## Tuesday, October 16, 2007

### Why a local black hole is a good idea

Despite my misgivings about the wanton destruction of an entire planet (and possibly several moons) a local black hole has a number of distinct advantages. By far the most certain and powerful reason to have a black hole is for its value to scientific study. Black holes are precisely the region of the physical world where we don't understand what is going on. Einstein's relativity and quantum mechanics don't get along well together, we know that on some level one theory or the other has to turn out to not be correct. String theory is grown mostly from the realm of quantum mechanics and so naturally assumes that it is special relativity that is the large scale limit of string theory. String theory however is built up of conjectures about objects that exist on distance scales of 10-33 m. Thanks to the Heinsenberg uncertainty principle in order to probe such small distances we need very very high energies. Say you wanted to be able to probe an object on the order of 10-33 m with light. You would need light particles with wavelengths at least as small and hopefully much smaller than the object you were looking at. plank's relation for a photon (a light particle) is E = hf where h is plank's constant `6.62 x 10-34 J*S, E is the energy of the light particle and f is its frequency. For a light particle c = L*f where L is the wavelength and again c is the speed of light. so to get a light particle of wavelenght 10-33 m the energy of the photon would have to be E = h*c/10-33 = 1.98 x 108 J When you consider that this is the energy of a single particle it becomes readily apparent that making particles with such energies is a difficult proposition at best. (if you want to do the same sort of thing for matter with mass then de broglie's relation is L = h/p , where p is the momentum of the particle)

The point is that probing validity of string theory based on reachable predictions of it is very difficult. In order to come up with a workable theory of quantum gravity we need to have access to very very high energies. Objects falling into a black hole get accelerated to incredible energies just before they pass the event horizon. A quick calculation concerning the energy gained by falling from 71000 km from the singularity to 1.3 m of the singularity (or in other words from the current outer radius of Jupiter to the event horizon) of M*3.846 * 1026 J so for the lowly electron with a mass of about 10-31 kg we get an increase in energy of 10-5 J which is about 1014 eV. Putting that number in perspective a little the lhc is going to be able to achieve collision energies for heavy ions of (hopefully) about 10^15 eV. The great thing about gravitational acceleration is that there is no loss due to radiation caused by the acceleration. Falling into a black hole is a free fall motion which means that the particle doesn't feel like it is experiencing acceleration. Achieving such high energies as 1014 eV on earth is a daunting prospect possibly not even feasible. For heavier ions just in free fall the particles can attain energies of about 1019 eV. I need to go take a physics test so I will stop there for now but expect a part 2.