In the twin paradox, one twin stays on Earth while the other twin travels away from Earth at a high velocity, then returns. The paradox arises because the traveling twin, who experiences acceleration to change direction, ends up younger than the twin who stayed on Earth.
In this scenario, the velocity of the traveling twin does not become negative during the return trip. The velocity can change direction, but it remains positive (or non-negative) throughout the entire journey. The twin paradox can be understood by considering the effects of time dilation and the asymmetry of the situation.
According to special relativity, time dilation occurs when an object is moving relative to another object. As the traveling twin moves away from Earth at a high velocity, they experience time dilation relative to the twin who stays on Earth. This means that time appears to pass more slowly for the traveling twin compared to the stationary twin. Consequently, the traveling twin ages less than the twin on Earth.
When the traveling twin returns to Earth, there is a change in reference frames. At this point, the traveling twin experiences acceleration to change direction and return home. During this period of acceleration, the twin's velocity changes, and time dilation is no longer symmetric between the twins. The twin who underwent acceleration experiences a different passage of time compared to the twin who remained at a constant velocity on Earth.
This asymmetry in time dilation is what resolves the paradox. The traveling twin, who underwent acceleration and experienced a non-inertial reference frame, ages less than the twin on Earth. The velocity does not become negative, and the effects of time dilation continue to apply consistently throughout the journey.
It's important to note that the twin paradox is a thought experiment that helps illustrate the principles of relativity and time dilation. In reality, we do not have the technology to achieve the high velocities required to observe significant relativistic effects like those depicted in the paradox.