
Say you have 2 twins age 10 each.
Assume that one stays fixed at a point in space. (A)
Assume that the other starts moving at a speed of 0.6c where 'c' is the speed of light in a spaceship and returns after 8 years (assuming constant relative speed throughout ... 4 years away from his twin and 4 years coming back). (B)
Thus, according to Special Relativity, the time observed by A should be calculated with a Lorentz transformation, correct? So, B will come back 18 but A will think he is 20 even though they are twins!
HOW IS THIS POSSIBLE?
_AVG_ wrote: 
HOW IS THIS POSSIBLE? 
Uh, you kinda just answered that yourself...
ocalhoun wrote:  _AVG_ wrote: 
HOW IS THIS POSSIBLE? 
Uh, you kinda just answered that yourself... 
NO, what I don't understand is how one twin can be 20 years old while the other is 18? Then one will appear older than the other, right? HOW? Okay, suppose it's a smaller amount of time. Say only 4 years. Then B will appear 15 when he comes back and A will be 14 ... and you know that during puberty, every year brings a large difference in the physical appearance of a person. So, since B appears older than A, he will appear taller or maybe have more facial hair / pubic hair or something. How is THIS possible?
It is possible, because time does not pass at the same rate in all situations. Time passes 'more quickly' for one twin than the other. What's so hard to understand about it?
Some of the things that relativity theory tells us are very strange, but that's only because we don't deal with them all the time.
_AVG_ wrote:  ocalhoun wrote:  _AVG_ wrote: 
HOW IS THIS POSSIBLE? 
Uh, you kinda just answered that yourself... 
NO, what I don't understand is how one twin can be 20 years old while the other is 18? Then one will appear older than the other, right? HOW? Okay, suppose it's a smaller amount of time. Say only 4 years. Then B will appear 15 when he comes back and A will be 14 ... and you know that during puberty, every year brings a large difference in the physical appearance of a person. So, since B appears older than A, he will appear taller or maybe have more facial hair / pubic hair or something. How is THIS possible? 
The question only arises because you are wedded to the idea that this is some 'trick' or some effect that influences clocks but not 'real' things.
Relativity is quite real  time passes at different rates depending on relative velocity (or gravity). It is not a trick. Suppose, for example, we stretch the point a little. I can't be bothered to do the exact math so I'll guestimate.
Imagine twin A (aged 30) sets off from earth at .9c and spends (to him) 30 years round trip. I'm guestimating around 2.3 for the Lorentz*  which means his twin is perhaps going to be dead  certainly a very old man
*You can calculate it yourself easily enough  1/SQRT(1v^2/c^2)
I have seen a lot of Youtube movies/wikipedia pages about this, I'm not an expert, but I think I have a pretty good idea of how this is possible.
You are making it too complicated with all your questions at the same time. Don't involve appearances, facial hair, etc. for just a second here.
This is 'Time dilation', and is described by the theory of relativity by Einstein. It basicly means that everything in the Universe is relative, even time. For what is a second to you, might be years for another observer, who is in another place, another speed, etc in the universe. This means that there is no time, that is correct for everybody.
What happens is if someone moves faster than something else (because everything is relative, what is fast? You always have to compare 2 positions), then time will move more slowly compared to the person who is standing still. By time I mean everything: your clock will tick more slowly, your hair will not grow so fast anymore, you will not age so fast. We experience this time dilation in a very, very, very tiny proportions, that is not measurable yet, but it has been proven.
Let's say you and me were brothers, both 16 years old, and I would leave in a spaceship that travels insanely fast (close to the speed of light), while you would stay here, on Earth. You keep waiting here, day after day, week after week, month after month. Let's say I would return after after six months. We both compare calendars. For you, on earth, six months would have passed. For me, having travelled on a space ship that experienced time dilation, it would be possible that only a week had passed. The funny thing is that you CANNOT notice time dilation when you are experiencing it. On the spaceship, everything would have seem normal. From my point of view, your time would have just proceeded faster.
This has been tested by placing four atomic clocks on planes. One remained inside an Air force base on the ground. The planes were flown 2 times around the globe and compared to the clock on the ground. It seemed that the clocks on the planes were some time (insanely small, like 1/1000th of a millisecond) off from the clock on the ground.
Here are some youtube links about it:
http://www.youtube.com/watch?v=6Vpu6yJPRVQ (time dilation)
http://www.youtube.com/watch?v=wteiuxyqtoM&feature=related (relativity)
http://www.youtube.com/watch?v=KHjpBjgIMVk (time dilation)
The problem is that I can explain it and demonstrate it very easily, but the explanation uses a 'light clock' and people get the wrong idea when they hear the word 'clock'. They think it is something which just affects timekeeping and not something 'real'. It is quite real. People experience time at different rates depending on how fast they move in relation to each other (and also depending on other stuff like differences in gravity, but that comes in General Relativity and we'd probably best stick with Special Relativity for the moment).
