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The wikipedia page repeatedly says that the twin travelling in space is the only one which travels, and also is the only one which faces acceleration and deceleration. So it does not age, while the twin which remains in one place ages.

However, this seems wrong as there is no such thing as staying in one place. The twin which presumably stays on earth is travelling at the same relative velocity, relative to the twin in the spaceship. Since the spaceship twin's acceleration is just the rate of change of velocity, so when the spaceship twin's velocity changes relative to the earth twin, the earth twin's relative velocity compared to the space twin also changes, and so the earth twin experiences the same relative acceleration as the space twin (in the opposite direction).

In fact, the space twin sees the earth twin as accelerating away from him, then decelerating and coming back, while he thinks his spaceship is at rest all the time. So then why should the earth twin age more than the space twin? Why not the other way around?

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Related :… – Kitchi Feb 6 '13 at 18:13
the other twin does not 'stay in one place', it stays in an inertial frame at all times; this assumes 'earth' as a synonym of 'inertial frame' – lurscher Feb 6 '13 at 18:52

In special relativity acceleration is absolute. You can measure your acceleration in many ways e.g. by holding a pendulum and watching to see if it tilts from the vertical.

So when you say the earth twin experiences the same RELATIVE acceleration as the space twin (in the opposite direction) this is incorrect. The Earth twin will measure no deflection of their pendulum while the twin in the rocket will measure a deflection. This introduces the asymmetry that is responsible for one twin aging differently from the other.

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Then what exactly is the rate of change of relative velocity? Isnt it relative acceleration? if not then what is it? – khushro Feb 7 '13 at 6:19
You can calculate a relative acceleration by differentiating the relative velocity, however the number you get is not relative in the way velocity is. In SR it isn't possible to assign absolute velocity, but it is possible to assign absolute acceleration. – John Rennie Feb 7 '13 at 8:17

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