Physics-Twin Paradox

Most people have heard of the twin paradox. Two twins exist on earth, one twin goes into a rocketship that can travel at near the speed of light, while the other twin stays on earth. The travelling twin returns a few years later in his time and finds that his twin has aged into an old man. Now we know that there is time dilation by the above equation, finding Δt', that in and of itself is not the paradox. The question is how do we know which twin to apply the formula too? The reason being that although the twin on earth is "still", if the twin in the rocket is moving at some velocity away from the twin on earth, the twin in the rocket can say its the earth moving away from the rocket instead and that he is still.

However, this can be clearly seen if we draw the appropriate spacetime diagram for this situation. The twin in the rocket must have accelerated twice, once to reach the velocity to apply the dilation effect, and the other to change direction to head back towards earth. This breaks the parity between the two situations and the assumption that the twin in the rocket is in an inertial frame for the entire duration of the trip.

Thus the twin on earth is the one that must age more than the twin in the rocket as defined by the dilation effect.