apart, their relative motions are equal and opposite.
Now take up my previous argument. Neither twin knows which of them has actually 'moved', only that they have changed position, relative to each other.
The actual distances they each observe the other one to have traveled is not really relevant. What is relevant is the fact that, when they finally meet (when their space time vectors coincide again) they will have different lengths of beard!
SR tells us that when the traveling one  (the one who uses his rockets)  returns to the original spot will have aged less because of time dilation and  he will appear younger.
But, from his point of view, it was the other one who went off at speed and then returned. So the other one will appear younger to him.
How can there not be a paradox there? if A>B, you can't say B>A.
But, if you allow for the effect of acceleration on one of them (which one of them could feel as a 'weight  force' on him), to alter the rate of progress of time on his ship.  That is a GR effect. As has been said previously,  effects on the passage of time  have  been observed, due both to high speeds ( the muon observations - SR) and due to gravitational fields (the Mossbauer effect - GR).
I think this answers your  question at the beginning of this post.
It is the initial impulse / change of speed  and the subsequent changes as he turns round and comes to a halt that affects his 'aging' rate. Clearly, on a longer journey, he would end up with a different actual age difference.

In a more straightforward situation, there is NO paradox, of course, if two ships pass each other and observe the one-second bleeps that they are each generating. Each ship will see the other one's bleeps at slower than  the one second rate of his own clock. That's simple (?!?!) S.R..

As far as I remember, having read the Einstein monograph  some time ago, as a posy undergraduate, he used the notion of two clocks and not twins, but, of course, the same applies. Personalising it , makes the phenomenon slightly more 'creepy'. He frequently used models or pictures first and then sorted out the maths later. There have certainly been lots of discussions of these effects on more than just light photons and electrons, socratus. And, in any case, if it's good enough for an electron, it's good enough for me and my brother.