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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.

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  • $\begingroup$ "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. $\endgroup$
    – Escaped dental patient.
    Mar 25, 2022 at 18:27
  • $\begingroup$ @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). $\endgroup$
    – Vilx-
    Mar 25, 2022 at 18:30
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    $\begingroup$ 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). $\endgroup$
    – AlexP
    Mar 25, 2022 at 21:19
  • $\begingroup$ @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? $\endgroup$
    – Vilx-
    Mar 25, 2022 at 21:26
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    $\begingroup$ 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.) $\endgroup$
    – AlexP
    Mar 25, 2022 at 21:35

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As I understand it, the best guess in current science is that the maximum possible for a single particle is the Planck energy, which in mass units is around ten micrograms and in everyday energy units is about a quarter ton of TNT. Which would be an astonishing amount of energy for a single particle, but well short of a planet buster.

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    $\begingroup$ The Plank Mass is about 20 micrograms. Are you talking about that converted to energy? But it has nothing to do with the maximum energy for a particle. $\endgroup$
    – Daron
    Mar 25, 2022 at 20:46
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    $\begingroup$ A quarter ton of TNT is still a big boom. Wouldn't want to be underneath that when it lands. But yeh, there's at least a safe distance for that one that's not measured in AUs. $\endgroup$
    – John O
    Mar 25, 2022 at 21:02
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    $\begingroup$ @Daron You don't know that. A particle with more than the Planck energy, would have a wavelength shorter than the Planck length, and frequency higher than the Planck frequency. These are conjectured – not proven, which is why I said 'best guess', but conjectured – to be physically impossible. $\endgroup$
    – rwallace
    Mar 25, 2022 at 22:04
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    $\begingroup$ @Daron a particle has a property known as the de Broglie wavelength, associated with its relativistic momentum. When its de Broglie wavelength becomes shorter than the Planck length, the particle will turn into a quantum black hole, which will then evaporate in very short order. A particle with a momentum of a little under 41kgm/s would exceed the limit. That's a lot for a proton, but not a lot by the standards of a planet-smasher. $\endgroup$
    – Starfish Prime
    Mar 25, 2022 at 22:32
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    $\begingroup$ (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) $\endgroup$
    – Starfish Prime
    Mar 25, 2022 at 22:33

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