Bomb#20
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Based on known science, yes, it's an engineering impossibility. There are two problems, the energy requirement and drag. From an energy perspective, the fastest we more or less know how to go based on current science is a couple percent of c, in a nuclear rocket. If we ever achieve controlled fusion, we could bump that up to maybe five percent. If you want a rocket to go seriously fast there's no substitute for using antimatter for fuel. If we can ever make that in quantity and store it safely then speeds on the order of half the speed of light become energetically possible.We all know that relativity forbids us going to light speed or beyond. But from an engineering perspective, what is the practical speed limit? Is there any reason to think we will be able to achieve 0.99c? Or is that just a engineering impossibility?
SLD
Alternately, we could skip the rocket and use an external energy source. With enough materials science advances we could build a big enough laser and a thin enough light sail to push a ship up to several percent of light speed just with the momentum of all the photons we hit it with -- probably somewhere intermediate between fusion rockets and antimatter rockets.
But at speeds like that the interstellar medium stops looking like a vacuum -- even an atom every two cubic centimeters is a lot of material to push your way through per second when you're covering thousands of km per second. And as you get closer to light speed those atoms effectively get relativistic mass increases, which means the power it takes to overcome the drag will rise faster with speed than it does in air -- and in air it rises as the cube of speed. Even if half your ship is antimatter fuel you aren't going to get anywhere close to 99% of c.