## How long could a black hole remain in the center of the earth?

The above question came up in conversation with Michael Vassar and some other nerds in New York City yesterday (before I went with relatives to see Gimpel Tam, an extraordinarily dark and depressing musical performed entirely in Yiddish). Look, I know a massive black hole would swallow the earth extremely quickly, and I also know that a microscopic black hole would quickly evaporate as Hawking radiation. So suppose we chose one of intermediate size so as to maximize the earth’s survival time—how long a time could we achieve? (Does the answer depend on the viscosity of the magma or whatever else is in the earth’s core?) Sure, I could try to calculate an answer myself, but why bother when so many physicists read this blog? Pencils out!

Comment #1 December 21st, 2008 at 6:46 pm

A related question: how long could we live on an Earth with a black hole in its centre? Would such a black hole, through radiation or disruption to the Earth core render the surface uninhabitable?

Comment #2 December 21st, 2008 at 6:47 pm

The earth’s inner core is believed to be solid iron. I wonder if it’s possible for a black hole to exist within that core in a semi-stable manner.

Comment #3 December 21st, 2008 at 6:51 pm

Assuming that all the relevant parameters are continuous, couldn’t you get a black hole that emitted Hawking radiation at the same rate that it took in stuff from the Earth? It seems like this has a lot more to do with the viscosity and density of the material, the velocity at which Hawking radiation is emitted, etc., than physics on a fundamental level.

Then again, IANAP, so I suppose I could be totally wrong.

Comment #4 December 21st, 2008 at 7:05 pm

As long as we’re positing an impossible scenario, let’s assume that the Earth in the vicinity of this black hole is hollow. Then choose a black hole of sufficient size that the Hawking evaporation ‘vapor pressure’ is balanced with its environment: matter/energy falling in = energy evaporated. Then both the earth and the black hole last arbitrarily long.

Much like the Gravity B probe, you’d have to guarantee that the black hole and the Earth were in identical orbits, because the black hole’s gravitational pull would largely cancel out.

How you’d create such a black hole is an entertaining question in its own right. You’d need an incredibly energetic implosion (like a supernova) with a far below stellar mass to sufficiently compress the starting material.

Comment #5 December 21st, 2008 at 7:07 pm

Harrison: You’re right, it should just be a straightforward calculation. But I didn’t feel like looking up the necessary facts about the viscosity of magma, etc. Far better to appeal to Ricardo’s Comparative Advantage Theorem: answer my black hole question, and you can ask me anything you want about complexity!

Comment #6 December 21st, 2008 at 7:21 pm

It like there should exist a fixed point because of the balance argument above. So, a zeroth-order technical answer might be “arbitrarily long”. But the fixed point is clearly unstable. So, do you want us to calculate the amount of time before fluctuations cause the black hole to either grow to Earth-sized proportions or evaporate?

Comment #7 December 21st, 2008 at 7:28 pm

I think the slowest one can hope for is a black hole which slowly converts the Earth into hawking radiation, growing smaller and smaller until it evaporates entirely at the moment that the earth is completely eaten.

I’m not sure how the asymptotics of this work, but it may be that as the black hole gets tinier and tinier, it eats material at a decreasing weight in such a way that the remaining mass of the earth tends to zero without ever reaching that in a finite time.

I think such a black hole would be highly unstable – that is, if a fraction more mass or less than predicted entered it, it would start growing or shrinking (respectively) exponentially and rapidly eat the earth / die.

Comment #8 December 21st, 2008 at 7:32 pm

You might want to ask David Brin (http://www.davidbrin.com/). He’s a former cosmologist turn science fiction novelist, who wrote a novel

Earthwith this as one of the premises. It was published in 1990, but if his physics predictions are as good as his social predictions were, it was at least vaguely plausible. I’m sure he already knows the answer, and he answers just about every comment posted to his blog (which is mostly political these days).Comment #9 December 21st, 2008 at 7:34 pm

Thanks for the observation, Steve! I suppose I was asking how long it’d take for a black hole epsilon larger than the critical size to swallow the earth.

Comment #10 December 21st, 2008 at 7:45 pm

re #7: Yes, it’s hopelessly unstable unless you surround the black hole with a fairly high vacuum. You certainly can’t have the molten core -in contact- with the event horizon or even particularly close to it.

