Will the Earth be sucked into a tiny black hole in June?

It is said that scientists involved in the Manhattan Project to engineer and implement the first nuclear bombs seriously considered the possibility that such a bomb could initiate a chain reaction that would destroy the Earth. Now it is being claimed that the production of miniature black holes by the Large Hadron Collider (LHC) at CERN in Switzerland could do the same. The LHC is scheduled to go on line in June.

This thought occurred to me the first time I heard that the LHC might be able to produce tiny black holes.

Apparently someone else had the same thought. Walter Wagner and Luis Sancho have filed a law suit in federal court in Hawaii to stop the LHC scientists from goofing up and ruining everything.

Walter L. Wagner and Luis Sancho contend that scientists at the European Center for Nuclear Research, or CERN, have played down the chances that the collider could produce, among other horrors, a tiny black hole, which, they say, could eat the Earth. Or it could spit out something called a "strangelet" that would convert our planet to a shrunken dense dead lump of something called "strange matter." Their suit also says CERN has failed to provide an environmental impact statement as required under the National Environmental Policy Act.

Although it sounds bizarre, the case touches on a serious issue that has bothered scholars and scientists in recent years -- namely how to estimate the risk of new groundbreaking experiments and who gets to decide whether or not to go ahead.


CERN scientists claim that they have considered this possibility and that it is not going to happen.

People who seem to know about this stuff
claim that this law suit is not likely to go anywhere.

Phil Plait, at Bad Astronomy, has this to say:

...off the bat, this sounds nuts, but really it's not so nuts that we shouldn't look into it. There are two causes for some concern: one is that LHC might create a black hole which would eat the Earth, and the other is that a very odd quantum entity called a strangelet might be created, with equally devastating results.

However, I don't think there's anything to worry about. I want to make that clear up front....

...If two subatomic particles collide at high enough speed, it's possible that they will collapse into a black hole. If that happens, it would fall through the Earth and, well, you can guess what bad things would happen then*.

However, studies done by CERN show that the energies generated will be too low to make black holes. Also, due to a weird effect called Hawking radiation, the tiny black holes would evaporate instantly. The two litigants, however, say that Hawking radiation is not an established fact, and therefore we should be more careful. While that's technically true, they forgot something important: the same rules of quantum physics that make a black hole in a subatomic collision also indicate they would evaporate. So if you're worried they won't evaporate, then you shouldn't be worried they'd be created in the first place.

This issue comes to mind because of an email I recieved today from Haanuddin, stating:

I want you to have a look at the new model I am advancing. If correct it is nothing short of revolutionary. But there is no time for resting on laurels. The model's most ominous implication is that it predicts that mini black holes will be stable, which is of immediate concern because of CERN's hopes to generate man's first mini black hole.

The model was written in more lay-language than is usual because once the implication of stable mini black holes was identified, the need to foment politic change was seen as only coming from the masses.

His model is outlined in a PDF file available here, and is being discussed on his Scientific American blog, here. This is a Theory of Everything, which is always a bit suspicious. Hasanuddin's model ...

...deductively presents seamless explanation for all major cosmological events from Big Bang to the present. The model continues to project how ... situations will align to produce the next Big Bang. ... The new model has undergone significant review on this blogspace. Detractors have been understandably vehement (their life's work is being called into question.) However, despite their best efforts, these detractors have not been able to supply any evidence against the new model, instead three of them ultimately supplied new evidence supporting the new Dominium model. The frontier of Physics is transforming before our very eyes. ...

The new Dominium model ... calls into question the risk analysis done by CERN to justify CERN's own current practice and direction with regards to the LHC machine. The new model deductively shows that mini and micro black-holes are expected to be "stable." This conclusion is contrary to the core safety assurances that CERN has used to justify the inherent risk of LHC. If mini black-holes are "stable," they will not harmlessly evaporate away as CERN cheerleaders would like us to believe. If mini black-holes are stable, then it is probable that the entire planet would ultimately be consumed over the course of several decades. Political, financial, and societal institutions would unravel. The expected sequence of events that would tightly mirror the omens forecast by both the Bible and the Quran. Is this newsworthy?

Well, OK, so you might think that Mr. Hasanuddin is crazy. Could be. But this is an interesting situation where the costs of being wrong are very high, even if the chance of being wrong is very small. Go back and read Phil's comments above: The best argument we have that nothing will go wrong is that if the black holes form, they will evaporate, but that the science predicting either is both a) uncertain and b) the same. So if the uncertain model of black hole formation is correct, they will evaporate. But since it is an uncertain model, how do we know?

Now, there is an empirical test of the black hole model, and I think we should get working on it right away.

It starts with the Sagan calculation. There are billions and billions of galaxies each with billions and billions of stars etc. etc. so the chance that intelligent life with advanced technology has evolved and developed elsewhere in the visible universe is pretty good. Now, we add one more step to the equation: Some of these intelligent life forms would have build a particle accelerator much like that at CERN, and by now would have carried out the activities pursuant to making these tiny black holes that are supposed to evaporate.

If they did not evaporate and instead became real, lasting black holes, then we should be able to see them, right? So look! Most black holes, as I understand it, occur near the central regions of large galaxies. But the stars most likely to support life occur medium distances out from these centers, not to near the middle of the galaxy, not too far out on the edges. They would be in the "just right" zone.

But the "just right for life zone" (JRLZ) would not be the same zone as the most likely zone for the formation of black holes. So we look in the JRLZs for evidence of excessive black holes.

If we see too many black holes in the JRLZ, we have two important likely results:

1) Don't fire up the black hole experiment because things may go very badly; and

2) We can now, for the first time, put an end-value on the Sagan equation, which would be cool (if not too informative).

OK, let's get to work on this, shall we?

UPDATE: Read more about it here.

UPDATE: For a completely different perspective on the large hardon collider, see this.


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Who is correct here? We don't know, you don't know, it is uncharted territory. Would you bet the entire human history and the existence of our solar system on it? I wouldn't. --from a user comment on my old website on the topic of the Large Hadron Collider Back when all the hype and hoopla…
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If a high energy particle collision had any significant chance of creating anything likely to 'eat the Earth' we wouldn't be here to talk about it right now. Because high energy (MUCH higher than anything mankind is likely to be able to ever create) particle hit the Earth every day. Many of them.

