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Chronos comments on Confidence levels inside and outside an argument - Less Wrong

129 Post author: Yvain 16 December 2010 03:06AM

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Comment author: Chronos 22 December 2010 12:37:52PM *  12 points [-]

I'm a bit irked by the continued persistence of "LHC might destroy the world" noise. Given no evidence, the prior probability that microscopic black holes can form at all, across all possible systems of physics, is extremely small. The same theory (String Theory[1]) that has led us to suggest that microscopic black holes might form at all is also quite adamant that all black holes evaporate, and equally adamant that microscopic ones evaporate faster than larger ones by a precise factor of the mass ratio cubed. If we think the theory is talking complete nonsense, then the posterior probability of an LHC disaster goes down, because we favor the ignorant prior of a universe where microscopic black holes don't exist at all.

Thus, the "LHC might destroy the world" noise boils down to the possibility that (A) there is some mathematically consistent post-GR, microscopic-black-hole-predicting theory that has massively slower evaporation, (B) this unnamed and possibly non-existent theory is less Kolmogorov-complex and hence more posterior-probable than the one that scientists are currently using[2], and (C) scientists have completely overlooked this unnamed and possibly non-existent theory for decades, strongly suggesting that it has a large Levenshtein distance from the currently favored theory. The simultaneous satisfaction of these three criteria seems... pretty f-ing unlikely, since each tends to reject the others. A/B: it's hard to imagine a theory that predicts post-GR physics with LHC-scale microscopic black holes that's more Kolmogorov-simple than String Theory, which can actually be specified pretty damn compactly. B/C: people already have explored the Kolmogorov-simple space of post-Newtonian theories pretty heavily, and even the simple post-GR theories are pretty well explored, making it unlikely that even a theory with large edit distance from either ST or SM+GR has been overlooked. C/A: it seems like a hell of a coincidence that a large-edit-distance theory, i.e. one extremely dissimilar to ST, would just happen to also predict the formation of LHC-scale microscopic black holes, then go on to predict that they're stable on the order of hours or more by throwing out the mass-cubed rule[3], then go on to explain why we don't see them by the billions despite their claimed stability. (If the ones from cosmic rays are so fast that the resulting black holes zip through Earth, why haven't they eaten Jupiter, the Sun, or other nearby stars yet? Bombardment by cosmic rays is not unique to Earth, and there are plenty of celestial bodies that would be heavy enough to capture the products.)

[1] It's worth noting that our best theory, the Standard Model with General Relativity, does not predict microscopic black holes at LHC energies. Only String Theory does: ST's 11-dimensional compactified space is supposed to suddenly decompactify at high energy scales, making gravity much more powerful at small scales than GR predicts, thus allowing black hole formation at abnormally low energies, i.e. those accessible to LHC. And naked GR (minus the SM) doesn't predict microscopic black holes. At all. Instead, naked GR only predicts supernova-sized black holes and larger.

[2] The biggest pain of SM+GR is that, even though we're pretty damn sure that that train wreck can't be right, we haven't been able to find any disconfirming data that would lead the way to a better theory. This means that, if the correct theory were more Kolmogorov-complex than SM+GR, then we would still be forced as rationalists to trust SM+GR over the correct theory, because there wouldn't be enough Bayesian evidence to discriminate the complex-but-correct theory from the countless complex-but-wrong theories. Thus, if we are to be convinced by some alternative to SM+GR, either that alternative must be Kolmogorov-simpler (like String Theory, if that pans out), or that alternative must suggest a clear experiment that leads to a direct disconfirmation of SM+GR. (The more-complex alternative must also somehow attract our attention, and also hint that it's worth our time to calculate what the clear experiment would be. Simple theories get eyeballs, but there are lots of more-complex theories that we never bother to ponder because that solution-space doesn't look like it's worth our time.)

[3] Even if they were stable on the order of seconds to minutes, they wouldn't destroy the Earth: the resulting black holes would be smaller than an atom, in fact smaller than a proton, and since atoms are mostly empty space the black hole would sail through atoms with low probability of collision. I recall that someone familiar with the physics did the math and calculated that an LHC-sized black hole could swing like a pendulum through the Earth at least a hundred times before gobbling up even a single proton, and the same calculation showed it would take over 100 years before the black hole grew large enough to start collapsing the Earth due to tidal forces, assuming zero evaporation. Keep in mind that the relevant computation, t = (5120 × π × G^2 × M^3) ÷ (ℏ × c^4), shows that a 1-second evaporation time is equal to 2.28e8 grams[3a] i.e. 250 tons, and the resulting radius is r = 2 × G × M ÷ c^2 is 3.39e-22 meters[3b], or about 0.4 millionths of a proton radius[3c]. That one-second-duration black hole, despite being tiny, is vastly larger than the ones that might be created by LHC -- 10^28 larger by mass, in fact[3d]. (FWIW, the Schwarzschild radius calculation relies only on GR, with no quantum stuff, while the time-to-evaporate calculation depends on some basic QM as well. String Theory and the Standard Model both leave that particular bit of QM untouched.)

[3a] Google Calculator: "(((1 s) * h * c^4) / (2pi * 5120pi * G^2)) ^ (1/3) in grams"

[3b] Google Calculator: "2 * G * 2.28e8 grams / c^2 in meters"

[3c] Google Calculator: "3.3856695e-22 m / 0.8768 femtometers", where 0.8768 femtometers is the experimentally accepted charge radius of a proton

[3d] Google Calculator: "(2.28e8 g * c^2) / 14 TeV", where 14 TeV is the LHC's maximum energy (7 TeV per beam in a head-on proton-proton collision)

Comment author: David_Gerard 22 December 2010 04:05:19PM *  10 points [-]

I wonder how the anti-LHC arguments on this site might look if we substitute cryptography for the LHC. Mathematicians might say the idea of mathematics destroying the world is ridiculous, but after all we have to trust that all mathematicians announcing opinions on the subject are sane, and we know the number of insane mathematicians in general is greater than zero. And anyway, their arguments would (almost) certainly involve assuming the probability of mathematics destroying the world is 0, so should obviously be disregarded. Thus, the danger of running OpenSSH needs to be calculated as an existential risk taking in our future possible light cone. (Though handily, this would be a spectacular tour de force against DRM.) For an encore, we need someone to calculate the existential risk of getting up in the morning to go to work. Also, did switching on the LHC send back tachyons to cause 9/11? I think we need to be told.

Comment author: Luke_A_Somers 16 January 2017 10:04:48PM 1 point [-]

Looking back over ancient posts, I saw this. I upvoted it earlier, and am leaving that, but I'd like to quibble with one thing:

this unnamed and possibly non-existent theory is less Kolmogorov-complex and hence more posterior-probable than the one that scientists are currently using

I think the bigger issue would be 'this unnamed and possibly non-existent theory is an accurate description of reality'. If it's more Kolmogorov-complex, so be it, that's the universe's prerogative. Increasing the Kolmogorov complexity decreases only our prior for it; it won't change whether it is the case.

Comment author: DragonGod 04 October 2017 09:14:04AM 0 points [-]

if the correct theory were more Kolmogorov-complex than SM+GR, then we would still be forced as rationalists to trust SM+GR over the correct theory, because there wouldn't be enough Bayesian evidence to discriminate the complex-but-correct theory from the countless complex-but-wrong theories.

I reject Solomonoff induction as the correct technical formulation of Occam's razor, and as an adequate foundation for Bayesian epistemology.