It’s also worth remembering that a significant fraction of matter falling into a black hole will get converted to energy before it gets there and not be captured. See supernovae or active galactic nuclei for comparison. I think the danger is less the earth getting eaten and winking out of existence as annihilated by the energy released in its core.

Comment #11 December 21st, 2008 at 8:58 pm

This is perfect for a Chicago-style “Fermi calculation”, in which a quantitative answer is expected, and we are given no access to the literature, no computer, and five minutes to complete the entire calculation.

My Fermi estimate is 200 nanograms/year, computed as follows.

The rate of mass ingestion is the product of a density, a velocity, and cross section. For the density, we take the density of iron. For the velocity, the speed of sound in iron. For the cross section, the unitarity bound for

l=o scattering, which we recall is, wavelength^2 (because, what else could it be?). For wavelength, the momentum associated with the speed of sound. Ignoring all factors of π, etc. (which I don’t recall anyway), the above Fermi estimate is obtained.Comment #12 December 21st, 2008 at 10:31 pm

My partial answer is that you should think of most interactions with a black hole as a kind of explosion and/or implosion. A rule of thumb in astronomy (in my lay understanding) is that about 10 percent of the mass of an object that falls into a black hole can be converted into energy from various kinds of violence related to tidal forces. Moreover, as you decrease the size of the black hole, Hawking radiation more and more resembles a supernova-style explosion. (I am not sure if it is comparable in size to a supernova, but it is not too many orders of magnitude away.)

If it were a teeny weeny black hole, it would just go pop and disappear in the middle of the earth, and presumably cause an earthquake. But as it gets bigger it would explode the Earth from the energy release of matter falling into the black hole, and in a certain size range from Hawking radiation. Finally if the black hole is big enough, the implosion from falling into the black hole would overwhelm the explosion. But I suspect that, unless the radius of the black hole is more than that of the Earth, even an implosion-dominated interaction would send a fair fraction of the matter outward, and a lot of X-ray radiation with it.

A black hole with enough radiation pressure to stave off lava would be fairly small. Once it starts to eat, the explosion would build quickly. Maybe the time for it to blow away the Earth — which again, is much easier than sucking it in — is about the same as for the smallest possible asteroid strike to blow away the Earth. My guess is that it is comparable to the radius of the Earth divided by the Earth’s escape velocity, which is about 10 minutes. But probably long before that, maybe after a minute or two, there would be an earthquake crescendo that would macerate the surface.

Comment #13 December 21st, 2008 at 10:34 pm

Thanks, Greg! (Especially for using the word “macerate.”)

Comment #14 December 22nd, 2008 at 12:08 am

Also, I assume that you want to know the amount of time as measured in the frame of an observer on Earth’s surface, right?

Comment #15 December 22nd, 2008 at 12:57 am

So, is this an ingredient in a terrorist plot you’re working on (sort of like holiday baking)?

Comment #16 December 22nd, 2008 at 2:24 am

CW: Of course! The fact that I blogged about it so openly means no one will suspect.

No … wait …

Comment #17 December 22nd, 2008 at 2:30 am

Shouldn’t wordpress filter comments containing the expression “a terrorist plot you are working on”?

Comment #18 December 22nd, 2008 at 2:38 am

To elaborate on the 10% conversion remark: The mass-energy conversion ratio for fusion is about 1/100; for fission it’s about 1/1000; and for chemical reactions it’s about 10^(-9). So if 10% of the mass of an object falling into a black hole is converted to energy, that’s 10 times as efficient as the fuel in a thermonuclear weapon. Placing a black hole in the middle of the Earth is thus similar to replacing the Earth’s core by a hydrogen bomb with comparable mass.

Also someone mentioned that it’s not possible for solid rock to touch an event horizon. In fact, it’s not just impossible because of relevant forces; it’s geometrically impossible. The event horizon really is just a horizon, in the sense of a limit of perception. As you fall into a black hole, the horizon recedes. (And then you’re shredded and vaporized before anyone thinks that you fell in. But if it was an unusually large and inactive black hole, then this discussion would actually be relevant.)

Comment #19 December 22nd, 2008 at 3:20 am

John Sidles answer roughly matched mine, which is what made me ask the question, as it seems to imply that the black hole would take practically forever to do anything, which is very surprising and yes, greatly contradicts David Brin (and Dan Simmons and the people worried about the LHC).

