MelissaSweet said:
Hi guys. Just a few quick questions:
Your calculations seem to be based on a constant rate of absorption, is this right? Wouldn't the absorption rate increase exponentially?
Yes, that is correct, but it won't change the conclusion very much (it will change the result by a few orders of magnitude).
As has been exposed (see link by pervect), even a billion ton black hole would need 10^28 years to eat the earth. But first, our nano 10^(-24) kg black hole needs to grow to a billion ton black hole and will thus have to eat about ~10^38 atoms. It is still smaller than the size of a proton during all that time.
The more pessimistic calculation by Orion (using more dimensions, and hence a higher effective G constant for the nano black hole) would become rather complicated, because this effective G constant would SHRINK as the nano black hole grows, and leaves its "quantum domain" to become more and more a classical black hole. So although its mass would increase, its effective cross section wouldn't rise proportionally.
In your cross section, are you looking only at the Schwarzschild radius? Doesn't gravity extend far beyond?
Yes, but the "cross section" is the quantified probability of ABSORPTION, not simply of interaction. The moon interacts gravitationally with the earth, but isn't ABSORBED by the earth. So anything much farther away from the BH than the Schwarzschild radius will simply undergo a deflection (talking classically). This interaction is extremely small: don't forget that outside of the Schwarzschild radius, the gravitational effect of a BH is the same as any other mass. So you'd get the gravitational attraction of a mass of 10^(-24) kg, which is normally utterly neglegible.
Also, there has been made a crude assumption: that is, when a nano black hole encounters an iron nucleus, that it eats the ENTIRE nucleus, even though the nano BH is much much much smaller than the nucleus. But this is probably entirely wrong: it would only eat at most a gluon or a quark, meaning that it would leave most of the mass of the nucleus behind (which would probably undergo a desintegration into another nucleus and a few pions or so).
Someone mentioned that the scientists failed to mention the effect that conservation of momentum has on nanoblackholes. Is that right? If they missed this very basic concept what else might they be missing?
No, the point was something different. Some people argued that eventual nano black holes produced in cosmic rays (of much higher energy than the LHC accelerator will produce) have high momentum wrt the earth, and hence will just fly once through the earth, so the fact that these collisions are regularly happening is no proof that nano black holes aren't dangerous.
That reasoning is correct: indeed, even if we underwent showers of nanoblack holes, they would at most eat one or two iron atoms before having traveled through the Earth and fly off in the blackness of space.
So the observation that cosmic rays exist, is no proof of the "safety" of nanoblack holes, is entirely correct.
However, the reasoning ALSO applies to the eventual nanoblack holes produced at the LHC. It is only in the case that they are produced in the exact center of gravity of the two colliding particles that they don't have any momentum left and hence fall to the earth. But this is a highly exceptional case, because colliding protons, at these energies, must rather be seen as the collision of two bags of potatoes, the real interactions being between the potatoes (quarks and gluons), and not between the entire bags. So normally, such collisions produce a lot of "debris" together with an interesting interaction (such as the production of a nano BH). It is what renders the experimental observation a pain in the a**: between miriads of uninteresting tracks in one and the same event, you have to find those three or four tracks which indicate something interesting. There is a priori no reason for any correlation between the debris, and the interesting interaction (this has already been established for many years in lower-energy interactions ; I did my PhD on part of the problem for instance). So there is no reason to assume that this interaction happens in the center of gravity of the bag of potatoes, it is rather in the center of gravity of the two potatoes who do the interaction. Now, this center of interaction usually has high momentum wrt the center of gravity of the interacting protons, so the resultant product (in casu a nano BH) also.
In that case, it flies right off the reaction event, through the earth, or through the sky, into outer space.
And, honestly, the possibility that all these exotic processes happen (only predicted by very exotic and speculative theories) is way more dubious than the (also speculative, but way more down to earth) prediction that Hawking radiation really happens. In fact, all these speculative theories which open the possibility of the production of nano BH, ALSO predict Hawking radiation.
And if this is true, a nano black hole will go POOF even before leaving the detector.
So the entire reasoning is flawed. Current established physics says that NO black holes will be produced at the LHC. One needs to switch to speculative theories to open up even their possibility. And those same speculative theories (just as well as a small extrapolation of currently established physics) foresee Hawking radiation. So it is a bit aberrant to speculate on the production of nano BH using these theories, and refute them at the same time when considering Hawking radiation, no ?
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