To determine how long it would take to travel a distance of 50 light-years, we need to consider the speed at which the travel is taking place. Since the speed of light is the maximum speed at which information can travel in the universe, any object with mass traveling at or near the speed of light would experience time dilation effects according to the theory of relativity. As a result, from the perspective of an observer on the spacecraft, time would pass more slowly compared to an observer at rest.
Let's assume we have a hypothetical spacecraft traveling at a significant fraction of the speed of light, such as 90% of the speed of light (0.9c). In this scenario, we can calculate the time experienced by the travelers on the spacecraft using the Lorentz factor, which accounts for time dilation:
Lorentz factor (γ) = 1 / √(1 - v^2/c^2),
where v is the velocity of the spacecraft and c is the speed of light.
For our example of traveling at 0.9c:
γ = 1 / √(1 - (0.9c)^2/c^2) ≈ 2.29.
This means that time would pass approximately 2.29 times slower for the travelers on the spacecraft compared to the outside world. Therefore, to determine the time experienced by the travelers during a 50 light-year journey, we divide the distance by the velocity of the spacecraft:
Time = Distance / Velocity = 50 light-years / (0.9c) ≈ 55.56 years.
Keep in mind that this calculation assumes constant velocity and does not account for acceleration or deceleration, which would be necessary for a realistic interstellar journey. Additionally, reaching such high speeds near the speed of light is currently beyond our technological capabilities and faces significant theoretical and practical challenges.
Therefore, while this calculation provides an estimate based on the assumptions, it is important to recognize that interstellar travel of this magnitude remains highly speculative and challenging with our current understanding of physics and technology.