Comment #20 December 22nd, 2008 at 3:53 am

Michael, John’s answer seems inconsistent with Greg’s. I understood Greg’s argument but couldn’t understand John’s, since he never explicitly brought in either the radius of the black hole or the Hawking radiation.

Comment #21 December 22nd, 2008 at 4:10 am

John Sidles,

what is “the momentum associated with the speed of sound” ?

Regardless of how you chose it, it seems to be 10 microns. At that size, I think you get a temperature of 30 K and 10^-13 Watts of Hawking radiation (or 10^-9; I’m doing something wrong). Greg Kuperberg points out a third, much more relevant, failure mode, but 10% of 200 ng / year is about a Watt.

Comment #22 December 22nd, 2008 at 7:50 am

A black hole with a temperature of 300 K has a mass of 1e-26 kg and a radius of 1e-62 m. This is much colder than the earth’s core, and the cross section for interaction is negligible. Based on no math whatsoever, I would expect such a black hole to remain insignificantly small for a time comparable to the age of the universe.

However, this is below the plank mass, and we almost certainly cannot use the quasi-classical theory of hawking radiation for this. If you start with a plank mass (2e-8 kg) you get a radius of 3e-35 m. This is much larger, but still far smaller than the radius of a nucleus.

If I take off from John Sidles, and assume that the black hole is traveling at 5 km/s through iron at a density of .1 mol/cc, I get approximately 1e33 seconds to absorb a second plank mass… I may have totally screwed up my dimensional analysis, but my 5 min is up and my plane is about to board.

Comment #23 December 22nd, 2008 at 8:27 am

Douglas: to put some more flesh on that Fermi calculation, a black hole with a mass of 10^11 kg has an evaporation time in excess of a billion years, and yet it has a Schwarzschild radius of less than a “Fermi” (in SI units, less than one femtometer = 10^-15 m).

Hmmmm … we reason that this small Schwarzschild radius implies that absorption has to come through the

l=0 partial wave, in which case a quantum unitarity bound applies (look up “optical theorem”). Lettingvbe the speed of sound, and estimating the incoming momentum of an iron nucleusp=mv=h-bark=2 π h-bar/λ, the maximum absorptive cross-section for the black hole, through thel=0 channel, is O( λ2)Physically speaking, only incoming iron nuclei having zero angular moment can fall straight into the black hole, whereas the orbits of incoming nuclei with

l>0 “swing around” the black hole and miss it. And within the earth’s interior, thel=0 “quantum conveyor belt” that feeds a black hole turns out to have a (surprisingly small) mass-flow capacity of only a few hundred nanograms per year.The same thing happens on stellar length scales at the center of our galaxy — stars swing around the black hole instead of plunging straight into it.

According to the above Fermi estimate, a meso-scale black holes having mass of order 10^11 kg might be in the “sweet spot” that Scott requested … on time scales that humans care about, its Hawking radiation is low enough for it to be quasi-stable, yet its Schwarzschild radius is sufficiently small, that unitarity bounds prevent it from absorbing mass fast enough to counteract its losses through Hawking radiation.

By the way, the gravitational field at a distance of one meter from such a meso-scale black holes would of order one “gee”, so the main physical danger in approaching one is (presumably) not tidal stress, but rather, being toasted by its Hawking radiation.

All of the above assumes that there were no slip-ups in the decimal places, and (1) the glowing furnace of Hawking radiation doesn’t burn itself a bubble of low-density iron-vapor plasma, which presumably would slow the mass absorption further, and (2) the black hole doesn’t electrically charge itself, or form a quantum-scale accretion-disc, with results of “who knows what”. It would be a pretty considerable undertaking to estimate these (and many other) real-world effects.

Bottom line: it definitely is not physically obvious that meso-scale black holes inside the earth would readily absorb mass — there is grounds for hope that the earth might well “not merely endure, it would prevail” — at least for a few billion years. So enjoy the holidays!

