Actually, we do, for the closest ones. Nuclear pulse propulsion. Basically, throwing thermonuclear bombs out the ass-end of the spacecraft and using them to generate thrust.

That gets you to about 10 or 12% the speed of light at the top end. If you're just interested in doing a fast flyby of the closest stars, that would get you to them in just X / .10 or X / .12 years, where X = distance in light years.

So for example, Alpha Centauri is 4.37 light years, so we could fly a probe through that system between 4.37 / .12 = 36.4 years to 4.37 / .10 = 43.7 years after launch.

We know that we can build space probes that are capable of lasting that long. The two Voyager spacecraft were launched in 1977, and are still operating. That's 45 years. Because of the huge amounts of payload that NPP allows for, we can have backups of backups of backups, and plenty of power generation.

But that's the maximum possible delta V, so if you want to actually slow down and explore the system over time, you're limited to using half that for acceleration, and the other half to decelerate at your destination, so you'll need between 72.8 years and 87.4 years before arrival. Conventional Plutonium powered RTGs won't be sufficient, but Americium ones would work, combined with a nuclear reactor activated to supply extra power to the systems during the exploration phase.

That's a problem for humans, though, because even a young, new engineer fresh out of school at launch is going to be 97 when the probe arrives. We don't really have will for multigenerational projects.

So there would have to be a compelling secondary mission for something like this. Measuring the parallax on nearby stars to refine our distance estimates would be a good one, and perhaps also super-dee-duper long baseline interferometric radio telescope observations would be another.

​

Of course, there are two things I've ignored so far.

First is cost. This would be a hugely expensive undertaking. Would we want to spend the money to do something like this? There'd have to be a really compelling reason to do so.

Second is that it's literally illegal. The 1963 Limited Test Ban Treaty forbids any and all nuclear explosions in space regardless of the reason for them. At least, it does for nations that have signed and ratified the treaty. Both the US and Russia have done so.

China has not.