Final answer:
The Twin Paradox involves a scenario where a space-traveling twin ages less than the Earth-bound twin due to time dilation in special relativity. The paradox is resolved when considering acceleration, as special relativity does not apply to accelerating frames, which is the situation for the traveling twin during their journey. Proper time differs from an observer’s measured time due to relative motion, revealing the 'paradox' to be a predictable outcome of relativity.
Step-by-step explanation:
The Twin Paradox arises in the context of special relativity and proposes a scenario in which one twin travels to a distant star at near light speed while the other remains on Earth. The twin paradox is grounded in the phenomenon of time dilation, a well-documented effect of special relativity, where time runs slower for an observer in motion relative to a stationary observer. The paradox emerges from our everyday expectation that time is absolute and should flow at the same rate for both twins, no matter their state of motion.
The resolution to the twin paradox lies in the fact that the traveling twin experiences acceleration when turning around to return to Earth, which is not accounted for by special relativity. Special relativity applies only to inertial frames of reference—those moving at constant velocity—not to accelerating frames of reference. Therefore, the paradox is resolved by general relativity, which includes the effects of acceleration and gravity on space-time and stipulates that the twin on the spaceship, who has undergone acceleration, will indeed have aged less upon returning to Earth.
Proper time is the time measured by an observer in their own frame of reference, where they are at rest or moving at a constant speed, while the observer's measured time may differ if measured from a frame of reference in relative motion. This differential aging is not a true paradox; it is a consequence of the laws of physics as encapsulated by Einstein's theory of relativity.