The Standard Anwer to the Twin Paradox of Relativity does not seem to work if the twin's ship doesn't return?

Question

The twin paradox of relativity is resolved by pointing out that there are three frames of reverence not two. The earth remains in one the whole time of the twin's ship's travels. But the space ship starts in one frame and then when it turns around it changes its frame of reference.

Refer to classic Twin Paradox at wikipedia

The standard explanation works so long as the ship turns around. What happens if the ship travels only one way and upon arriving, decelerates and again rejoins the frame of reference of the earth. Adjusting for simultaneous time with earth, the traveling twin has still aged only half the time as the twin on earth. Why is the slower time dilation assigned to the traveling twin, when the earth was speeding away from the ship as fast as the ship was speeding away from the earth.

If answering, be careful. Try not to be confused by the distance between the ship and the earth. Imagine simultaneous clocks on earth and at the ship's destination placed long ago.

Answer 1

In the simplistic version of the twin paradox usually discussed in class where elapsed time in the two frames differs by the Lorentz Factor, the point of view of the twin on Earth is correct - that is, the traveling twin ages less than the twin on Earth. This is because the Earth is, very nearly, an inertial frame of reference and the spaceship, which accelerates and deccelerates during the problem, is not. Since the traveling twin is NOT in an inertial frame of reference, the simplistic time-dilation equations given in class don't apply and that prediction is incorrect. This applies whether or not the twin returns to Earth.

If you're a sci-fi fan, read "The Pusher," a short story by John Varley.

Answer 2

Everybody seems to know about time dilation and length contraction, but everybody forgets about Relativity of Simultaneity.

Observers moving relative to each other disagree on which events are simultaneous. The clue that this is the important key to the paradox is that you feel the need to remind everyone that SIMULTANEOUS (i.e. synchronized) clocks were placed on Earth and Vega long ago. Synchronized in whose reference frame?? Why, the Earth's of course.

Consider the rocket ship when it is still at Earth, but traveling at nearly c. The pilot observes the Vega clock to NOT be synchronized with the Earth clock. He's right next to the Earth clock and sees that it reads 0 (the trip just started), but the clock on Vega reads 9.5 years! If the trip takes 1 year to get to Vega, he gets there in 1 year at which point (because Earth's and Vega's clock has been running slow) the clock reads 10 years.

In the Earth's reference frame, the clocks ARE synchronized and when Earth's clock reads 0, so does the clock on Vega. Vega is 10 light years away, so the trip takes 10 years and the pilot gets to Vega when the clock there reads 10 years.

Note that this does NOT prove that the spaceship's clock is somehow slower than the Earth's clock in any absolute sense. Each observer observes the other's clocks to run slow during the entire trip.

Also note that this IS the standard answer to the problem. If the rocket then turns around, he gets into a frame where the Earth's clock is 9.5 years ahead of Vega's. The moment the rocket turns around, Earth's clock changes from reading 0.5 years to reading 19.5 years as the rocket changes reference frames.

(also also note these numbers are all bullshit, I just made them up, but you get the idea)

Answer 3

A very good question, and the answer is that the traveling twin is the one who feels the acceleration.

Of course the earth feels an acceleration too, but it is tiny compared to what the ship experiences. Try this thought experiment: if the universe consisted of nothing but two identical space ships with identical occupants, would they both experience the same acceleration (in opposite directions) if only one started its engines and moved away?

Answer 4

Firstly, a paradox does not "work". Hence it being called a paradox.
Do not think of the two twins events as being symmetrical, they are not.
What happens to one twin does not happen to the other, you need to read more about this, and so do I. But a mathematician told me once that the problem with most peoples understanding of this, is they assume the situation of events to be symmetrical.

And if the twins ship never returned, we wouldnt know how far away he went, or how long he had travelled, so according to schrodinger, he is both old and young....
lol