We are still here (as are the other planets, the stars and much other stuff). Ergo, the risk is negligible.

By Benjamin Franz (not verified) on 11 Apr 2008 #permalink

Uh oh. Am I being cited as someone who "knows about this stuff"? Or, hopefully my commenters are--I think they are much more reliable sources.


I was thinking about the logical and ethical side of it, not necessarily the physics. NOBODY knows about the physics....

I've blogged about this myself:

"Nobody" knows about the physics? Come on, Greg -- some of the best particle theorists in the world have weighed in on this, more than once. CERN physicists have studied the matter not once, not twice, but THREE times -- the third safety assessment report is currently undergoing rigorous peer review and will be released before the start-up in June (although it might be later, though not because of any frivolous lawsuit).

If planets were out there, eaten by black holes created by other intelligent life, we wouldn't be able to see it. Black holes don't change the rules of gravity, they're only as massive as what goes in, in this case a planet about the size of earth. We're only beginning to be able to detect planets of this size and only very close to us, not in other galaxies. So at most we can detect these sorts of black holes within a few hundred lightyears, and we're looking at them anyway while we search out extraterrestrial planets.


Jennifer, Drekab ... you do realize I'm making fun, yes? I mean, really... /end whisper...

Jennifer, thanks for that link, I've added it to the post.

Oh crap.
I've booked my summer vacation in July.

The risk evaluation forum is not using any recognized methodology to justify their advocacy to shut down LHC.

Review of physics for risk management professionals:

Protons are composite particles, with a radius of about 10^-15 m = 1 femtometer = 1 fm

Quarks and leptons (electrons, neutrinos) are hypothetically non-composite and point-like.

Subatomic nature of solid matter: Most matter at the sub-femtometer scale is empty space with a distribution of relativistic fermions.

All fundamental fermions (quarks, leptons, etc.) have an angular momentum of h/4π (or 3h/4π if you assume SUSY).

GR Schwarzschild black holes are non-rotating. They have radius r_{Schwarzschild} = 2Gm/c²

Black holes work by a central force, so they conserve angular momentum. This mean they do not hoover up star systems, but are sloppy, inefficient eaters at best. For a GR black hole, the capture cross-section for relativistic particles is a small multiple of the geometric cross-section: σ = πkr² = 4πkG²m²/c^4 (Where k might be some number larger than 4.25 -- I used 9 in my table).

The rate at which a sub-femtometer scale black hole consumes the Earth can be closely approximated by treating it as carving a cylinder. For a Earth of approximate diameter, 2 r_{Earth} = 1.27×10^7 m, density D = 8000 kg/m³, and ½ LEO period, T=44 minutes, we can compute the rate of mass consumption as D(2 r_{Earth})σ/T (LEO = Low-Earth-Orbit, if you aren't a rocket scientist.)

This rate is highly optimistic since even a small non-zero motion relative to Earth's center will cause the period to increase and the chord of Earth to be a non-diameter.

GR can't be the end-all to black hole physics, since GR has no quantum effects.

* Effect one: Hawking evaporation

According to Hawking, black holes lose mass due to evaporation at a rate of hc^4/(30720π²G²m²)

This means they have a lifetime of 92160π²G²m³/(hc^4)

This also means that there is a minimum mass, below which the black hole evaporates faster than it gains, m_0 = (c²/G) ((2640 s) h/(245760π³k(8000 kg/m³)(1.27×10^7 m)))^(1/4)

* Effect two:

Black holes with too much angular momentum aren't black anymore (they are naked singularities). This limit on angular momentum is related to mass. Just below the Planck mass is a mass where a spin-less black hole cannot absorb a fermion without losing it's black-ness. This means that for smaller black holes, their capacity to absorb matter must be severely reduced from the non-quantum estimates.

LHC throws protons together with a center-of-mass mass-energy of about 14 TeV, but the interesting collisions are the quark-quark collisions which are designed to happen with a center-of-mass mass-energy of 2 TeV.

There is no records of collider experiments producing products with zero velocity in the lab frame. Since most products are highly relativistic, a crude estimate of quark-quark center-of-mass velocities < 10^-5 c is 0.001% which is 2 orders of magnitude less than Walter Wagner's lowest estimate.

LHC has a planned luminosity of 10^38/m²s so that events with a cross-section of less than about 3×10^-51 m² have less than even odds of being seen in a billion years of continuous LHC operation. For comparison, a 2 TeV GR Black Hole has a cross-section of about 10^-100 m²

A hypothesis (notably discussed in CERN Courier) with as yet no experimental data, called XLD, for Extra Large Dimensions, speculates that 2 TeV black holes might have a radius larger than the 5.30×10^-51 m predicted by GR, with correspondingly larger cross-section. XLD does have Hawking evaporation, as its authors started with quantum theory to get to XLD. There seem to be no good reason for equating 2 TeV with a XLD black hole radius of 0.0001 fm, except for the publicity reasons that just happens to make the luminosity-cross-section product near the 1 black-hole per second that makes the paper inflaming to the imagination.

The black hole disaster scenario uncritically accepts 2 TeV = 0.0001 fm, which begs the question about growth. It seems obvious that a 0.0001 fm XLD 2 TeV black hole would have far less gravity than a 0.0001 fm GR 67,500 ton black hole, so that the factor k would be exactly 1. It also seems obvious that the XLD-mass-radius curve must approach the GR mass-radius curve so that macroscopic GR (which is observed) is preserved. So XLD black holes must increase in radius very slowly over the 2-TeV to 67,500 ton mass range ( 31 orders of magnitude! ). This means that growth is not geometric, but linear, taking billions of billions of years to grow to 67,500 tons -- if we suppose (as they insist) that we discount Hawking evaporation for the trifling reason that we haven't observed it yet. (This is highly inconsistent, since we haven't observed sub-stellar-mass black holes or evidence for XLD, but they insist on those.)

