In the twin paradox, one twin stays on Earth while the other travels through space at high speeds and then returns. According to the theory of special relativity, time dilation occurs for the traveling twin, causing their clock to run slower relative to the stationary twin on Earth. This effect is due to the relative motion between the two observers.
It's important to note that both twins can consider themselves to be at rest in their respective frames of reference. From the perspective of the traveling twin, they can claim to be at rest and observe the Earth twin as moving away and then returning. Similarly, the Earth twin can consider themselves at rest and view the traveling twin as moving away and returning.
However, when it comes to comparing the ages of the twins, there is a difference. During the journey, the traveling twin undergoes acceleration to change direction, which introduces an additional factor into the situation. Acceleration is not symmetric and affects the aging process differently than relative motion alone.
When the traveling twin accelerates, their frame of reference changes, and they experience non-inertial effects. This acceleration breaks the symmetry between the twins and introduces a preferred frame of reference. As a result, the traveling twin's clock runs slower during the periods of acceleration and deceleration. This is a different effect from time dilation due to relative motion alone.
Therefore, while both twins can consider themselves at rest in their respective frames of reference, the acceleration experienced by the traveling twin introduces an asymmetry in their aging process, leading to the twin paradox. The twin on Earth remains relatively stationary and ages more while the traveling twin experiences time dilation during the journey.