Talk:Twin paradox

It turns out that twin positions are not symmetrical. One is twin never accelerates, while the other twin moves away, changes direction and returns back. Although some have incorrectly stated otherwise, this problem is perfectly solvable using special relativity. Using special relativity one can calculate the elapsed time in the reference frame of each twin and the twin who moves away and comes back will have the shorter elapsed time.

Consider a spaceship that travels to a star four light years away in five years and returns five years later. In the reference frame of earth, the spaceship leaves at (x=0, t=0), moves to the star at (x=4, t=5), and returns to earth at (x=0, y=10). The time elapsed for the person on earth is 10 years.

Now let us look at things from the reference frame of the spaceship. The key equation in special relativity is that the spacetime interval (s^2 = x^2 - t^2) is the same in all reference frames. Consider the spaceship moving to the star. In the reference frame of the ship, its position (x') is fixed. Thereform the time elapse t' must obey the equation - t'^2 = x^2 - t^2, which means that in the reference frame of the ship, three years have elapsed between leaving earth and reaching the star. Using a similar argument, one can see that the time elapsed in moving from the star to the earth is also three years. Hence in the reference frame of the ship, six years have elapsed.

This paragraph does not resolve the paradox at all: From the viewpoint of the ship, the brother on Earth is moving away, then coming back. So the twin on the ship could perform the exact same analysis as given above, but with roles of the twins reversed, and would conclude that the "trip" by the brother on earth will be seen from the ship as being longer than it is experienced on Earth itself. The crucial difference between the brothers is that one sits in an inertial frame, the other doesn't. --AxelBoldt

This just in from someone who created a duplicate article:

The Twin's Paradox is a classic problem concerning apparant violations of Special Relativity, which posits that no privileged frames of reference exist in the universe with regards to motion.

The basic idea is this: one of a pair of twins blasts off on a spaceship and accelerates to near light-speed, travels around some nearby stars, and then returns to find his sibling greatly aged due to time dilation. The question is, if there are no privileged frames of reference, why does only one of the twins age? Couldn't the twin who was travelling say that he was at rest, and it was his sibling that was in motion?

The correct Lorentz[?] transformations are provided by including General Relativity, since accelerating objects reside in warped spacetime, and must take that into account to fully describe their frames of reference. The paradox results from only taking differences in the twins' positions into account, and not their respective local spacetime curvatures.

See also: acceleration