Autistic space post coming through.

Tin foil hat back on.

Rolling out a thin sheet of foil, only a couple of tens of atoms across, in space, we can easily carry enough material to cover several footballfields with the stuff today.

On one side of the foil wich can be made from any non-radioactive material, is another foil made from a radioactive material.

Two foils side by side, one radioactive and one not, the net result is a gentle push, a rocket engine that will last the halflife of whatever material you put on the engine side of the foil.

A gentle rotation will ensure uniform unfoiling and a uniform thrust.

At the center of this enourmous sheet of engine, is a probe, smaller than a usb-stick.

You could make it two probes for reduncancy, but why not just launch another ship.

This space probe will acellerate for years, and even with an extremely low acceleration rate, if you do it for long enough, you will quickly reach relativistic speeds.
One problem with space, is that it is not a vacum, there are tiny grains of particles even in interstellar space that will hit your ship with sufficient force to penetrate just about anything.

Lucky for us, we don't care if there are holes in our engine, it will continue to work just fine, our entire ship is an engine with no moving parts and no weak points (apart from the probe).

At the halfway point between sol and for example Gliese 581, we turn the ship around and begin to decelerate.

After perhaps 50 years, we will have a probe at our nearest habitable star.

Now the fuel for our engine is largely used up and we will use this foil as a solar sail, relying on the stars solar wind and the gravity of its satelites for an infinite source of propulsion.