According to the theory of relativity, when an observer switches between inertial frames, there can be a difference in the measurement of time between the two frames. This phenomenon is known as time dilation.
In the twin paradox, which is a thought experiment commonly used to explain time dilation, one twin stays on Earth (in an inertial frame), while the other twin travels in a high-speed spacecraft and then returns to Earth. During the journey, the traveling twin experiences acceleration and changes inertial frames. The key point to note is that acceleration introduces a difference in the measurement of time.
When the traveling twin undergoes acceleration to change their frame of reference, they experience a different rate of time compared to the twin who remained in the original inertial frame. This is because acceleration affects the passage of time, as described by the theory of general relativity.
During the turnaround phase of the twin paradox, the traveling twin experiences a change in their frame of reference, which can result in a difference in the measurement of time between the two twins. As a result, when the traveling twin returns to Earth, they may find that less time has passed for them compared to the twin who remained on Earth. This is known as the twin paradox because it seems paradoxical that one twin has aged less despite experiencing acceleration.
In summary, when switching between inertial frames, there can be a difference in the measurement of time due to time dilation. Acceleration plays a crucial role in introducing this difference in the twin paradox and other scenarios where inertial frames are changed.