Comment #24 December 22nd, 2008 at 12:59 pm

Michael Vassar says:

John Sidles answer roughly matched mine …Hey, your web site is cool, Michael. Just to apply some transhumanist perspective on this question, let’s begin by noticing that the needed partial-wave expansion of the optical theorem can be found in many “old school” quantum textbooks (it is on-line as eq. 957 of Richard Fitzpatrick’s

Quantum Mechanics: A Graduate-Level Course, for example).But yikes … eq. 957 … we have covered almost one thousand equations before getting to the one we need … so graduate students are led to ask (with justified trepidation) the meta-Fermi question: “How many first-year graduate-level quantum equations are there?”

Let us construct a Fermi estimate. We will take

anothergraduate-level quantum textbook, and ask ourselves how many equations appear inbothtextbooks. Assuming both textbooks have randomly samplednequations out of a universe ofNequations, and thatmequations appear in both books, then the Fermi estimate forNis simplyN = n^2/m.Without belaboring the point, a comparison of Nielsen & Chuang with almost any of the “classic” quantum mechanical texts of last century, suggests that

n ∈10^3–10^4 andm ∈10^1–10^2, so our Fermi estimate for the universe of first-year graduate equations in quantum mechanics isN ∼10^5 or so.A test prediction of this meta-Fermi estimate would be, that there are

O(1)first-year graduate textbooks that cover both partial wave expansions of the optical theorem, and Kraus decompositions of strictly positive maps (POVMs) … and in my experience this is about right.This suggest that an important distinguishing feature of graduate education in quantum mechanics is the choice of a

narrativethat guides the selection of the equations. It is very desirable that graduate students pick a narrative that is congenial to their personal values and goals.Michael, the transhumanists obviously are attempting to provide a new narrative for science … so it is natural to ask, what would a transhumanist selection of fundamental quantum-mechanical equations look like? How would it differ from selection of a quantum chemist, condensed matter theorist, cosmologist, information theorist, stellar dynamicist, combustion engineer, or complexity theorist?

Also, is there a discipline, that attempts to view this quantum universe synoptically? That profession

usedto be physics …then for awhile it was mathematics … now it is the turn of engineering. All three disciplines are ambitious to provide an encompassing narrative, but we all have to be realistic about what can be achieved … and we all have to pay the bills during our studies … and we all have to help keep this planet glued-together during what will be a severely challenging century.Comment #25 December 22nd, 2008 at 1:19 pm

The section 4 of this paper seems relevant:

http://arxiv.org/abs/0806.3381

Comment #26 December 22nd, 2008 at 1:29 pm

I concede this missing step in my argument: How long it would take for the black hole to start growing quickly. I think that what I described would happen eventually, but it is possible that the equilibrium black hole is so small, and yet still massive enough, that it would take ages for it to double in size.

I’m a priori a little skeptical, but here is a calculation. The pressure at the center of the Earth is 380 billion pascals. Now you want to find a black hole whose Hawking radiation has 380 billion pascals of radiation pressure. I think this is a black hole who temperature is 7.7*10^-17 joules or 5.6 million Kelvin. (This is using the black-body radiation pressure formula on the Wikipedia page for radiation pressure.) This is 25 orders of magnitude less than the Planck energy. There is a factor of 8pi in the Hawking radiation formula, so you will get a black hole with roughly 10^24 times the Planck mass, which is then 10^16 kilograms or 10 trillion tons. The Schwarzschild radius is very small; the black hole would be maybe 3*10^-11 meters in radius, which is a little smaller than an atom.

Well, this is so small that it is plausible that the black hole wouldn’t grow all that fast. But it still doesn’t feel right. The matter from the Earth’s core doesn’t have to fall all the way in order to create a gravitational instability, it only has to fall some of the way in. The black hole would be surrounded by some kind of plasma soup fed by the iron from the Earth’s core, and it’s not clear whether it would be stable or unstable, or how quickly it would grow.

Okay, here is a little evidence for instability: The proton mass, is energy units, is much more than the calculated equilibrium temperature. (It’s 1.5*10^-10 joules.) So the plasma would not be relativistic. Most of its mass would be from iron and not from Hawking radiation, and the iron would be cold enough that it could fall closer to the black hole if it wanted to.

The discussion needs a stellar astronomer who understands stability of plasmas.

Comment #27 December 22nd, 2008 at 1:45 pm

Yes, Chouza’s reference was posted while I was writing my comment. This is exactly the plasma accretion calculation that I asked for in my last sentence.