So even if LHC makes stable 2 TeV, 0.0001 fm black holes at a rate of 1/second for 1500 years (50 billion black holes), and even if each we produced at exactly zero relative motion relative to Earth's center, over 10 billion years they would only grow to 3.8×10^-13 kg (each) for a total mass of 19 grams of black hole against the Earth's mass of nearly 6×10^24 kg. (Except that even 3.8×10^-13 kg is well below the Kerr limit which keeps tiny black holes from absorbing fermions.)

The problem with risk analysis and the black hole disaster scenario, is even when we assume as facts the hypotheses they come up with, the numbers indicate the risk is actually zero.

Black Hole GR Hawking Hawking In-Earth
Mass Radius Lifetime Mass Loss Mass Gain
(kg) (m) (s) (kg/s) (kg/s)
3.57E-024 5.30E-051 3.80E-087 3.13E+062 3.05E-092 2 TeV = LHC quark-quark energy
2.50E-023 3.71E-050 1.30E-084 6.39E+060 1.50E-090 14 TeV = LHC proton-proton energy
5.35E-016 7.94E-043 1.28E-062 1.39E+046 6.87E-076 300 EeV = Observed cosmic rays
1.54E-008 2.29E-035 3.06E-040 1.68E+031 5.69E-061 Limit for black hole to absorb fermion and stay black
2.18E-008 3.23E-035 8.63E-040 8.41E+030 1.14E-060 Planck Mass
1 1.48E-027 8.38E-017 3.98E+015 2.40E-045 LHC Safety limit on GR BH creation
6.75E+007 1.00E-019 2.58E+007 8.74E-001 1.09E-029 GR BH Radius = 0.0001 fm
1.73E+011 2.57E-016 4.34E+017 1.33E-007 7.18E-023 Hawking Decay time = age of universe
1.00E+015 1.48E-012 8.38E+028 3.98E-015 2.40E-015 Hawking/GR safety limit Earth-internal black holes
5.97E+024 8.87E-003 1.79E+058 1.12E-034 -- Mass of Earth
1.99E+030 2.95E+003 6.59E+074 1.01E-045 -- Mass of Sun (no known black holes smaller than this)
6.00E+039 8.91E+012 1.81E+103 1.11E-064 -- 3 billion solar masses, largest known black hole

Risk Analysis for non-professionals:

When I said that the risk is zero, I am not saying that the risk is almost zero, but actually zero. Since the probability that the hypothetical physical laws assumed by the disaster scenario are right is almost zero, but the cost of the hypothetical physical laws assumed by the disaster scenario being, by accident, right about both the 2 TeV black hole radius and the non-existance of Hawking radiation is zero, since the Sun's expansion to Red Giant phase ("The Sun is expected to become a red giant no later than 7.5 billion years." - Wikipedia and every undergrad astronomy textbook) will return real estate values to zero before the total mass of LHC-generated black holes grows to be even 19 grams.

Thus I calculate: risk = chance * cost = almost-zero * zero = zero

Mudane risks, including Walter, Luis and other scenario advocates starting a riot, or power systems blowing up, injuring LHC staff, have almost-zero chances but non-zero costs, so their risks are merely almost-zero. These are simple calculations, but these various hypotheses are simple beyond the point of being physical models.

Now I have to go before Dr. Laden tells me to get my own blog.

For a completely different perspective on the large hardon collider, see this.

They're going to fling male porn stars at relativistic speeds at each other?

BTW, it could lead to a "Dies the Fire" incident. Check out author "S. M. Stirling" for details.

Oops, I said k should be larger than 4.25, but I meant 2.25 (9/4). Now I'm worried that I need to recheck my tax form.


Oopes? Ooops? You are giving us oops? And we are to believe that the world is not ending in June?

By Elizabeth (not verified) on 11 Apr 2008 #permalink

Because it is a harmless error, and it's in the direction that favors the disaster scenario.


By Elizabeth (not verified) on 11 Apr 2008 #permalink

I think we can pretty much ignore the two idiots who have filed this law suit. If they cannot work out CERN is located in Switzerland and France and that a court in Hawaii is not the relevant place to file such a suit then they would not seem to know much about anything. Certainly law and geography are closed books to them. I believe a spokesman for CERN questioned why a US Federal court in Hawaii has anything to do with what CERN does.

By Matt Penfold (not verified) on 11 Apr 2008 #permalink

Keeping it simple for the CERN cheerleaders, the earth can't move an inch without getting hit by cosmic rays, that's why we're still here. For the dense, this means we're not moving at light speed.

Now the protons in the LHC will be traveling at each other at light speed till they smash. Do you still want CERN to perform this experiment?

Think CERN sheep, you have a brain! USE IT!

By Physicist (not verified) on 12 Apr 2008 #permalink

People keep saying that the events CERN will create are happening all the time on the earth, so don't worry. But if the events CERN will create are really happening all the time on the earth, then why are they building CERN? This argument does not hold up.

We're doomed.

Terbok, these events happen all the time in the upper atmosphere. We want them to happen in repeatable, controlled conditions where we can easily see what is going on.

(I'm not going to respond to "Physicist" other than to note that you need to at minimum learn some actual physics)

rpenner, thanks for your detailed account. It differs positively from all the pseudo-scientific bull that is often generated by pro-LHC bloggers. However, the assumption that black holes are subject to linear growth defeats the logic, I think with all due respect to your calculations, since - plainly spoken - the gravity of the mass accumulating in a black hole increases relative to its environment in a non-linear way. It may start off in a seemingly linear way, but the threshold towards non-linearity would be transgressed soon enough. Thus I don't agree with the zero-risk result.

By brickinthewall (not verified) on 13 Apr 2008 #permalink

I'm still worried about Y2K

By Saeid Ghandi (not verified) on 13 Apr 2008 #permalink

But did all you really smart people do these do the calculations in Y2K-compliant manner? Have you checked?

I hear that a spinning black hole looks like a donut with its event-horizon and all that stuff. That's what got my attention.

But now it looks like the donut may eat us.

I think that's really scary.

