It might be acceptable to send a robot probe on a 50-year journey to a nearby star, but human interstellar travel is going to demand much shorter travel times and therefore much higher speeds. The fact is that crewed starships, to be practical, will need to move at a significant fraction of the speed of light—300,000 kilometers per second.
Fortunately, physics is on the side of super-fast, long-distance trekkers. According to Einstein’s special theory of relativity, time slows down significantly for anything that’s accelerated to very high speeds. Imagine making a trip to Arcturus, which lies 36 light-years away, and suppose you do it at constant speed, ignoring the acceleration and deceleration phases. At a steady speed of half that of light, the journey would take 62 years according to clocks aboard the spacecraft, but 72 years as measured back on Earth. This effect is known as time dilation, and we know it’s real because of measurements in the lab involving the decay of fast-moving particles. Step up the speed to nine-tenths that of light and you’d age only 17 years en route to Arcturus. Crank it up even more to 99.9 percent of light-speed and it would seem to you as if only 19 months had passed by, while everyone on Earth had aged 36 years!
Travel fast enough and you could reach the center of the Galaxy, or even cross the whole universe, in less than a lifetime. But the price of relativistic time dilation is being cut off from everything and everyone you left behind. Astronauts travelling to a galaxy far, far away might be able to get there well within their lifetimes if they closed to within a hair’s-breadth of the speed of light, but back home millions of years would have gone by.
Schemes, which are viable in theory, have been proposed by which spacecraft might attain relativistic speeds. For example, some types of engines powered by the annihilation of matter and antimatter fall into this category. But the amount of matter-antimatter fuel the ship would have to carry, and the amount of exhaust material it would have to expel every second, would be enormously high. All rockets that carry their own fuel, however energy efficient they may be, suffer from this problem. A solution is to harvest fuel continuously along the way, by drawing in hydrogen from the interstellar medium. But an interstellar (or Bussard) ramjet based on this concept has its own difficulties, the chief of which is maintaining thrust that exceeds the drag caused by the material into which the spacecraft is slamming.
Final mention should be made of the possibility of bypassing the light-barrier altogether. There are various ways, in theory, that faster-than-light (FTL) transport might be accomplished. It may, for example, become possible to engineer the fabric of space and time to achieve something like the “warp drive” of Star Trek. In broad terms this would involve placing a starship within its own bubble of normal spacetime while simultaneously shrinking the spacetime ahead of the ship, and expanding it behind, so that the distance to be travelled was drastically reduced. If that seems fantastic today, remember that many people as recently as the 1940s thought the notion of travelling to the Moon was absurd!