The Twin Paradox is a thought experiment often used to illustrate the effects of time dilation in special relativity. In this scenario, one twin stays on Earth (the stationary twin), while the other twin travels into space at high speed and then returns (the traveling twin). The paradox arises when the traveling twin is younger than the stationary twin upon their reunion.
The resolution of the Twin Paradox lies in understanding the asymmetry of motion between the two twins. From the perspective of the traveling twin, who is in a non-inertial reference frame due to the acceleration required to change direction, the situation is not symmetric. Special relativity's time dilation effects are only applicable to inertial frames of reference.
During the outbound and inbound journeys, the traveling twin experiences acceleration and deceleration, which breaks the symmetry between the twins. When the traveling twin changes direction, they are no longer in an inertial frame and, therefore, cannot apply the time dilation formula directly.
From the perspective of the stationary twin on Earth, they observe the traveling twin's clock running slower due to time dilation throughout the entire journey. However, for the traveling twin, who experiences acceleration and deceleration, their perception of time is affected differently.
When the traveling twin returns to Earth, they have aged less than the stationary twin due to their experience of time dilation during the periods of acceleration. In a sense, the traveling twin's acceleration acts as a distinguishing factor that breaks the symmetry and results in their younger age.
To summarize, the apparent paradox arises from the asymmetry introduced by the non-inertial motion and acceleration experienced by the traveling twin. Time dilation is a real effect, but its consequences are not symmetric in the context of the Twin Paradox.