If i travel at .9c in a spaceship from earth to a star 20 lightyears away, and come back (assuming uniform motion the entire time). When i arrive back to earth why does is my twin older than me? My twin moved at .5c relative to me, so why does time slow down for me and not him? when reading about special relativity the book said i would arrive on earth and see my twin much older than i am, but isnt my twin and everyone on earth moving at .9c relative to me in the space ship?
Congratulations! You have re-discovered the "Twin Paradox!" As long as you are both at rest in different inertial reference frames, clocks at rest in your frame will be measured to run slower than clocks in the other frame (when the clocks at rest in the other frame are used to measure the rates of your clocks). And, using clocks at rest in your frame, you will measure clocks at rest in the other frame to run slower. When you decide to return, however, you must initially change (accelerate) into the earth's rest frame. You will, at that time, conclude that it was actually clocks at rest in your initial frame that were running slower than clocks in the earth frame. The whole process repeats when you return to earth.
As GRD points out, how are you going to go from 0 to .9c when leaving Earth, then .9c to zero once you reach your star, then go from 0 to .9c again for the return trip, then .9c back to 0 upon reaching home ... without accelerating and decelerating?
There's probably a hundred threads about this already. I'm quoting myself from the most recent one: You could say that. It's not wrong, but it's still a bit misleading. It makes it sound like it was wrong to think that the Earth clocks were slower in the first place (it wasn't), and it's leaving out the most important point (if we are going to describe this whole sequence of events in terms of inertial frames instead of talking about the proper time of the world lines): The moment before you turn around, you're simultaneous with a much earlier event in Earth's history than the moment after you turn around. So when you turn around, your brother's age "jumps ahead" by a large amount (if we insist on describing things in terms of inertial frames). Check out the first of the two spacetime diagrams I mentioned for details.
The moment before you turn around, the coincident clock of your brother's rest frame reads far later than your onboard clock, owing to the fact that, from the perspective of your ship's rest frame, the clocks in the other frame are not "in fact" synchronized. When you come to a halt in your brother's rest frame, you reassess simultaneity and acknowledge that the clocks in that frame are in fact synchronized. Among other things, you conclude that your brother is in fact much older than you are. The whole phenomenon repeats on the trip back home. It might be helpful to check out the link "Yet Another Look at the Twins" on the homepage of www.maxwellsociety.net. Bon Voyage.
It's definitely "earlier", not "later", unless you interpreted "the moment before you turn around" as a moment in your twin's rest frame, rather than as a moment in your own rest frame. See my spacetime diagram.
Fig. 4-8 in "Special Relativity" (A.P.French) illustrates clearly that the clocks of another IRF, coming toward you (at rest in your own IRF) read later than your own clock when the clocks in both IRFs have been synchronized as per Einstein. When you are accelerating(/decelerating) to a state of rest in another IRF, its clocks don't spin wildly in their dials. Once you have come to rest in the other IRF and accept that the clocks at rest in that frame are all synchronized, it is clear that your brother's coincident clock (back, say, at the Origin) has advanced more than your onboard clock (and your own body).
At "the moment before you turn around" your twin's clock is moving away from you (in your co-moving frame), not coming toward you. If "you" (the twin on the rocket) describe things from the point(s) of view of co-moving inertial frames, then the Earth clock will be described as "spinning wildly", or just taking a big jump ahead if we only consider two co-moving inertial frames. I don't know why you're talking about synchronization, but if you stop for a while before you go back (that seems to be the scenario you're describing), and describe things from the point of view of your co-moving inertial frame, then yes, your twin is older than you.
As Kev pointed out one party travels in a straight line in spacetime and one party travels on a path with two separate legs. The straight line is always the shortest path.
Why all the emphasis on the turnaround? Suppose the traveling twin arrives at his destination and stays there, wouldn't he still be younger than the earth twin? After one year at his destination suppose both he and the earth twin leave at the same time and travel at .9c and meet in the middle. They compare ages. Wouldn't the twin who stayed on earth be older? Thecla
How would they know? They have to meet again (i.e. return to a common frame of reference) to compare. Yes he would. By half as much as if he'd stayed on Earth.
Do you know the triangle inequality? That the sum of the lengths of two sides of a triangle is always greater than the length of the third side. The turnaround is important because it determines which twins worldline is two sides of a triangle and which is one side of a triangle.
Let me see if I understand this. The twin travels at .9c a distance of 20 light years and stays at his new planet. No return. Doesn't the traveling twin have to be younger even without a change in direction for the return voyage? How will he know he is younger? Both twins can send each other pictures and compare. The question I am asking:Does the traveling twin have to make a return trip to earth to be younger? Thecla
Yes. Place a clock on the destination planet, in advance, and synchronize it with the clock on Earth. This can be done either by using light signals, in a way described in many introductory treatments of relativity, or by "slow transport," taking a clock from Earth to the destination slowly enough that time dilation effects are small enough so as not to be significant.
This is only true in the Earth frame. From the point of view of an observer that is always travelling at 0.9c relative to the Earth, the travelling twin is stationary and the Earth is moving at 0.9c. This observer sees the "travelling" twin as ageing faster than the Earth twin and he says the Earth/planet system sees it the other way around because the clocks of the Earth and the planet are not synchronised from his point of view. Until the turn around happens and the travelling twin returns, the validity of which twin is older is entirely relative and depends upon the state of motion of the observer. In other words it is impossible to determine which twin is experiencing "real" time dilation, until one of the twins turns around and returns. Until then, it is just a point of view.
To illustrate what kev just said, consider this "quadruplets paradox". Alice and Bob set out from Earth at 0.9c. Carol and David stay on Earth. After 9 years 8 months have passed on Earth, David follows out on the same route and speed as Alice and Bob. Carol remains on Earth. Meanwhile, after 9 years 8 months have passed on Alice and Bob's ship, they reach their destination (20 light years from Earth). Alice jumps off ship, decelerates and stops (relative to Earth), but Bob continues at 0.9c away from Earth. David is at rest relative to Bob. When they compare their ages by exchanging messages and allowing for the delay, they find that, at the moment P that David left Earth he had aged 9 years 8 months since the experiment began but Bob had aged 22 years 3 months. Alice is at rest relative to Carol. When they compare their ages by exchanging messages and allowing for the delay, they find that, at the moment Q that Alice arrived at the planet she had aged 9 years 8 months since the experiment began but Carol had aged 22 years 3 months. To summarise, Alice and Carol agree that Carol is older, and David and Bob agree that Bob is older. But, until they separated, Alice and Bob travelled together and so were the same age; until they separated, Carol and David travelled together and so were the same age. According to David & Bob, immediately after David left Earth (P), Carol = David < Bob. According to Alice & Carol, immediately after Alice landed on the planet (Q), Bob = Alice < Carol. So everyone disagrees over whether Bob or Carol is the oldest. Complications like this are the reason why the twins paradox is formulated in terms of twins who meet each other again so that there can be no disagreement over who is older.
In response to KEV I don't think there has to be a return trip to establish an age difference. Consider the following: A third planet is situated exactly halfway between the Earth and target planet that the twin landed on. This planet is stationary with respect to the other two planets and the three planets form a straight line. The halfway observer has a very powerful telescope and points it East to see the Earth twin ten light years away. He swings the telesope West and sees the traveling twin just landing on the target planet 10 light years away. According to the halfway planet observer looking through his telescope, which twin has more gray hair and wrinkles? Thecla