# Can a Relativistic Kill Vehicle be a single particle?

To those that don't know what an RKV is: a projectile (could be a spaceship, could be a bullet) that moves with a significant fraction of lightspeed. Maybe even close to lightspeed. Anything it hits will get vaporized just as well as in a nuclear explosion.

So far so good, but how big would one need to be? Obviously, the larger the mass, the larger the impact. Twice the mass, twice the kaboom. But also... the closer we get to lightspeed, the bigger the kaboom. To get to lightspeed would take infinite energy, so this implies that we can pack in arbitrary much energy by simply speeding up ever more.

So, to take this to the extreme, would it be possible to accelerate a single particle (say, an electron or maybe a muon since it's a bit heavier) so fast, that it could destroy a planet?

Or would there be some other laws of physics that would start to get in the way? Or maybe at those speeds it would just pass through harmlessly, creating a microscopical hole along the way?

If it's the latter case, then how big would a relativistic projectile have to be in order to deliver devastation to a planet? What equation governs this?

Let's assume that expense and technology are no barrier, but the laws of physics are as we know them.

• "the closer we get to lightspeed, the bigger the kaboom" - not necessarily, it could reasonably pass straight through with a little kaboom if it were say a small black-hole. Mar 25 at 18:27
• @EveninginGethsemane - True, but I wasn't thinking about black holes... those are much more fun when they're slower. And they're heck of a lot harder to accelerate. I was thinking of regular matter, just really sped up (AFAIK there is nothing in Special Relativity that would prevent this). Mar 25 at 18:30
• The Large Hadron Collider at CERN accelerates protons to 0.999,999,990 c, which is only about 3 m/s slower than the speed of light. At that speed each proton acquires an energy of 6.5 TeV (teraelectronvolts), which is gigantic for a proton, but comes out to about a not very impressive 1 µJ (microjoule); for comparison, you spend about 1000 times as much energy to blink an eye. The most energetic cosmic ray particle ever recorded had an energy of about 30 EeV (about 50 J or 0.01 kcal). Mar 25 at 21:19
• @AlexP - True, but that doesn't mean you couldn't go even further. Those last 3m/s require exponentially more energy. And... Yes, you'd obviously need a Dyson Sphere or something to power the thing, but in theory it's possible, right? Mar 25 at 21:26
• That "most energetic cosmic ray particle" I mentioned, dubbed the Oh My God particle by the researchers, was travelling at 99.999,999,999,999,999,999,999,51 percent of the speed of light... And the fun thing is, nobody has any idea what kind of physical process could conceivably accelerate a proton to such speed. (We know that such a process exists, because we have recorded several particles with such stupendous energies. We just have no idea what it is.) Mar 25 at 21:35

• (I was going to write an answer much like rwallace's, but with more latex because $\ell$ doesn't get used enough, but really this answer is basically the correct one given our current understanding of physics) Mar 25 at 22:33