These guys are deriving a much better answer to the question than I can. In fact, when I skim this paper, I’m no longer confident that the temperature that I picked for the black hole really is the equilibrium temperature. It seems non-trivial to decide the threshold size of a black hole that defines Scott’s question.

Anyway I still am somewhat confident of one prediction, that the black hole would blow up the Earth before it ate the Earth.

Comment #28 December 23rd, 2008 at 1:27 pm

I think all these estimates give way to much credit to our understanding what a very small black hole would be like. I mean we are only right now getting some 1% error level predictions of how QCD acts inside a proton – from base principles. All the acclerator stuff is ignoring gravity anyway.

With a Black Hole of say 0.001 (10^-18m) the size of a proton, we are talking interaction cross sections with virtual quarks, gluons, virtual pions, and others as the BH moves through the proton. How would this work? what is its interaction cross section? Do we even have any theory to predict it? What if it interacts and removes a virtual pion from a proton? What about gluon interactions? Where does the color charge go if a quark is consumed and would it actually pull MORE energy from the black hole because a particle to preserve the color balance must be created?

This whole color charge interaction with quark level black holes is really nasty and is not understood at all. Virtual Black Holes of mass on the order of current particles do not seem to be produced or we would see electron magnetic moment effects. So what the heck is going on at that level? QM and the GR rules are breaking down and we cannot predict anything.

Thus this whole question is about an area we really don’t have a theory about. What does angular momentum mean at this level when you are really talking spin states? So you couldn’t have “orbits” as we think of them.

Comment #29 December 23rd, 2008 at 2:55 pm

With a Black Hole of say 0.001 (10^-18m) the size of a proton, we are talking interaction cross sections with virtual quarks, gluons, virtual pions, and others as the BH moves through the proton. How would this work?The physicists are clever enough to draw some conclusions. First, the black hole is so small that you should think of it as a point-like gravitational disturbance. It will mess up a region around because of both gravity and Hawking radiation. For the most part, those effects will be classical physics — but not necessarily easy classical physics. Plasma physics is a complicated topic.

Second, what is going on right at the black hole is weird, but you can still make some rough guesses as to what happens. You’re right that the standard model of particle physics is not completely understood by any means, but the physicists can obtain a lot of interesting partial results that should apply to subatomic black holes.

But again, one tricky point of Scott’s question is that it isn’t clear how big a black hole needs to be to eventually destroy the earth. I was thinking that the radiation pressure from Hawking radiation needs to be more than the pressure at the center of the earth for the black hole to shrink. But I actually don’t know if even that makes the black hole small enough.

Comment #30 December 23rd, 2008 at 2:59 pm

Markk Says:

I think all these estimates give way too much credit to our understanding what a very small black hole would be like …Markk, everything you say about our limited understanding of physics at small length scales is correct. The thrust of the calculations presented in this thread, though, centers upon “ordinary” quantum physics, at femtometer scales and larger, which is pretty well understood.

The main physical point is that the maximal rate at which “ordinary” matter can flow through a femtometer^2 “hole in space” is too small for meso-scale black holes to grow at any significant rate. Which is kind of kill-joy news for science fiction writers … but oh well.

You folks who enjoy Fermi calculations that lead to sobering results might try calculating the elastic energy stored in a space elevator cable — how does this elastic energy density compare with, say, the energy density of explosive primacord?

Another sobering Fermi calculation is the energy-efficiency of chemical rockets. What fraction of the kinetic energy in a rocket exhaust can be captured by the kinetic energy of payload? How does this efficiency compare with (say) a diesel engine? Is there much room to improve the energy efficiency of chemical rockets? What do these physical limits imply for the practicality space tourism?

Not every Fermi calculation yields a sobering result … it would be cheerful holiday fun (and a considerable intellectual challenge) to put together a talk called “Top Ten Cheerful Fermi Calculations (CFCs)”.

Heck, we’ve already got one example …

——–

CFC #1: We don’t have to worry too much about black holes swallowing up the earth!

Comment #31 December 23rd, 2008 at 4:47 pm

“Implications of primordial black holes on the first stars and the origin of the super–massive black holes.”