By Homer Simpson (not verified) on 13 Apr 2008 #permalink

If the fear is actually a good probability, it would be an excellent time to borrow a great deal of money with which to enjoy the last 6 or 8 weeks of life!!!

By v j rannik (not verified) on 13 Apr 2008 #permalink

If the fear is actually a good probability, it would be an excellent time to borrow a great deal of money with which to enjoy the last 6 or 8 weeks of life!!!

By v j rannik (not verified) on 13 Apr 2008 #permalink

If physicists know what will happen before, during, and after the experiment, why do it all?

Clearly I'm not a scientist, but you do experiments because you don't know what the outcome will be, correct? Seems like there is an element of uncertainty. At least that's the way it looks.

I'd sorta like the scientists to be a little more sure of themselves before they power this thing up. Once done, it sounds like it can't be undone, and I have plans for the rest of my life I'd sure like an opportunity to carry out.

The other thing is, what no one has really addressed about this device (that I've read, anyway) or what it does is what it might be used for some day. Why have they made this device? Will the LHC become mankind's next global annihilation device, to be used to threaten the world?

Am I being niaive? I am being overwrought to ask?

Thank God, because I was really starting to worry about the prospect of President Hillary. As it turns out, worst (and shortest!) summer vacation ever.

By Richardson (not verified) on 13 Apr 2008 #permalink

a completely different perspective on the large hardon collider


Historical comments:
There was concern at the time of the Manhattan Project that the intended chain reaction could cause a chain reaction in other materials and "set the atmosphere on fire."
Collapse of the Vacuum. Discover magazine once wrote, "An abrupt, disastrous phase transition is a possibility. Very early in the history of the universe, according to a leading cosmological model, empty space was full of energy. This state of affairs, called a false vacuum, was highly precarious. A new, more stable kind of vacuum appeared and [...] quickly took over. This transition unleashed a tremendous amount of energy and caused a brief runaway expansion of the cosmos. It is possible that another, even more stable kind of vacuum exists, however." There have been conjectures that a collider experiment producing conditions not found in nature could product another phase transition, in effect restarting the universe (and ending ours).

We could call these the "Is the Universe Fireproof?" questions. The second does not only concern us who inhabit Earth. If we are not alone, it appears, first, that our counterparts elsewhere have not yet unleashed a cosmic catastrophe and, second, that they have not intervened to prevent us from doing so, either because they don't know about us, or aren't worried, or can't.

Has anyone payed any attention to rpenner? Sub-atomic particle collisions like those that take place CERN and LHC happen ALL the time in deep space, even on earth. If such collisions did generate threatening black holes that didn't evaporate as soon as they became into existence, our universe would be a very, very different place.

As for those of you who think the world is going to sucked up into an infinitely dense, infinitely bright ball of mass in June... you had might want to go see your therapist.

Woe! It just occurred to me....June is my birthday! ....anniversary of when it did once happen to me! 62 years ago. It was a primal scream! In I went and out came two, a Gemini! Should we see a therapist too? ~CG

By Colin G Garvie (not verified) on 13 Apr 2008 #permalink

Thanks, Andrew.

Norman raises the issue of vacuum collapse, except that cosmic rays have a million times the energy of LHC particles and have for billions of years. Colliders don't produce effects not found in nature. They just localize them and subject them to human scheduling. (Paragraph 10 of the complaint is wrong when it says "[t]he purpose of the LHC machine is to create novel conditions of matter never previously existent on earth". Scientists are still playing by Nature's rules.)

Wren, the scientists are sure that what will happen will have only local and short-lived effects. (The most intersting things will be gone in a billionth of a billionth of a second.) Not one of the doomsayers has a model of physics, but only asking questions. What if the quantum theory-based hypothesis XLD (with maybe 10 supporters in the world) was true, what if Hawking radiation (which all quantum theories of gravity have) is not true, what if things were just right for CERN to form black holes, what if those black holes were (contrary to all descriptions of 2 TeV black holes) dangerous? "Dangerous" isn't a physics model -- it's fear-mongering. The correct thing is to start with a physics model and work out the consequences. If you believe them, then the whole universe should be filled with a dilute gas of black holes. This has not been observed, so therefore that is proof that it is not dangerous in the way they told you it might be dangerous.

The reason that they made the device (LHC) is that it's a type of microscope, better than any made before. They hope to see direct evidence that some of their long-held (30 years) hypotheses are true and hold their breath if some new ideas are also shown to be true. They are searching for answers to questions like: Why is the muon 400 times heavier than the electron? And this benefits you largely indirectly, like driving the development of high-speed internetworks. Much like the space race gave you mylar, integrated circuits and Tang.

Matt Penfold, I raised that issue with Walter Wagner directly about a year ago. I can't even imagine the pain of a judge who has to deal with TWO pro-se plaintiffs. How is it even possible to have TWO pro-se plaintiffs? Only one of them can speak at a time, and thus acting a lot like the others lawyer. :( Also, Walter has been trying to raise money with his website, but isn't it approaching fraud to raise money to file a suit and not actually hire a lawyer? How will these two pro-se plaintiffs represent the corporate concerns of their sponsors (if any)?

The accelerator is not a microscope. A microscope is for seeing very small things. An accelerator is for accelerating very large numbers of particles to very high speeds to cause extraordinarily unlikely collisions between one particle and another (of similar or different types) to happen under very high energy conditions.

Then you watch what happens.

I am not a physicist, but I can tell you that this rhetoric that this or any other collider/accelerator is doing the same exact thing that is happening all the time anyway is very, very misleading and there will be no more of it unchallenged on this site.

The new CERN project is undoubtedly a very, very dangerous set of complex and costly machines. My own personal feeling is that the questions being asked are critically important. As an American, I feel embarassed that the United states is not more involved in this research, and I blame that on many years (off and on) of anti-science administrations and ant-science congress. That will change in a few months.

I personally have no idea if the EIS work done on this machine is adequate, in other words, as a smart guy with an avocational interest in high energy physics and a lot of experience in the Environmental Impact field, I would love to be able to explain to my readers what is and is not going on, but I cannot do that.

