This is actually a two part question. The reason why the title mentions “particle” is because I want to know this for a photon and a proton.
Apparently the minimum wavelength of electro-magnetic radiation is the Planck length. What would the corresponding energy be? Would anything interesting happen if I fired it at a wall in a vacuum? Would there be a crater?
So the universal speed limit for anything is c. A proton has rest mass and E=mc^2. Is there any (theoretical, not practical) limit on the amount of energy I can put into a proton. It’s speed would never reach c no matter how much energy I pack into it, as I understand it. What if I packed in the same amount of energy released by the meteorite that killed the dinosaurs and then aimed it at the earth? Would it go right through the middle with out much of a fuss?
The highest energy ever observed for a single subatomic particle was the Oh-my-God Particle, an ultra-high energy cosmic ray detected in 1991, with an energy of 51 Joules (far, far short of the dino-killer asteroid). In principle, there is no known upper limit for how energetic a particle can get, though: It just gets really difficult to get those high energies. Of course, something like what you’re asking about would be so far beyond anything ever actually observed that it should not be surprising to see some new physical phenomenon showing up, but we don’t have any idea what that might be.
I’m not a physicist, but as to the question of what happens when a high-energy particle hits a solid object, this may give some inkling for the lower end:
Cecil did a column on “whats the maximum temperature” which is more or less the same question. Basically, beyond 10^32 kelvin, our ability to model what happens with current physics breaks down.
So the proton I mentioned earlier would certainly become a black hole, based on Cecil’s column.
What about the photon? There must be someone smart enough to work out how much energy it would have when it has a wavelength equal to the planck length.
E = hc/λ = about 12x10[sup]9[/sup] Joules, when λ is the Planck length. That’s about a 3-ton explosion of TNT.
But I’m not sure this is really an upper bound on photon energy. That is, although there’s no natural process producing photons of this energy level anyway, or anywhere near it (I don’t think), that doesn’t mean wavelengths shorter than the Planck length are disallowed.
Cecil was being overly glib there. We don’t know what would happen at the Planck scale, and it might not be anything particularly interesting at all. Plus, a material consisting of many particles all with about that energy (what something with temperature is) is very different from a single isolated particle.
That would be the Planck energy, about 2 billion Joules.
Factors of 2pi are irrelevant, anyway, since the Planck scales are all just back-of-the-envelope guesses in the first place. Nobody ever expects those to be correct to within factors of 2pi.