The central 'paradox' comes from the observation that light travels at a constant rate EVEN FOR PEOPLE MOVING AT DIFFERENT SPEEDS.
This is boggling. Normally if you are moving away from me at (say) 50mph, then we see things move at different speeds, and a stationary sign for me would be moving at 50mph for you. That is what we call Relativity  only this is Galilean/Newtonian relativity  the notion that you cannot measure speed against a fixed universal point, because there isn't one. All movement is relative to some other object and who can say if the train is moving at 50mph, or the train is stationary and I am moving at 50mph? Thus we loose the notion of absolute speed and talk about relative speed.
Now this was blown out of the water by experiments in the 19th century that showed electromagnetism moving at a fixed speed, no matter how you were moving. Thus on your train, if I shine a torch at you, you would expect to see the light 50mpgh slower than when it left me, but you don't. I see it leave the torch at speed c (I'll use c rather than having to keep type the number) AND YOU SEE IT AT THE SAME SPEED.
Now, that is the fundamental reason for all the rest of it. If the speed of light is constant, and we know that speed = distance / time, then weird things must be happening with distance and time when you move. That is Special Relativity.
So, yes, you really would 'age' at a different rate, but you would both perceive that as perfectly normal because who can say what 'normal' is? There isn't a 'normal'. A second is a second to me, and a second is a second to you, but if we move apart or towards each other at high speed then your second is not the same as my second. And it isn't a trick of the clock  if we move fast enough and far enough then I could come back to you, my former twin, and I would still be young, but you would be long dead.
But, hang on (I hear you say)! Surely that is just maths  how do you know that it really happens?
Well, there are some radioactive particles which we know pretty well. We know how long they last before the 'decay' into other things. There is one really useful particle called a Muon. We know it lasts, on average, 1.56 microseconds before it decays. BUT here on earth we can generate muons and fire them at a target, and what we see is that they 'live' longer than they should. This confirms special relativity. It has been confirmed in a variety of other ways as well, including flying atomic clocks round the world on jets.
Here's some pictures
http://hyperphysics.phyastr.gsu.edu/hbase/relativ/muon.html
What should really boil your noggin is what this says about other things we take for granted  like 'simultaneity'. We are used to saying that 'such and such' happened at 'such and such a time'. Trouble is, now we know that our watches are moving differently, so it doesn't happen at the same time for both of us. I might see an event happen, then sometime later you see it happen.
Relativity is an interesting subject. I my opinion, if the twin is moving away, he will appear to age slower. If he is moving closer, he will appear to be aging faster. The net age will still be the same once he reaches his starting place. This may be completely wrong, but I still submit it as a possible answer.
Just a point to note. For the twin to actually come back without accelerating is impossible (even if he travels a circular path at constant speed, his velocity changes i.e. he still accelerates). And remember, time dilation applies only to inertial reference frames. Also, don't forget gravitational time dilation as well. So, ultimately, I know I started the topic, but if you come to think of it, this is quite an idealistic paradox ... and not a symmetrical situation to say the very least.[/quote]Correct. The symmetry (remember that time slows down for both) is broken when the inertial frame becomes noninertial (ie acceleration). You can model this as well using Special Relativity rather than GR.
The frames then look like this:
And the maths gets a bit more hectic, but it can be done.
So say you're standing still and you mange to look inside the spaceship, with a turning telescope or something. How would it look inside, would people be going insanely fast around? I can't imagine this in any way
anakonda118 wrote:  So say you're standing still and you mange to look inside the spaceship, with a turning telescope or something. How would it look inside, would people be going insanely fast around? I can't imagine this in any way 
Nope, the other way around. They would be going insanely slow, and you will be going extremely fast from their point of view.
Remember, this only happens at extremely high speeds, approaching the speed of light. It happens on for example an airliner too, but it is almost unnoticable.
joostvane wrote:  They would be going insanely slow, and you will be going extremely fast from their point of view.  Sure about that are you?
'Fraid not. The time dilation produced by velocity (Special Relativity) is reciprocal. I see you go slow, you see me go slow. It's a really bugger when you try to use common sense to do relativity  it nearly always bites you on the bum  I know from experience.
PS  add the fact that gravitational time dilation is NOT reciprocal  and it is even more of a bugger to form a nice mental map of it...
Bikerman wrote:  joostvane wrote:  They would be going insanely slow, and you will be going extremely fast from their point of view.  Sure about that are you?
'Fraid not. The time dilation produced by velocity (Special Relativity) is reciprocal. I see you go slow, you see me go slow. It's a really bugger when you try to use common sense to do relativity  it nearly always bites you on the bum  I know from experience.
PS  add the fact that gravitational time dilation is NOT reciprocal  and it is even more of a bugger to form a nice mental map of it... 
I was also reading about something known as the "Sagnac Effect" or something. Does that apply here?
