According to our current understanding of special relativity, time dilation occurs as objects approach the speed of light. Time appears to move slower for objects in motion relative to an observer at rest.
If we consider a hypothetical spacecraft traveling at a substantial fraction of the speed of light, the crew on board would experience time passing more slowly compared to an observer on Earth. This effect is known as "time dilation." As the velocity of the spacecraft increases, time dilation becomes more pronounced. However, the crew would still experience time passing, and they would age accordingly.
To estimate the time experienced by the crew during a 40-light-year journey, we need to know the speed at which they are traveling relative to Earth. Let's assume they are traveling at 90% of the speed of light (0.9c).
Using the time dilation formula from special relativity, the time experienced by the crew on board the spacecraft (Δt') would be calculated as follows:
Δt' = Δt / γ
where Δt is the time measured by an observer on Earth (proper time) and γ (gamma) is the Lorentz factor given by:
γ = 1 / √(1 - v²/c²)
In this case, v is the velocity of the spacecraft (0.9c), and c is the speed of light.
Plugging in the values, we get:
γ = 1 / √(1 - 0.9²) = 2.29
Assuming the observer on Earth measures the journey taking 40 years (Δt = 40 years), we can calculate the time experienced by the crew:
Δt' = 40 years / 2.29 ≈ 17.5 years
According to this calculation, the crew on board the spacecraft would experience the 40-light-year journey as approximately 17.5 years. So, while the journey would still take a considerable amount of time, it would not span multiple generations for the crew.
However, it's important to note that we currently do not possess the technology to travel at such speeds or overcome the practical challenges of long-duration space travel. This calculation is based on theoretical principles and assumes ideal conditions.