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Natural Science Forum / Physics / Relativity / November 2006Do baryons generate mesons from the tidal forces around small black holes?
It is my understanding that as the quarks in a baryon get pulled apart in an accelerator collision, the potential energy from the color force gets converted into a quark anti-quark pair, regenerating the original baryon and producing a meson. It seems to me that the tidal forces around a small blackhole (very curved spacetime) could differentially accelerate the individual quarks and cause the same effect. I assume that the energy for this process would come out of the gravitational potential energy of the baryon falling into the event horizon, but particularly in the case of a partical in orbit around the blackhole I don't quite see how this would work. Any comments? > It is my understanding that as the quarks in a baryon get pulled apart > in an accelerator collision, the potential energy from the color force > gets converted into a quark anti-quark pair, regenerating the original > baryon and producing a meson. It seems to me that the tidal forces > around a small blackhole (very curved spacetime) could differentially > accelerate the individual quarks and cause the same effect. What you are talking about is a quantum effect. We only have a quantum theory of gravity valid to about the plank scale - at energies beyond that (ie what you seem to be talking about) we don't know. http://arxiv.org/abs/gr-qc/9512024 Thanks Bill > I assume that the energy for this process would come out of the > gravitational potential energy of the baryon falling into the event > horizon, but particularly in the case of a partical in orbit around the > blackhole I don't quite see how this would work. > > Any comments? > > It is my understanding that as the quarks in a baryon get pulled apart > > in an accelerator collision, the potential energy from the color force [quoted text clipped - 7 lines] > (ie what you seem to be talking about) we don't know. > http://arxiv.org/abs/gr-qc/9512024 Let's do some order-of-magnitude calculations. The maximum force with which the baryon tries to hold the meson in ought to be about the rest energy of the meson divided by the radius of the baryon. Using the rest mass of the lightest meson, the neutral pion, which is 135 MeV/c^2, and the radius of a proton, about .8 femtometers, the maximum restoring force is about 3*10^4 Newtons. The proton ought to be able to pull the pion inward at a maximum acceleration of that force divided by the pion's mass, which would give us c^2/(.8 femtometers), or 10^32 m/s^2. Divide that by .8 femtometers again and we have an idea of how much curvature might be required -- around 10^47 s^-2. Granted, this was a classical calculation in a quantum mechanical situation, but I would be surprised if quantum-mechanical effects changed the order-of-magnitude. Let's put the proton as close to the black hole as possible, which would be just outside the event horizon. If I recall correctly, the component of the curvature trying to tear the proton apart is 2GM/r^3, so if r = 2GM/c^2, we have a curvature of c^2/r^2. That means we need a black hole about the size of the proton, or smaller. It would be a very small black hole, but still a lot larger than the Planck scale. And if the formula at Wikipedia [http://en.wikipedia.org/wiki/Hawking_radiation#Black_hole_evaporation] is right, such a black hole would take hundreds of billions of years to evaporate, so it would be stable for all intents and purposes. I don't know how throwing quantum mechanics in would affect things, but my guess would be that it would be possible. >> > It is my understanding that as the quarks in a baryon get pulled apart >> > in an accelerator collision, the potential energy from the color force [quoted text clipped - 38 lines] > I don't know how throwing quantum mechanics in would affect things, but > my guess would be that it would be possible. Thanks for the details. My concern is because we don't have a valid quantum theory of gravity to all energies exactly how valid what you wrote is. You may be correct and it gives valid order of magnitude effects - or it may not. We simply do not know. As Tom mentioned Hawking radiation is a similar quasi classical calculation so I suppose it has the same issues as well. Thanks Bill > It is my understanding that as the quarks in a baryon get pulled apart > in an accelerator collision, the potential energy from the color force > gets converted into a quark anti-quark pair, regenerating the original > baryon and producing a meson. Well, it's MUCH more complicated than that. What you describe is the most likely process, simply because the u and d quarks are the lightest and therefore the easiest to "pull out of the vacuum", but other things can and do happen, with probabilities not much smaller than what you describe. Indeed, at the Tevatron there is a reasonable rate for events with particle multiplicities exceeding 100. > It seems to me that the tidal forces > around a small blackhole (very curved spacetime) could differentially > accelerate the individual quarks and cause the same effect. Yes, for particle-antiparticle pairs "pulled out of the vacuum" this is the basic mechanism of Hawking radiation. > I assume that the energy for this process would come out of the > gravitational potential energy of the baryon falling into the event > horizon, but particularly in the case of a partical in orbit around the > blackhole I don't quite see how this would work. It's difficult to get sufficient energy at a distance large enough for a particle to orbit. But quantum mechanics affects this strongly, and we don't have a theory of quantum mechanics that include gravity and applies to black holes (Hawking radiation is a quasi-classical _guess_). Tom Roberts |
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