Cosimo Bambi (Tokyo U., IPMU) , Douglas Spolyar (UC, Santa Cruz) , Alexander D. Dolgov (Moscow, ITEP) , Katherine Freese (Michigan U.) , Marta Volonteri (Michigan U.) . IPMU08-0096, Dec 2008. 10pp. Temporary entry

e-Print: arXiv:0812.0585

My previous comment still awaits moderation, perhaps because it cites unpublished work. So here’s a reference germane to this thread.

Cosimo Bambi et al argue that primordial microscopic black holes swallowed some of the first stars 200,000,000 years ago.

They assumed that the primordial black holes had about the mass of Ceres, smaller ones having evaporated. A star forming in the middle of a dense dark matter concentration would have about 1,000,000 of these black holes intermixed with ordinary mater.

They calculate that the holes eat the star in under 1,000,000 years, gaining somewhere between 10 and 1,000 solar masses in the process.

There are the order of magnitude estimates, and the citation. Let the backs of the envelopes continue.

Comment #32 December 23rd, 2008 at 8:24 pm

Will the black hole stay at the center of the Earth? Like the proof mass of a drag-free satellite, the black hole will be immune to some orbit perturbances that act on the Earth. At some point the hollow-sphere restoring force may be too small to keep the black hole away from the un-eaten shell.

Comment #33 December 23rd, 2008 at 8:58 pm

g Says:

Will the black hole stay at the center of the Earth?You raise a very good point, Mr. G — tidal forces (from the moon, for example), will cause black hole(s) inside the Earth to “slosh” back and forth. This in turn will exert drag forces on the Moon, causing its perigee to advance or retard, relative to Newtonian predictions. Of course, the oceans do the same thing, so it is not realistic to use lunar orbital observations to observe black holes inside the Earth.

If only the Earth had no oceans … if only the Moon were closer … wait a minute … aren’t we describing the planet Mars and its moon Phobos?

A check of the literature finds that exactly such a non-Newtonian motion of Phobos is observed; there is in fact quite a considerable body of recent literature on it (see appended BibTeX).

This motion has never been fully accounted-for, and so we are led to ask the Fermi question: “How much black hole mass (or better, dark matter mass) need be gravitationally trapped within Mars, and how much need its motion be damped, to account for the secular acceleration of Phobos?”

This IMHO would be a fine undergraduate-level research project … certainly there is plenty of astrometric data available to constrain models.

—-

@article{Journal = {Nature}, Title = {Solar eclipses of Phobos and Deimos observed from the surface of Mars}, Author = {Bell, J. F. , and Lemmon, M. T. and Duxbury, T. C. and Hubbard, M. Y. H. and Wolff, M. J. and Squyres, S. W. and Craig, L. and Ludwinski, J. M.}, Month = {07}, Number = {7047}, Pages = {55–57}, Volume = {436}, Year = {2005}}

Comment #34 December 23rd, 2008 at 11:23 pm

Given Hyperion, this is a trick question – its not about physics, but computation. Simply create the AI which tricks the Kiev team into creating the black hole which sinks to the center and eats the planet. Once the AI is created, you don’t need to worry about the calculations (assuming an efficient AI).

All of which fits the interpretation that Scott is the AI, or at least the precursor to it. Not that there’s anything wrong with that.

Comment #35 December 24th, 2008 at 1:38 am

Yeah I am not knocking the discussion, it’s fun and more interesting than most! And the BoE calculation of the amount of matter that can pass through a proton sized hole is pretty conclusive in its way. How closely that is related to the real world is a very open question is what I am saying.

Even at the proton sized level, are there any papers trying to created an actual model of a black hole and its quantum field implications? Hey where are you string theory when you could do some good? The whole color charge vs black hole thing bothers me. Did Hawking come to terms with that in his work? Electrical charge is discussed, color charge is just as fundamental. I won’t ever have time to look. There must be calculations about the variation in apparent size of the event horizon, to get estimates of radiation, but at what level? I’m not believing GR spacetime metric functions hold at this size. Aside from “classical” means, how would one calculate a real quantum interaction probability?

I am really just hung up on this – this question hits right where the two big physical theories break down, and why we consider them both incomplete. Thus I don’t trust any extrapolations in this area, I guess. On the other hand, if someone forced me to bet on rates of growth I would have to go with the “Fermi” calculations.

Comment #36 December 24th, 2008 at 2:54 am

#28: “Where does the color charge go if a quark is consumed and would it actually pull MORE energy from the black hole because a particle to preserve the color balance must be created?”