On the other hand, I'm not totally sure that I can point readers to a really good and detailed description of this issue. Virtually all the descriptions Ive seen (and I have NOT done a systematic or exhaustive search) have "And then a miracle happens" at some point int he description.

Wren, I think you are asking good questions, and I wish the answerws were better articulated than they are. Rpenner: I think you might be right that the doomsayers yave not said anything coherent. That's comforting.

Well, not literally a microscope.

But the analogy is strong since relativistic quantum physics associates high energies with short distance scales, and the LHC has particle energies an order of magnitude above Tevatron and RHIC.

Thus the LHC works well at "seeing" fine details of the fundamental physical particles, for the same reason that electron microscopes see surface features better than UV microscopes better than light microscopes, better than radio telescopes.

Perhaps you could articulate why you feel that references to high energy cosmic rays are "very, very misleading" when evaluating saftey scenarios? I thought similar arguments were used for evaluating saftey of fruit-fly mutation experiments, if say critics were to ask how can you be sure you won't create a type of Andromeda Strain. It would be interesting to hear an actually learned saftey question for a change.

Yes, that analogy to a microscope does work.

articulate why you feel that references to high energy cosmic rays are "very, very misleading" when evaluating saftey scenarios?

I can't articulate that because I didn't say it!

I'm talking about the frequent assertion that the events happening in a collider happen every day a all over the place on the earth. This simply is not true. The whole point of this particular "microscope" is to make an event happen that is otherwise very unlikely.

I am not a physicist, but I can tell you that this rhetoric that this or any other collider/accelerator is doing the same exact thing that is happening all the time anyway is very, very misleading and there will be no more of it unchallenged on this site.

Since Special Relativity (Einstein, 1905) reformulated Lorentz's equations as a consequence of a basic symmetry of space-and-time, the old Newtonian idea of absolute rest was tossed out of physics. So we, and repeatable experiments, no longer feel a need to describe a collision between A and B in terms of v_A and v_B, but only in their relative velocity v_AB, and for measurements sake, v_cm -- the lab velocity of the center of mass. Unlike the Newtonian formula, relative velocity is no longer calculated as v_AB = v_A - v_B, but as v_AB = (v_A - v_B)/( 1 - (v_A v_B)/c²).
If v_A = c ( 1 - x ) and v_B = -c ( 1 - y ), then v_AB = c/(1 + xy/(2 - x - y))) which is (when x << 1, and y << 1) close to v_AB = c ( 1 - xy/2).

Likewise kinetic energy is no longer ½ m v² but mc²( 1/√(1 -v²/c²) - 1).

For LHC, protons are accelerated to a high speed relative to Earth. v_A = -v_B = c (1 - x) where x is about 10^-8.

(A 7 TeV proton has 7000 time the energy of a proton at rest in the laboratory, so we expect 1/(1 - (v_A/c))² to be 7000, which means v_A is smaller than c by 1 part in 100 million.)

So v_AB is close to c ( 1 - 5×10^-17) which is how one proton sees the other proton. This is the same situation as when a proton at rest is struck by a proton at the speed v_AB, or in energy terms a 100,000 TeV proton, a 0.1 EeV proton. It just so happens that cosmic rays from space are nuclei, including protons, of up to 300 EeV.


So in Nature, collisions of they type that the LHC seeks to observe happen all over the universe, and on Earth mostly in the upper atmosphere. The LHC is a cheap way to observe these events. The LHC luminosity is 10^38/m²s and if a proton-proton collision has a cross-section of about 10^-30 m², then we should expect about 100 million of them per second rather than having to hunt for them over the upper atmosphere.

No one, not ever Walter Wagner, is asserting that different laws of physics apply to collisions at LHC as opposed to collisions in nature. The collisions themselves need to have qualitatively the same nature as natural interactions or we learn nothing of natural law.

Walter Wagner asserts in his affidavit that there is the qualitative difference that the collisions happen with v_cm of near zero relative to Earth, but since protons are composite objects, what collides are the parts of protons, which have very high intrinsic motions. Escape velocity of Earth is 3.7× 10^-5 so the fraction of collision center of masses which are slower than escape velocity is on that order. Walter quotes in a footnote fractions from 1.4× 10^-1 to 1× 10^-4 but without calculation or reference to calculations. Detailed calculations from 2002 consider this question and agree closer with 10^-5 (but I didnt save the reference to the paper). But why let friends quibble over 4 orders of magnitude? (My prior calculations assumed the ratio was 1.) We can rule out stable dangerous easily-formed black holes by the long life of the Earth, Moon and other bodies. If cosmic-ray energies were enough to form black holes, and said black holes were stable, then they would form a dilute gas filling the universe. Thus they arent dangerous or arent stable or arent formed at cosmic ray energies.

I welcome any questions you might have.

Sorry, I lost some of my punctuation.

If v_A = c ( 1 - x ) and v_B = -c ( 1 - y ), then v_AB = c/(1 + xy/(2 - x - y))) which is (when x and y are much less than 1) close to v_AB = c ( 1 - xy/2).

Likewise kinetic energy is no longer ½ m v² but mc²( 1/√(1 -v²/c²) - 1).


(A 7 TeV proton has 7000 time the energy of a proton at rest in the laboratory, so we expect 1/√(1 - (v_A/c)²) to be 7000, which means v_A is smaller than c by 1 part in 100 million.)

v_AB = v_A - v_B, but as v_AB = (v_A - v_B)/( 1 - (v_A v_B)/c²). If v_A = c ( 1 - x ) and v_B = -c ( 1 - y ), then v_AB = c/(1 + xy/(2 - x - y))) which is (when x Likewise kinetic energy is no longer ½ m v² but mc²( 1/√(1 -v²/c²) - 1).

Right, right I get that. You have fallen into the bloogers fallacy. When a blogger says "I'm not an X" it usually is a trap. I am indeed not a physicist but I've probably read more of the primary literature on this kindergarten level stuff than most graduate students.

