Based on our current understanding of physics, it is not possible for humans or any objects with mass to travel at the speed of light. As I mentioned earlier, the theory of special relativity states that as an object with mass approaches the speed of light, its energy requirement becomes infinite, time dilation occurs, and its mass appears to increase. These factors make it impossible for humans to achieve or surpass the speed of light.
Regarding the time it would take to reach far galaxies like Andromeda or beyond, it depends on the distance between us and the target galaxy and the speed at which we could hypothetically travel. The Andromeda Galaxy is approximately 2.537 million light-years away from us.
To give you an idea, let's consider a hypothetical scenario where we could travel at 99% of the speed of light (which is still impossible based on our current understanding). At this speed, time dilation would cause time to pass more slowly for the traveler compared to an observer on Earth. However, from the perspective of the traveler, the journey would still take a significant amount of time.
Using the Lorentz factor formula from special relativity, we can calculate the time dilation factor (γ) for a speed of 0.99c (99% of the speed of light):
γ = 1 / sqrt(1 - v²/c²) γ = 1 / sqrt(1 - 0.99²) γ ≈ 7.089
This means that for the traveler moving at 99% of the speed of light, time would pass roughly 7.089 times slower than for an observer on Earth.
Taking into account the distance to Andromeda (2.537 million light-years), we could calculate the time it would take from the perspective of the traveler:
Travel time = Distance / Velocity Travel time ≈ (2.537 million light-years) / (0.99c) Travel time ≈ (2.537 million) / (0.99) years Travel time ≈ 2.562 million years
So, in this hypothetical scenario, traveling at 99% of the speed of light, it would take approximately 2.562 million years from the traveler's perspective to reach the Andromeda Galaxy.
However, it's important to note that this hypothetical scenario assumes technologies and capabilities far beyond our current understanding and technological capabilities. Currently, our most advanced spacecraft can only travel at a tiny fraction of the speed of light, making intergalactic travel to distant galaxies like Andromeda an unachievable goal with our current technology.