Not even wrong. You can’t pull color out of a proton by throwing one of its constituent quarks into a black hole. You are neglecting or misunderstanding Caltech’s David J. Gross, and Frank Wilczek working together), plus H. David Politzer (working independently) who won a Nobel Prize for proving that the strong force between quarks becomes weaker at smaller distances and that it becomes stronger as the quarks move apart, thus preventing the separation of an individual quark.

Comment #37 December 24th, 2008 at 4:22 am

I really agree with Markk, though it is a really fun idea to speculate about (though I am not trained enough in these matters to contribute).

At the risk of sounding crankish, I wonder, if the Hawking radiation Greg expects were as great as he suspects, wouldn’t it be a nice mechanism to explain the internal heating of Earth (and other hot celestial bodies)? So the crazy question: is there any way to modify current gravitational theory to allow a black hole inside Earth that results in the major observed qualities, like the internal structure (scales, densities, observed speeds of sound, maybe a perturbed black hole?), and the internal heat (I know we attribute it to radioactive decay, but it seems poorly understood).

Of course there is the obligatory crazy follow up question: how radically different would our understanding have to be to permit such a radical explanation?

I suspect that gravity is more poorly understood than we think, simply because we cannot measure masses too far outside our own scale, and because modern cosmology appears to contain a lot of ad hoc adjustments (dark matter, dark energy, and inflation). The alleged Pioneer anomalies, galaxy rotation, and apparent cosmological constant could all be hints to improve GR. (Or they could be insignificant of course.)

Comment #38 December 26th, 2008 at 11:24 am

Jonathan, ahh…, we (humans) pull quarks out of protons all the time. The Tevatron is doing it every day by colliding quarks together, that is, when protons interact what is happening is that (well sometimes) quarks are interacting with each other. and quarks get “ejected” from a proton or anti-proton. What happens is that other quarks are created with the energy from the collision and breaking bonds such that color charge is kept balanced from “far away” (i.e the “asymptotic” in asymptotic freedom). That is what the “jets” are at accelerators. We understand this fairly well with things like the current Nobel prize CKM matrixes and many other QCD calculations.

What we are talking about here though is a black hole with an event horizon so small that it is 100th the diameter of a proton. It could interact with a quark INSIDE the proton and if the quark is suddenly inside the event horizon, what happens to the color charge? That is the open question. SU(3) and asymptotic freedom play here, but this whole area is a mess. Most of the mass of a proton is in its binding energy, i.e. in the energy of its virtual gluons and pions. How the heck would these interact with a black hole of this size?

Comment #39 December 30th, 2008 at 10:29 am

Hmm.

As long as you’re outside the event horizon, the gravitational field of the blackhole just depends on the mass of the blackhole and the distance to it.

I see that the earth’s inner core is 1200 km in radius and made of solid iron (its very hot but stays solid because the pressure is high).

A blackhole with a radius of approximately 0.5 cm would have a mass equal to 1/10 of the earth’s mass.

That wouldn’t create enough extra gravitational pull to chip away at the inner core material (and any material that’s swallowed wouldn’t affect the mass of the black hole, so no sort of gravitational collapse chain reaction is possible here).

I’m just not clear how long it would take for such a small black hole to “vaporize” into radiation.

We could probably increase the black hole mass by 10, for a radius of 5 cm and a mass equal to earth’s and it still wouldn’t create any collapse (although that would put some strain on life at the surface).

Comment #40 December 30th, 2008 at 10:37 am

According to the wiki entry on black holes

“In order to have a Hawking temperature larger than 2.7 K (and thus be able to evaporate) a black hole needs to be lighter than the Moon (and thus have diameter of less than a tenth of a millimeter).”

So a black hole that’s 1 cm in radius (20 times the mass of the moon, 1/5 of earth’s mass) should be stable enough?

Comment #41 December 30th, 2008 at 8:31 pm

I seem to remember that there is a connection

between quantum computing and quantum groups, at least

quantum SU(2).

Any reference or opinion?

The closest I found were holonomy models for quantum computation.

Any opinion on these?

Thanks

Ivan

Comment #42 January 3rd, 2009 at 12:48 pm

Scott ->

You should read Death from the Skies.