Yes, but the question is can we launch and protect a payload for 100 years that can self-reproduce where it arrives? Otherwise all our ships can do is explore a tight X-lightyear sphere around Earth.
Can we propel a ship that can sustain 100 years of human (or AI) life and protect it from cosmic rays and provide it with enough equipment to build a self-sustaining colony on arrival?
It's not a limitation in physical laws, but the sheer scale of the undertaking that I wonder about.
Like, is the mass required for a self-sustaining interstellar generation ship, with all the required shielding needed to handle high-velocity interstellar travel (blasting through the interstellar medium an appreciable fraction of c means absorbing a crapload of high-energy particles, and the occasional micrometeorite that can't be detected until it's too late that hits the ship with the energy).
For example, hitting a little 10 gram rock at 0.1C would be a kinetic energy transfer in the gigajoules - like a small (1 kiloton) nuke.
So we've established our ship needs to have armor that's thick as hell. In order to make that economical, it must be huge. Also, in order for it to do useful work there, it needs to contain factories worth of machinery.
The sheer scale of this ship would be staggering. And then that raises the question: is there enough energy available to propel such a thing?
Can we propel a ship that can sustain 100 years of human (or AI) life and protect it from cosmic rays and provide it with enough equipment to build a self-sustaining colony on arrival?