Twins paradox need clarification

[Lakshminarayanan.V]

hi all

i m new to this forum but would like to know a lot abt relativity.
I read through a dialogue in one of the threads on twins paradox. What exactly do you mean by saying one of the twins will be younger than the other? As far as i understand biologically neither of them is younger. Pls clarify.

 

[HallsofIvy]

They mean precisely what they say: If one twin sits still while the other goes off on a rocket ship at a very high speed and then turns around and comes back, while the twins were the same age before (they are, after all, twins) when the twin who went on the trip returns he will find he is younger than the one who did not move. The "traveling" twin will be biologically younger.

The "paradox" comes from the fact that, since motion is relative, each twin sees the other as moving and, at first glance, each twin should observe the OTHER as aging more slowly. And the age difference does NOT depend upon the direction.

The resolution to the "paradox" is that, in order to return so that we CAN compare the twins ages simultaneously, the moving twin must accelerate. If you take the acceleration into account, then the paradox disappears.

 

[harsh]

Special theory of relativity isn't biased towards a particular sort of "clock". All clocks are treated the same way, and biological clock is no exception. In hindsight, its a good check for it.

- harsh

 

[Garth]

The resolution to the "paradox" is that, in order to return so that we CAN compare the twins ages simultaneously, the moving twin must accelerate. If you take the acceleration into account, then the paradox disappears.

Only to reappear again as the Cosmological Twin Paradox

 

[Lakshminarayanan.V]

Precise were the answers. Now i m the sure of the fact but i long for the reason. How does the aging process adapt to the motion? thanks in advance.

 

[yogi]

You will get different answers from different folks. Suggest you go to the source - Einstein's 1905 article on special relativity called the "Electrodynamics of moving bodies" - then look at part 4 - physical consequences. (you can Google it)

 

[eNathan]

hi all

i m new to this forum but would like to know a lot abt relativity.
I read through a dialogue in one of the threads on twins paradox. What exactly do you mean by saying one of the twins will be younger than the other? As far as i understand biologically neither of them is younger. Pls clarify.

This is not a paradox at all. It is very east to understand and belive. Time runs slower for one twin, so he is younger than the other. I guess people have called this a "paradox" because they simply cannt grasp 2 twins at different ages. The fact that they are twins have nothing to do with it.

 

[selfAdjoint]

Precise were the answers. Now i m the sure of the fact but i long for the reason. How does the aging process adapt to the motion? thanks in advance.

As the accelerated twin moves through spacetime, his worldline curves, while the stay-at-home twin's worldline is straight. The way to calculate the proper time at the differential level is the square of dt minus the square of ds (the spatial diff). So the traveling twin always has a ds to subtract because of the curvature, but the homebound twin does not. You integrate these differentials to get the twins' experienced proper time. When they get back together the proper time of the accelerated twin, which governs his aging because it is the time he actually experiences, is less than the proper time of the stay-at-home twin. This is a real difference and if it were great enough the returning twin would still be young while the nontravelling one would be old, with wrinkles and white hair perhaps.

 

[Lakshminarayanan.V]

How is the proper time or biological time affected by the increasing mass of the traveling twin? Is it applicable for all clocks or only clocks based on light like radiation? Throw more light on the clocks used. Pls explain thanks in advance.

 

[yogi]

Any clock will do - Einstein even referred to pendulum clocks - the clocks measure time - and it is the lapsed time that is different for the two twins.

SelfAdjoint - are you saying the path is curved because one twin is continuously accelerating ...because he is flying a large circle at a constant velocity?

 

[HallsofIvy]

This is not a paradox at all. It is very east to understand and belive. Time runs slower for one twin, so he is younger than the other. I guess people have called this a "paradox" because they simply cannt grasp 2 twins at different ages. The fact that they are twins have nothing to do with it.

Then you've missed the point. Time runs more slowly for which twin? "Simple" special relativity says that motion is relative. Person A sees himself motionless (everyone is motionless relative to himself) and person B moving at high speed relative to him- thus A sees B as aging less slowly than A. Person B sees A moving at high speed and so sees A as aging less slowly. That's the "paradox". Of course, as long as A and B are never in the same frame again, their ages can't be compared directly so it remains a matter of "perception".

 

[RoboSapien]

This is not a paradox at all. It is very east to understand and belive. Time runs slower for one twin, so he is younger than the other. I guess people have called this a "paradox" because they simply cannt grasp 2 twins at different ages. The fact that they are twins have nothing to do with it.

...When they get back together the proper time of the accelerated twin, which governs his aging because it is the time he actually experiences, is less than the proper time of the stay-at-home twin. This is a real difference and if it were great enough the returning twin would still be young while the nontravelling one would be old, with wrinkles and white hair perhaps.

I am a rookee amature so excuse my knowledge on the topic.

I had heard that there cannot be 0,0,0 cordinate in the universe, not even at the point where bigbang exploded. If this is true then why will only one twin age when the fact is that both will see each other part away at same speed ?

Some people in this thread are not taking about meeting of the twin after the high speed space trip why ? It seems they are saying that when they meet they will be of same age, when in fact experiments have already show that clocks in Earth's orbit run at a slower pace and permanently loose time ?

Why r U all confusing newbees here ?

 

[russ_watters]

I had heard that there cannot be 0,0,0 cordinate in the universe, not even at the point where bigbang exploded. If this is true then why will only one twin age when the fact is that both will see each other part away at same speed ?

Well, they can't both see each other part ways at the same speed - only one is firing an engine. The other twin is stationary.

There are, however, lots of variations people like to kick around...

 

[HallsofIvy]

First I have no idea what you mean by "cannot be 0,0,0 coordinate in the universe". We can put a (0,0,0) coordinate anywhere we please!

Second: imagine two people moving, relative to each other, at 0.9c. At time t= 0, the pass through the same point and set their clocks to 0 at that instant. In that situation, you are correct- each person sees the other aging more slowly. But that itself is not a contradiction. What one person observes does not have anything to do with what another person, in a different frame of reference sees. In order to have a "paradox" you would have to bring them back together- that requires either acceleration or a very great mass. In either case you are out of special relativity and into general relativity.

 

[russ_watters]

First I have no idea what you mean by "cannot be 0,0,0 coordinate in the universe". We can put a (0,0,0) coordinate anywhere we please!

I took that to mean an abolute rest frame. Not sure though...

 

[RoboSapien]

First I have no idea what you mean by "cannot be 0,0,0 coordinate in the universe". We can put a (0,0,0) coordinate anywhere we please!...

This is deveating but would you like that point to be a GMT for the universe ? Or can it be so ?

 

[RoboSapien]

... In order to have a "paradox" you would have to bring them back together- that requires either acceleration or a very great mass. In either case you are out of special relativity and into general relativity.

Yes after that what ? U r the expert, arent U ?

 

[JesseM]

In order to have a "paradox" you would have to bring them back together- that requires either acceleration or a very great mass. In either case you are out of special relativity and into general relativity.

SR can deal with acceleration as long as you are looking at the accelerated object from the point of view of an inertial reference frame. If the twins separated at [tex]t_0[/tex] and reunited at [tex]t_1[/tex] in the coordinates of some inertial reference frame, and during that time the accelerating twin's velocity was given by some function v(t) [with v and t defined in terms of the same inertial reference frame], then you could calculate how much time would elapse on the accelerating twin's clock between these two moments by evaluating this integral:

[tex]\int_{t_0}^{t_1} \sqrt{1 - v(t)^2 / c^2} \, dt[/tex]

See The Spacetime Diagram Explanation section of this page on the twin paradox for more info.