ok... quick calculation here:

density of earth = 5513.3 kg/m^3 (from Wikipedia)
radius of earth = 6372.797 km (from Wikipedia)

so you have 7.03e+11 kg per square meter column through the planet, and at around 6.022e+23 atoms per kg (give or take an order of magnitude) you get 4.2e-11 atoms per square meter column.

now, if we assume that the mini-black hole has the mass of a proton, then we get a schwarzschild radius of around 2.5e-54 meters. That's pretty freaking small, so just to be generous, I'll assume the mini-black hole has the size of the classical radius of the electron, i.e. 2.8179e-15 meters (from Wikipedia), almost 40 orders of magnitude larger.

therefore, the cross-section for the black hole is pi*r^2 = 2.5e-29 m^2.

this then leaves us with about 1.06e-39 atoms along the path of this mini-black hole through a single pass of the Earth.

so, assuming that the mini-black hole is moving at the speed of light, it would take about 0.4 seconds to pass through the Earth, and about 4e+38 seconds to encounter one atom. That's about 1e+31 years.

Someone should check my logic and math here. Now it is possible that the geometric area is not the appropriate interaction cross-section. So, for the sake of argument, let's assume that I got the interaction cross-section off by 20 orders of magnitude. That would still seem to mean that it would take on average about the age of the universe for the mini-black hole to encounter one atom.

does this look right?

Very good, just the BH would not move at c. As it has v=0 after its creation it should move quite "slowly" towards earth gravitational center. At surface it would accelerate with 9,81m/s^2 and would be accelerated stronger the closer it gets to the core.
EDIT: No it would not be accelerated stronger. The mass between the BH and the core is decreasing the closer it gets as it is now inside earth and the outer part should even pull it outwards...
So ,what would that mean for the resulting gravitational force?

My head is spinning.

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Looks pretty good to me. I once went through this exercise for a science fiction novel I wrote (unpublished). It included the accidental creation of a 400 ton BH, which then fell into the Earth. I had to make some pretty huge assumptions for this to be the terrible threat I wanted it to be.

First, I had to assume that the BH was drawing in enough matter to counteract the Hawking radiation (or, I could have assumed that Hawking was wrong.) If I didn't make that assumption, the BH would have evaporated almost instantly -- with a very large kaboom, but no "eat the Earth" concerns.

Then, I had to assume that the BH's effective radius was much, much larger than its Swartzchild radius due to tidal effects. If I didn't make that assumption, the BH would have picked up only a few atoms each pass through the Earth, far too little to worry about over the life of the Sun. Naturally, this would also have meant it would evaporate too quickly.

So I did quite a bit of hand waving to make the story go the way I wanted. And that was with a BH of 400 tons, not two particles. And even then, the threat was not immediate, but might have started to show effects in a few hundred or thousand years. "Not on my watch," as my fictional President remarked.

I ended up being thoroughly convinced that micro black holes were very low on the list of things to be worried about.

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Relight the Firefly!

"It is quite clear that Occam's razor does not sharpen in your pyramid." (Nicolas)

"Still, a man hears what he wants to hear and disregards the rest." (Paul Simon)

I'm worried the LHC might break something. Snap, and we won't even know it. The thing that breaks could be the thing called Symmetry. And we all turn into zillion-degree quark-gluon plasma at the speed of light. Uh, no, it'll be even hotter than that.

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You might be referring to the idea that we (meaning everyone in the universe) are living in a false vacuum? Or perhaps this is just a real example of the type of thing you could be talking about.
It's been thrown out there that if this (the false vacuum) is the case, particle accelerators could trigger the end of existence as we know it - check out the wiki article on false vacuums. Check out the last section titled Vacuum Metastability Event.
I read about this years ago and I'm not sure the current thought on this topic though.

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Sounds like fun to me. Just relax bmpbmp.

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actually, wow, i screwed up big time...

i accidentally had 6.022e-23 instead of 6.022e+23 in my code!!

so, basically i'm off by 46 orders of magnitude in my numbers... so, now it does become important whether i use the Schwarzschild radius or the classical radius of the electron.

so, i guess it all depends on what the interaction cross-section for the mini-black hole with atoms in the Earth would be...


sorry... i'm quite embarassed...

Or if everything else fails you can always wait for:

did you correct for the speed?

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"Who does not know anything, must believe everything."
Baroness Marie von Ebner-Eschenbach 1830-1916
our animal welfare board and organisation

Well due to the higher density of the core relative to the mantle, the gravitational pull actually does increase until you get close to the outer core, then it begins decreasing again, and is 0 at the center. So a black hole with 0 initial velocity will basically orbit inside the earth forever.

The important questions are, will it evaporate due to hawking radiation, and if not how quickly will it accrete mass. The answers as we know them are "almost definitely" and "so slow the earth will be gone before it even weighs a measureable amount".

What you are forgetting is that, as has been pointed out repeatedly in this thread and others, there are natural events hundreds of millions of times as energetic as those in the LHC that take place naturally at a considerable rate on Earth and probably pretty much everywhere in the universe except the big voids between galaxies. If high energy particle collisions had the potential to destroy the universe it would have already happened and we wouldn't be here.

