[saspinski (OP)]

I have found the question below in an old thread about the twin paradox. I could not get an answer at that thread or from other sources. The problem for me is: if the situation is totally simmetric, both twins return at the same age. But isn't it against SR theory?
I assume that all acelerations and desacelarations are the same for both the traveller twins, so GR should not explain any difference.

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?

[Toffo]

The problem for me is: if the situation is totally simmetric, both twins return at the same age. But isn't it against SR theory?

You mean this chronological sequence of assessments uttered by one traveling twin seems kind of impossible:
 
1: Me and the other guy are the same age
2: The other guy is time dilated, I am normal
3: The other guy is time dilated, I am normal
4: The other guy is time dilated, I am normal
5: Me and the other guy are the same age

[jeffreyH]

Two twins on earth measure the expansion of the universe and determine the redshift of light for selected galaxies. Then one twin goes on a space flight at close to the speed of light to a distant planet. Both twins carry on measurements of their selected galaxies. While the earthbound twin gets the predicted results the journeying twin finds the galaxies redshifted directly behind and blue shifted in front. From this he can determine he is in motion. Therefore both twins can determine who will be time dilated and age more slowly. Thus when they meet up again they won't be surprised at the age difference. No paradox.

[hamdani yusuf]

Two twins on earth measure the expansion of the universe and determine the redshift of light for selected galaxies. Then one twin goes on a space flight at close to the speed of light to a distant planet. Both twins carry on measurements of their selected galaxies. While the earthbound twin gets the predicted results the journeying twin finds the galaxies redshifted directly behind and blue shifted in front. From this he can determine he is in motion. Therefore both twins can determine who will be time dilated and age more slowly. Thus when they meet up again they won't be surprised at the age difference. No paradox.

Let's replace the earth with another planet moving at constant high speed relative to the earth, while other conditions stay the same.
Is your logic still applicable in this situation?

[Alan McDougall]

Although this is a bit off topic it is still about relativity.

What if the two twins were approaching each other at 90%c  how would their relative time "Zones" be effected relative to the perspective of each other?

Or

If the were separating from each other at 90%c how would their relative time "Zones" be effected relative to the perceptive of each other?

Alan

[jeffreyH]

Two twins on earth measure the expansion of the universe and determine the redshift of light for selected galaxies. Then one twin goes on a space flight at close to the speed of light to a distant planet. Both twins carry on measurements of their selected galaxies. While the earthbound twin gets the predicted results the journeying twin finds the galaxies redshifted directly behind and blue shifted in front. From this he can determine he is in motion. Therefore both twins can determine who will be time dilated and age more slowly. Thus when they meet up again they won't be surprised at the age difference. No paradox.

Let's replace the earth with another planet moving at constant high speed relative to the earth, while other conditions stay the same.
Is your logic still applicable in this situation?

Then that may be the twin planet paradox. It is an entirely different situation since the time dilation due to motion is not the only consideration. The time dilation due to the gravitational fields of the planets also have to be taken into consideration.

[saspinski (OP)]

1: Me and the other guy are the same age
2: The other guy is time dilated, I am normal
3: The other guy is time dilated, I am normal
4: The other guy is time dilated, I am normal
5: Me and the other guy are the same age

It is really very strange.
But on the other hand, if
1) both leave earth to opposite directions,
2) acelerate until some relativistic speed, and remain some some time at that speed,
3) acelerate to the opposite direction until get the previous speed, but now direction home.
4) brake to meet again on earth.

If A is now younger than B, B is also younger than A, so they must have the same age.

[Toffo]

A human being can easily tell apart a ticking clock from a stopped clock, right? A clock that is ticking has some moving parts that are aging slowly because of the ticking motion.

If a human being itself is a moving part of a clock, the human being can be aware of that fact, then said human being says: "I am a human being that is time dilated because of motion".

A goldfish is quite different: Its memory does not last long enough for it to be aware of either it's own motion or any paradoxes.

So both human beings and goldfish are living in a paradox free world.

[hamdani yusuf]

Two twins on earth measure the expansion of the universe and determine the redshift of light for selected galaxies. Then one twin goes on a space flight at close to the speed of light to a distant planet. Both twins carry on measurements of their selected galaxies. While the earthbound twin gets the predicted results the journeying twin finds the galaxies redshifted directly behind and blue shifted in front. From this he can determine he is in motion. Therefore both twins can determine who will be time dilated and age more slowly. Thus when they meet up again they won't be surprised at the age difference. No paradox.

Let's replace the earth with another planet moving at constant high speed relative to the earth, while other conditions stay the same.
Is your logic still applicable in this situation?

Then that may be the twin planet paradox. It is an entirely different situation since the time dilation due to motion is not the only consideration. The time dilation due to the gravitational fields of the planets also have to be taken into consideration.

What If the other planet is identical in size and density with earth?

[jeffreyH]

Unlike the case of the twin paradox the masses involved are not negligible. For an earth like planet travelling at relativistic speed you have gravitational radiation to take into account. Frequency shift also becomes more complex, involving both the motion of the planet and the state of its gravitational field. The latter will be affected by its motion due to radiation of gravitational waves.

