Time dilation can cause a trip that would take one year for an observer to appear to take a longer duration, such as 100 years, when observed from a different frame of reference. This effect arises due to the relative motion between the observer and the reference frame.
According to special relativity, when an object moves at a high velocity relative to another object, time dilation occurs. As the velocity approaches the speed of light, the time dilation becomes more significant. For simplicity, let's consider a scenario where an observer is traveling at a substantial fraction of the speed of light.
From the perspective of the observer on the spacecraft, their own time appears to pass normally. If they embark on a one-year journey, they will experience one year of time elapsed. However, from the perspective of an observer in a stationary reference frame, such as someone on Earth, the observer's time will appear to pass more slowly.
This means that the observer on Earth will perceive the time on the spacecraft as dilated or stretched out. Due to the time dilation effect, what appears to be one year for the traveler will appear to be a longer duration for the observer on Earth. The exact calculation of the observed duration would depend on the relative velocity between the observer and the spacecraft.
For example, if the observer on Earth measures the duration of the trip to be 100 years, it means that the observer sees the time on the spacecraft passing 100 times slower compared to their own time. This is due to the time dilation effect resulting from the high velocity of the spacecraft.
It's important to note that the time dilation effect is reciprocal. So, from the perspective of the traveler on the spacecraft, they would observe the time on Earth as passing more quickly relative to their own time. This reciprocal effect is a consequence of the symmetry in relativity and is known as time dilation symmetry.
In summary, time dilation caused by relative motion can lead to a discrepancy in perceived durations between observers in different frames of reference. This effect allows a trip that would take one year for the traveler to appear to take a longer duration, such as 100 years, when observed from a different reference frame due to the time dilation effect.