And everything you say is essentially correct, however, it is simply not true that thee interactions happen in the upper atmosphere at anything like a density that they can be used for research. The CERN machine is not a cheap way of doing something that is happening "all the time" in the upper atmosphere. "all the time" to most people would mean if we built a lab up there we could just observe what is happening around us!

(Indeed, the side effects of these upper atmosphere events to make up part of the BR which is studied on a regular basis, pending funding of course.)

Ah, illumination dawns.

You are saying that that luminosity of LHC, which directly related to the frequency of observations of events, as well as its top energy, which relates to the scale of inter-particle interaction examined, are both vitally important parameters for this research tool.

I think, that on the order of 10,000 cosmic rays/second hit over the entire surface of the Earth with energies above 0.1 EeV. By contrast, meaningful proton-proton collisions at LHC are expected to happen about a billion times per second inside of heavily instrumented chambers.

But the point I was emphasizing was that it was the same natural law that controls the particles, not the details of the machine, thus the risks due to as yet unknown physical law can be studied by the longevity of the components of the solar system.

While it is overstatement to say that no research can be done with this natural flux, it would be prohibitively expensive to deploy detectors with the sensitivity of ATLAS for the faint hope that cosmic rays of appropriate energy would strike them enough times to gather a meaningful statistic picture of the quantum rules related to these particles at this energy scale. Thus, the LHC is a cheap way to observe these events turns out to be offensive understatement to your ears.

Cosmic ray experiments tend to be innovative in frugality trying to capture the most particle data for the cheapest price, so that the team can afford to deploy the experiment over as wide an area as possible for as long as possible.

Sorry if my habit of posting instead of sleeping has corrupted this communication.

Right on. I see your cheap/expensive analogy here.

But who can say how much a Higgs boson is worth?

Right now, I cannot think about a single consumer/engineering application for QCD, let alone SUSY or Higgs. That's why I pointed out to Wren that while chasing the Higgs, the industry that supports LHC actually creates new technology which does have a positive impact on the consumer/engineer experience.

Grid computing: http://atlasexperiment.org/pdf/A-Big-Bang-of-Innovation.pdf
Vacuum technology: http://physicsworld.com/cws/article/indepth/30525
Electromagnetic engineering and cryogenics: http://www-conf.slac.stanford.edu/ssi/2006/lec_notes/evans071706.pdf

And while the comparative biochemistry of zebrafish development might actually lead to discoveries which improve human medicine, LHC (like the Space program) has the capacity to create awe, which might lead to a pro-science cultural shift. (At less than 10 billion euros, that may be cheaper than a certain planned attempt to create a cultural shift.)

To a physicist, fundamental physics beyond the standard model must exist -- there must be a way to relate particle physics and gravity. But the empirical data record is incomplete. Finding the Higgs boson would experimentally link particle physics to mass which would be progress. Actually finding it would be a type of vindication similar to finding Tiktaalik when and were predicted (or the thousands of other vindications of common descent). Not actually finding it, after doing an exhaustive search would tell us something different, like not finding whales in the Cambrian strata. But without data, Natural Philosophers are at risk of becoming mere philosophers and mathematicians.

Update: The trial has been scheduled for June 2009. (But I expect it to be eviscerated in the next 14 days.) The plaintiffs have not served court papers on even half the named defendants yet, and the Department of Energy's earliest notes suggest that this case is essentially still-born.


Reposted from http://scienceblogs.com/pontiff/2008/03/oh_noes_blak_holz_are_eatn_my.p…

Open letter to Professor Hawking

Dear Professor Hawking

The safety of micro black hole(mBH) production in the CERN LHC accelerator, operating in COLLIDER MODE, has not been properly addressed.

Six LAYERS OF PROTECTION for the Earth and all its inhabitants have been ASSUMED and discussed during the last decade or so:

[Ill briefly outline the first five, and then explain a FATAL MATH ERROR in the sixth]


Ten years ago we were assured that mBHs could not be produced by any conceivable accelerator on Earth. The Plank Energy 10 ^ 19 GeV was supposedly required to produce a micro black hole. This would require an accelerator thousands of light years across.

Today CERN and others are assuring us(if that's the right word!) that the LHC will be a "BLACK HOLE FACTORY, operating at only about 10 ^ 4GeV. Thus people believe a certain version of string theory with extra dimensions, and it is now thought that mBHs are 10 ^ 15 times easier to produce. And can be produced in an accelerator 10 ^ 15 times smaller in diameter than the hypothetical galactic version.

A revision of 15 orders of magnitude should make people more modest about the certitude of their pronouncements. According to CERN:

PROTECTION #1 NEVER EXISTED, for sufficiently high energy collisions, but dont worry, they are absolutely certain of the next layers of protection, just like they used to be absolutely certain about #1..(1)


The 5 x 10 ^ 3GeV mBHs they are confident of producing would have a lifetime of around 4 x 10^ -86sec according to what was believed a decade ago and more ago. Since this is about 42 orders of magnitude smaller than the Plank time(5.4 X 10 ^ -44sec), not surprisingly, mBHs of that mass were deemed impossible.

Now their lifetime is supposed to be in the order of 10 ^ -26sec, because of higher dimensions at small scales.

So we're supposed to REVISE THE LIFETIME OF AN mBH UPWARD by a whopping 60 ORDERS OF MAGNITUDE, and SUPPRESS HAWKING RADIATION (HR)by the same amount. To put things into perspective, the ratio between the Plank time 5.4 x 10 ^ -44sec and estimated age of the universe is about 10 ^ 62. We could hardly be more unsure of the actual mBH lifetime, in a quantitative sense, since the predicted values are so dependent on the flavor of the month version of string theory.

Even if we are confident that a mBH must decay by Hawking Evaporation(HE):

PROTECTION # 2 INVOLVES MAGNITUDES THAT ARE TOO WILDLY SPECULATIVE TO RELY ON. The fact that HAWKING RADIATION HAS NEVER BEEN OBSERVED in cosmic ray showers, suggests a process too slow to save us, even if it occurs.