[saspinski (OP)]

Anybody knows how relativity theory explains the twin (or better the triplet) paradox, as stated in my initial post?

[jeffreyH]

There is no fixed background in relativity against which to measure things. This means that any observer in a non accelerating inertial frame of reference will judge other to be in motion relative to themselves. They assume another object is moving away at a constant speed. An observer on the other object will in turn see the first observer moving away at a constant speed. Who is correct? Relativity says both since all things are relative. The reason I suggested the fixed stars as a stand in for a fixed background is that they are to all intents and purposes fixed. It even uses the relative redshift of expansion to prove the point. However this would only be an assumption in relativity as the fixed stars could in fact be moving in a preferred direction with respect to something exterior to the observable universe.

[Toffo]

You mean this chronological sequence of assessments uttered by one traveling twin seems kind of impossible:
 
1: Me and the other guy are the same age
2: The other guy is time dilated, I am normal
3: The other guy is time dilated, I am normal
4: The other guy is time dilated, I am normal
5: Me and the other guy are the same age

At most one of sentences 2,3,4 is true.
So at least two of those sentences is wrong.
Accelerating person is allowed to say "I am normal" at any time.
Accelerating person is not allowed to say "I am normal" every time.
If an accelerating person says "I am normal" two times, he contradicts himself.

[hamdani yusuf]

There is no fixed background in relativity against which to measure things. This means that any observer in a non accelerating inertial frame of reference will judge other to be in motion relative to themselves. They assume another object is moving away at a constant speed. An observer on the other object will in turn see the first observer moving away at a constant speed. Who is correct? Relativity says both since all things are relative. The reason I suggested the fixed stars as a stand in for a fixed background is that they are to all intents and purposes fixed. It even uses the relative redshift of expansion to prove the point. However this would only be an assumption in relativity as the fixed stars could in fact be moving in a preferred direction with respect to something exterior to the observable universe.

Since the accepted result of this thought experiment is that traveling twin would be younger than staying twin, it means that traveling twin's observation is invalid. Is it invalid because of the accelerations?

[jeffreyH]

There is no fixed background in relativity against which to measure things. This means that any observer in a non accelerating inertial frame of reference will judge other to be in motion relative to themselves. They assume another object is moving away at a constant speed. An observer on the other object will in turn see the first observer moving away at a constant speed. Who is correct? Relativity says both since all things are relative. The reason I suggested the fixed stars as a stand in for a fixed background is that they are to all intents and purposes fixed. It even uses the relative redshift of expansion to prove the point. However this would only be an assumption in relativity as the fixed stars could in fact be moving in a preferred direction with respect to something exterior to the observable universe.

Since the accepted result of this thought experiment is that traveling twin would be younger than staying twin, it means that traveling twin's observation is invalid. Is it invalid because of the accelerations?

In order to start the journey the travelling twin has to accelerate with respect to the stay at home twin. The traveller is therefore already in a non inertial frame of reference with respect to his twin on the ground. If the earth were in a very extended elliptical orbit it could itself be considered to be in a non inertial frame of reference with respect to the sun. etc etc. So yes the accelerations are the cause but more importantly it is knowing about them. If the travelling twin were to make no attempt to determine his rate of motion with respect to a known source, the fixed stars, then he has no way to determine his rate of acceleration with respect to his earthbound twin. Accurate information is always important in any experiment. Otherwise people can easily cry foul and state an error in a theory that really doesn't stand up to close scrutiny if viewed in light of the correct assumptions.

[Atomic-S]

https://en.wikipedia.org/wiki/Twin_paradox

[jeffreyH]

Take two clocks synchronised at a position on earth directly away from the sun on the dark side of the earth. Let one remain stationary for 24 hours while the other travels at a speed that keeps it directly away from the sun on the dark side of the earth. When they meet again 24 hours later will the clocks differ and by how much?

[saspinski (OP)]

Since the accepted result of this thought experiment is that traveling twin would be younger than staying twin, it means that traveling twin's observation is invalid. Is it invalid because of the accelerations?

That is why the paradox is stronger if we make both twins to travel, but to opposite directions. If they suffer all the acelerations and desacelerations necessary to a meet in earth, after some years,  it seems reasonably, due to the simmetry of the situation, that they will have the same age.

[guest39538]

Since the accepted result of this thought experiment is that traveling twin would be younger than staying twin, it means that traveling twin's observation is invalid. Is it invalid because of the accelerations?

That is why the paradox is stronger if we make both twins to travel, but to opposite directions. If they suffer all the acelerations and desacelerations necessary to a meet in earth, after some years,  it seems reasonably, due to the simmetry of the situation, that they will have the same age.

Take two twins at birth and separate the twins, place one twin in a constant inertial reference frame and the second twin in constant motion.
At birth we attach one Caesium clock and one digital stop watch with a lifetime battery to each of the twins.
50 years later the twins meet up in a lab to compare clocks, both digital clocks show an equal amount of time for both twins to the exact nano second, the Caesium clocks both show a difference in time.


They conclude they are both the same age  and not the same age at the same time, so both agree that one of the methods to keep time is broken. I wonder which one that could possibly be?

[Bill S]

http://home.earthlink.net/~owl232/twinparadox.pdf

This is worth a read.