Yes, according to Einstein's theory of relativity, if two observers synchronize their clocks and then one of them travels away at a significant fraction of the speed of light and later returns to meet the other observer, there will be a time difference between their clocks. This phenomenon is known as time dilation.
According to the theory of special relativity, time dilation occurs due to the relative motion between two observers. When an object is moving relative to an observer, time appears to pass more slowly for the moving object compared to the stationary observer. This effect becomes more pronounced as the velocity of the moving object approaches the speed of light.
As the observer traveling at high velocity returns to the other observer, they will find that their clock has registered less time compared to the stationary observer's clock. This means that the traveling observer will have experienced less time during their journey due to the time dilation effect.
It's important to note that the observed time difference depends on the relative velocity between the observers and the duration of their journey. For significant fractions of the speed of light, even short journeys can result in noticeable time differences. This phenomenon has been experimentally confirmed in various experiments, including the famous Hafele-Keating experiment.
It's worth mentioning that the time dilation effect is not limited to the special theory of relativity. The theory of general relativity, which deals with gravity and the curvature of spacetime, also predicts time dilation in the presence of strong gravitational fields.