Purely from the HEALTH AND SAFETY point of view, we must assume therefore



False analogy. Natural fission has been going on in the Solar System for Eons, without ever causing nuclear explosions(exponentially growing reactions). By changing the GEOMETRY of the experiment, TRINITY, the first atom bomb test, succeeded first try.

ALL mBHs produced by bombardment by high energy cosmic rays are NECESSARILY RELATIVISTIC. The CENTRE OF MASS VELOCITY of the collision is relativistic, and this is CRUCIAL TO THE SAFETY OF THE EARTH, Moon, Sun etc,.

These mBHs would cross the full diameter of the Earth in 0.042sec, Jupiter in 0.46sec, and the Sun in 4.6sec. Because of the small size and enormous speed, they would fly through like very heavy neutrinos, and have plenty of time to decay in the vastness of space. They would NEVER BE CAPTURED, AND SO WOULD POSE NO THREAT.

Operating the LHC in COLLIDER MODE, ensures that the centre of mass velocity of the collisions are distributed about zero, and not just under the speed of light. It CHANGES THE GEOMETRY of the experiment. This guarantees that some of the mBHs produced by the LHC IN COLLISION MODE would be GRAVITATIONALLY CAPTURED IN THE BULK OF THE EARTH, something UNPRECEDENTED in its history.

Any such mBH can never escape, and if it starts to absorb nucleons before it has time to evaporate, then it constitutes an EXISTENTIAL DANGER to the Earth. The only thing that matters then, is the TYPICAL DOUBLING TIME T2, analogous to T 1/2, the half-life for radioactive decay.

Such mBHs would have all the time in the world to grow exponentially. And "all the time in the world" might be very short.



All the mBHs produced by such very high energy particles are relativistic, and are harmless, for the reasons described above. OPERATING THE LHC IN COLLIDER MODE REMOVES THIS PROTECTION IMMEDIATELY, so:



False analogy. The energy of the neutrons that triggered the exponential process in the TRINITY ATOM BOMB TEST 1945 in the New Mexico Desert was many orders of magnitude less than this, but STARTED AN EXPONENTIALLY INCREASING PROCESS. During the short time the U235 is explosively brought to a supercritical state, EVEN ONE SLOW NEUTRON causing fission is sufficient. Doesnt take much energy to LIGHT A FUSE.

[Of course a relativistic neutron produced by cosmic rays, that zipped thru the core of an A-bomb with no chance to cause fission, would be pretty harmless]


PROTECTION #2-5 are constantly quoted by CERN, whose attitude to RISK ASSESSMENT is really about PUBLIC RELATIONS and not the PRECAUTIONARY PRINCIPLE..(5)

CERN is so blase about the weakness of the arguments for the PROTECTION #2-5, because even if they are rubbish, they think the next protection is surely a clincher:

CERN quote a mBH with a mass equivalent to 5000 nucleons, which might be typically produced, which absorbs one nucleon per hundred hours(which appears to be an underestimate, and probably should be amended to about one whole IRON ATOM with 56 nucleons absorbed in a few hours, say an initial rate of at least 5 nucleons per hour).


[At that rate, even if one did not take into account the fact that each black hole would slow down every time it gobbled up a proton, and thus suck down matter at an even slower rate, "about 100 protons would be destroyed every year by such a black hole, so it would take much more than the age of universe to destroy even one milligram of Earth material](6)

Let's see now, one mg contains about

M/u nucleons, where M=10 ^ -6 kg and u = 1.67 x 10 ^ -27kg

So number of nucleons to be destroyed is

N = 6 x 10 ^ 20 (ie Avogadro's Number divided by a thousand, as we would expect)

So divide this by 100 to get a time to destroy that many nucleons of

T = 6 x 10 ^ 18 years, much more than the age of the universe.

Note the AMAZING ASSUMPTION OF LINEARITY. This must be the BIGGEST SCIENTIFIC BLUNDER IN HISTORY, and the most EXPENSIVE, if it literally costs the Earth.

A classical mBH accretes exponentially even as it slows down.(7)

Speculative extra dimensions reduce the rate until the effect of the extra dimensions is no longer noticeable. On coming to a halt at the centre of the earth, material is forced towards the entire AREA(think N-squared) until conservation of momentum forces accretion to occur along the equator. So we could get a brief period of asymptotic growth, followed by exponential. In the exponential process N = No e ^ kt, the e time is less than 60 years, revised to about 0.12 years, using my accretion rate! We cannot observe the minutae of the actual processes within the Earth. And extra mBHs are being added, presumably with variable starting masses and accretion rates, which depend on the size. The overall result is similar to that for analogues in the Economy. The growth of an investment portfolio for example, but one in which the individual investments cannot ever lose, cannot stay still, and after the initial settling period, cannot increase as slowly as a linear rate. ALL BOOM, and NO BUST. Such investments grow exponentially, until something runs out..in this case, the EARTH ITSELF.

It is easier for mere mathematical mortals like me to understand it in terms of something like the growth of an investment. With CERNs initial rate, he period is 100 hours, and the rate is .02% COMPOUND INTEREST. That approach is familiar to non-scientists in business etc, and this is an open letter. The best way to do the math then is in terms of the DOUBLING TIME T2, the time to double the investment. Even wild fluctuations in the rate, can be accommodated by corresponding reductions in T2. It still only takes a certain number of doublings to consume the Earth.

N = No(2 ^ n) where n is the number of doublings each taking T2.

No = 5000, then with dN/dt starting at 1 per hundred hours(2.8 x 10 ^ -6 nucleons per sec), the mBH doubles in 40 years, and gobbles the earth in just under 160 such doublings, or about 6400 years.

AT A RATE OF 5 NUCLEONS PER HOUR INITIALLY, the doubling time T2 is just under a month, and we have under 160 months.

( the factor is 2 ^ 160 = 10 ^ 48 approx, and we started with 5 x 10 ^ 3.)

There is another huge problem:

A classical mBH of mass about 5GeV has a radius of approx 10 ^ -50m, so much under the PLANK SIZE, as to be pretty meaningless. No wonder it used to be thought that such mBHs were impossible.