There are also almost certainly even more energetic events which take place in extreme environments like neutron stars and magnetars which would be even more likely to disrupt the basic functioning of the universe if it was possible to do so as easily as you are worried about.

Such as collisions of galaxy superclusters...

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our animal welfare board and organisation

For those interested, this is the LHC home page. It discusses the current status of construction and the describes the experiments that will be going into the interaction regions. They have written up a report on the exceedingly remote chances of the LHC causing TEOTWAWKI which one can find here. For those concerned about the state of the Earth check here for the current status.

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"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

I have read the document and have no clue what they are talking about the CERN LHC one I mean as for the earth detroyed one that is a joke site right

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Don't Hate Me Cause I Am Dum

Well, bmpbmp, you wanted the scientific reasons why physicists aren't concerned about the LHC ending the world. I gave it to you in the physicist's own words. What more did you want? How did you understand the imagined threat if you didn't understand the report. Frankly, it's better than any summaries from wiki, etc. The paper is actually aimed at a knowledgeable, but non-scientific audience. Hopefully you at least understood the abstract.
Or do you just think they're trying to whitewash the issue?

As to the Earth destruction status page. Yes, it's a joke. But the links through it that describe various ways to destroy the world, and the vanishingly low likelihood of any of them happening are educational. You'll probably find most of your fears discussed there.

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

Well, if I were thinking of doing something that had a realistic chance of ending the world, I'd whitewash it. That way, after I'd done whatever it was I was going to do, if the world did end nobody would be looking to blame me for it.

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Never attribute to malice what can be adequately explained by ignorance or stupidity.
Isaac Asimov

Well obviously you are not an EVIL GENIUS. Don't you know that every Evil Genius and Mad Scientist has to tell all the details of their plan to destroy the Earth, just before they put it into affect?

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Quite so, AND they do not pass the plan to their 8 year old Evil Geniuses Quality Control Dept. either......

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Strictly speaking, it's more dangerous to muck around with the 1918 Spanish Flu Virus than the Large Hadron Collider, (and no I am not saying that Canadian Researchers should have not re-created the virus to study it) and yet no panic about it....

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I think it is far more likely for the earth to be destroyed by an accidental deployment of self-replicating nano-machines. (I could've sworn there was a whole other hemisphere, over there...)

I'm not so sure even that is very likely.

The earth is swarming with self-replicating nanomachines (not to mention self-replicating micro- and macro-machines), but it seems that in all cases, the raw material and power requirements are too stringent, and none of them can quite make the leap from "viable" to "unlimited".

I suspect we would have to go greatly out of our way to craft a nanobot capable of overcoming the natural obstacles to a nano-apocalypse. It would probably never happen, simply because nanobots of this type would be totally useless, and it would be difficult to create nanobots with this capability as an unforseen side effect.

Nano-apocalypse? A disaster so small it takes an electron microscope to notice it?

I'm not worried.

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Relight the Firefly!

"It is quite clear that Occam's razor does not sharpen in your pyramid." (Nicolas)

"Still, a man hears what he wants to hear and disregards the rest." (Paul Simon)

You're thinking of the nanocalypse.

Also not worrisome: the microcalypse, the picocalypse, and the femtocalypse.

Doing something New a DANGER???? How do you know? (How can you know?) How do you intend to find out? Do you intend to find out?

Thog the caveman: Don't light that fire. It might anger the Gods and cause them to destroy the world.
Grok the other caveman: Shut up. It's freezing and dark up here, and it might be useful.

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Agreed. Hawking's radiation theory for black holes (is that still valid) indicates they'd self-radiate themselves away nearly as fast as they were created, and long before any accumulation of additional matter. I think there's a certain critical mass required to continue to attaining additional mass, but that critical mass is quite large, even in the presence of considerable additional mass. From what I remember, it's many powers of times more massive than what the hadron colliders could ever hope to achieve.

I recall a similar fear among the atomic bomb scientists. A couple of them feared the bomb would be powerful enough to smash adjoining matter into other matter with sufficient force to create a sustaining chain reaction.

Back then, only a few knew differently, but even some had admitted later they had their doubts, too. Know we know differently.

We might be wrong about the current experiements, but I doubt it, as we're operating with a vastly more detailed understanding and experiential evidence than the Los Alamos folks.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

A BH can grow only if its initial energy density is above 10^10 GeV/fm^-3 assuming a plank mass of 1TeV.

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"Who does not know anything, must believe everything."
Baroness Marie von Ebner-Eschenbach 1830-1916
our animal welfare board and organisation

Why is the Large Hadron Collider so damned big if it is not using that much energy at all??

Be mindful of the relative scales here. On a "destroy the planet" scale, the LHC is generating the relative power of being punched in the face by a gnat. On a "light up a city block at night" scale, its a significant amount of energy required. Its large because the strength of its magnetic fields require that level of machine muscle to achieve it.

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The last time I felt a warm fuzzy feeling, I was informed by my doctor that it was just gas.

I already told you about that.
The majority of the used energy goes into the magnets and computers.
To accelerate a neutron to 1 GeV you need exactly this energy....
The rest is used to make it constantly alter its course.

__________________
"Who does not know anything, must believe everything."
Baroness Marie von Ebner-Eschenbach 1830-1916
our animal welfare board and organisation

I thought it was Tev??