Time dilation does have a significant impact on the feasibility of travel to distant Earth-like planets, especially when considering high speeds approaching the speed of light. However, it is important to note that achieving speeds close to the speed of light is currently beyond our technological capabilities.
When an object is traveling at speeds comparable to the speed of light, time dilation becomes more pronounced. As the relative velocity of the moving object increases, time dilation effects become increasingly significant. The Lorentz factor, γ, which determines the degree of time dilation, approaches infinity as the object's velocity approaches the speed of light.
For instance, if we assume a speed of 0.6 times the speed of light (0.6c), we can calculate the corresponding Lorentz factor as γ = 1/√(1 - (0.6c)²/c²) = 1.25. This means that time will appear to pass 1.25 times slower for travelers on the spacecraft compared to observers on Earth.
From the perspective of the travelers, their journey might feel shorter due to time dilation. However, when considering the time experienced by observers on Earth, the duration of the journey will be significantly longer. This effect becomes more pronounced as the speed of the spacecraft approaches the speed of light.
As a result, even though time dilation could make the subjective experience of travel time shorter for the astronauts on board, the actual time that elapses on Earth would be much longer. This poses a significant challenge for interstellar travel, especially for one-way missions to Earth-like planets that are located many light-years away.
Additionally, there are other practical challenges associated with long-duration space travel, such as resource management, crew health, and spacecraft technology. These factors further complicate the feasibility of interstellar travel.
While time dilation is an intriguing aspect of special relativity, it is not the only consideration when assessing the viability of travel to other Earth-like planets. We must also take into account technological limitations, energy requirements, and the sustainability of such long-duration missions.