Isn't this kinda like mounting a fan on your car's roof to charge the battery? You have accelerated your spaceship to 0.995C (or whatever) and now you are encountering space dust at a phenomenal rate. Some of that dust is moving away from you, some of it toward you, some of it is at rest. On average it's all just sitting there unaware that your vessel is about to smack into it. The energy is in the difference between your speed and the particle's. If you try to harness it, you slow down.

(I'm asking genuinely here. My analogy might be wrong because it's too classical!)

I think in principle you should be able to generate thrust greater than drag orthogonal to the particle flow. That's what wings do.

The old Bussard ramjet concept was to capture these high velocity protons (with some kind of magnetic field), cause them to fuse, and use the fusion energy for propulsion.

There are a few engineering difficulties with the idea but it makes for some good SF stories...

The spaceship in Poul Anderson's Tau Zero uses a Bussard ramjet.

Also all Stat Trek Federation ships

Fantastic book. I read it for the first time about a year ago but I still think about it once every week or two. Thought about it as soon as the "spaceship" started to accelerate towards light speed.

Relativity effects will start to bite. The proton's going to stop being interested in your magnetic field[1], and you're approaching the velocity of the exhaust mass of the fusion reaction.

[1] The momentum vector just completely flattens almost any other physical characteristic. I'm not sure there's even enough time for nuclear fusion to take place.

This is a bit like driving into a brick wall, and then asking if you could use the released energy to go faster ...

Imagine you drive into a wall of tnt, break through it, and as you exit it explodes and gives you an extra boost. Yes, you’ve lost some speed at the beginning but you’ve gained much more

The tnt has potential energy. The only reason those protons have energy is because you’re smacking through them with energy you’ve already found.

There's two different kinds of energy here - the kinetic energy of a moving thing hitting you in opposition is a problem. No way to capture that as far as I know - it's like running into a wall and asking how it can help you go faster.

But then there's e=mc^2, so if the stuff you're running into is the fuel source for your fusion engine (could be a fission engine, but unlikely you'll run into heavy atoms like Uranium or Plutonium) then you have an unlimited source of energy...

So maybe sort of? Running into things slows you down, but then you capture that mass and release the energy out of it to go faster... because of the nature of e=mc^2 you'll usually get more energy out of something if you convert its mass than what you lose by running into that mass.

I’m imagining a ship with a hole in it and a piece of fuel at the backside where the particles hit. It would slow you down first since you’re tethered to the particles, then the explosion would push you forward.

The issue is that the energy for that explosion comes from the slowing down of your ship, so it doesn’t work.

The energy that comes from a mass-energy conversion greatly exceeds kinetic energy losses.

For the same reason that the power of an atomic bomb does not depend on how fast you smash the sections together - it depends on how much mass is converted to energy in the resulting reaction.