Imagine an expedition to the center of our Galaxy, which is about 27,000 light years away. It takes the light from the center of our Galaxy 27,000 years to reach Earth. In the year 2100 young, 25-year old astronauts would board a new kind of interstellar spaceship. The ship would start accelerating at 1g and keep accelerating for 10 years. Due to the constant acceleration of 1g, the astronauts would feel the same as on the surface of Earth. After 10 years have passed, the ship would turn around and start decelerating. After another 10 years it would stop decelerating and arrive at the center of our Galaxy. It would take 20 years total to get there. After gathering scientific data and refueling their spaceship, the astronauts would return to Earth to retire. The trip back would take them another 20 years.
The problem is that the Special Relativity Theory would come into play. For the astronauts only 40 years would pass. During this time they would travel a distance of roughly 55,000 light years. However on Earth, roughly 58,000 years would pass. If they left in the year 2100, they would return in the year 60,100! This would be the result of time dilation.
A drive capable of accelerating constantly for 20 years would be the peak of conventional space drive technology. It would not make any sense to make more powerful drives, because it would be hard for humans to live in higher artificial gravity conditions for so long.
In my opinion such trip would not make much sense. The humans left on Earth would have thousands of years to develop better technology and get to the destination before the conventional space ship. Developments in artificial intelligence could lead to smarter machines which would help us better understand physics, ultimately leading to the development of drives such as the Alcubierre drive and the like. Today we think such breakthroughs are impossible and the Special Relativity Theory forbids anything, including information, to get to distant places faster than the speed of light. Still there is yet so much we don’t know about physics and our Universe…