The SAME mBH is now supposed to be around 10 ^ -19m. ANOTHER WHOPPING REVISION, 31 MAGNITUDES!

So the CROSS SECTION, and ability to interact with matter is INCREASED by about 62 MAGNITUDES. And no-one at CERN is modest enough to say WE DONT KNOW WHAT THE HELL WE ARE DOING!

In view of the wild variations in the order of magnitude of the cross-section, depending on the particular model, we should note that if the mBH starts accreting at one nucleon per hour, the Earth has only 64 years, and if we start with 100 nucleons per hour, the Earth has less than 8 months, the last of which would be horrific in the extreme.

Even if the size of the mBH is correct, CERNs initial accretion figure seems to be wrong. Probably it should be revised to at least 5 per hour. The mBH should cut out a volume about the size of a typical IRON ATOM, in under 10 hours. Only if the doubling time is long in Geological terms, EONS, is the COST to the Earth negligible..(8)

Yet CERN have an AMAZING FAITH that:

A black hole absorbs only one nucleon per hundred hours or roughly 10 ^ 2 per year indefinitely.........IRRESPECTIVE OF HOW BIG IT GROWS

When it is a million times, or a billion times, or a trillion times more massive, the mBH still gobbles only one nucleon per hundred hourseven when it grows from N = 5000 to N = 6 x 10 ^20, and presumably even when it grows to 3.6 x 10 ^ 51(the number of nucleons in the Earth). In a linear model, this sure would take a long time. Let's restate it:



dN/dt = a constant for a black hole in the Earth.

This constant is INDEPENDENT OF THE MASS AND SIZE, an astonishing state of affairs. At just what scale does this break down?

A 10 ^ 9 solar mass black hole in the nucleus of a Quasar perhaps? The density of space in the central region of a Galaxy near a SUPERMASSIVE BLACK HOLE is nowhere near that in the interior of the Earth. And as we have seen, the people at CERN think that SIZE DOESNT MATTER! I believe that Astronomers, if they actually thought about it, would LAUGH THEM TO SCORN.

But this is TRAGIC COMEDY:

If CERN was a Bio Weapons Lab, just imagine the assurance about an accident: Since the Plague Vector infects one person per week, it would only infect 52 people per year, a small village in decades! Wed all the time in the World to take countermeasures. But what really happens is that two people infect two per week, four infect four, etc. So in only 20 weeks, a million. If the whole population were available to infection, and not immune, then in 26 weeks the Plague could infect everyone in France, and in 33 weeks could infect everyone on Earth(since 2 ^ 26 is about 64 million and 2 ^ 33 is around 8 billion, so room to spare).

To apply a CERN type RISK ASSESSMENT to the TITANIC would find that it could not possibly sink, since the rate of taking on water would be independent of the size of the hole, so tearing a 100 meter long gash would do no more harm than drilling a millimeter diameter hole. How could it possibly sink? FORGET THE LIFEBOATS!

After all, starting with a microscopic hole, it should be possible to cut it to any arbitrary larger size without increasing the rate at which water is entering! I suppose we could cut away the entire ship, which is what they may succeed in doing with our Spaceship Earth. We might be tempted to laugh at the idiocy of all this. But that would be like whistling in the cattle cars trundling down the track towards Auschwitz.

And it would be unfair to compare the new LHC GAMBLE to the launch of the TITANIC, because:

The designers and operators of TITANIC were optimists but CERN

1. Did not seek out dangerous objects like icebergs.

2. Had credible detection methods for potentially dangerous objects. Foghorns and echoes. Men with binoculars on watch.

3. Had credible methods of detecting damage, and if not too severe, of effecting temporary repair. Sound of collision, crew reports of shipping water, plates and braced beams etc.

4. Had watertight compartments to contain flooding, if not too severe.

5. Had some lifeboats, so that at least some people would survive.

6. Had radio communication, to call in outside help.

7. Had the whole world outside the ship to be rescued to.

8.There was no conceivable way for the rest of humanity to go down with the ship.

1. Gleefully seeking to operate BLACK HOLE FACTORY.

2. No detection of mBH that doesnt evaporate harmlessly.

3. No detection of damage, until it is terminal for the Earth. No repair.

4. No containment of mBH that doesnt evaporate harmlessly.

5. No escape.

6. No rescue from E.T!

7. Nowhere to go.



I suggest that the fairest comparison would be to a monstrous slow motion version of the original TRINITY ATOM BOMB TEST, with all of us NOT JUST OBSERVERS, BUT PARTICIPANTS.

Note that a CERN style risk assessment would conclude that the original atom bomb could not possibly explode, because

1. Natural fission has been going on in the earth for billions of years, and the Earth is still here.

2. We never detect even small natural nuclear explosions in seismic records.

3. Neutrons produced by cosmic rays on the surface of the moon must cause fission events, but we never witness explosions.

4 .The amount of fissile material available for natural fission events in the Earth, Moon, and Solar System is vastly bigger than anything we could pack into a bomb.

5. A single fission produces less energy than a mosquitos heartbeat.

6. A slow neutron capable of causing fission has less energy than a mosquitos thought about its cardiovascular health.

7.Before the concentration of fissile material can become supercritical, the heat produced will A. Make it expand or
B. melt or
C. vaporize and so become sub critical.

8. And this is the clincher, natural fission occurs, and the process takes billions of years before a fraction of the fuel is used. Otherwise thered be no fissionable elements left!

9. The 35kg of U235 contains about 10 ^ 26 nuclei. If the time for one fission to trigger another, T2 is say 10 ^ - 8 seconds, then it would take 10 ^ 18 seconds for the bomb to run its
course, or longer than the age of the universe. It would hardly get warm.because of course, according to CERN the process would be linear. Of course if it wasgolly gosh, exponential, it would take about 87 doublings, or in this case under a microsecond!

Please check my claims, and get colleagues and grad students to do the same. A lay person like me has zero credibility in the CLOSED MINDSET at CERN.

If you are alarmed by CERNs DISREGARD for the PRECAUTIONARY PRINCIPLE, and their failure to understand that a possibly small, BUT WILDLY UNKNOWN PROBABILITY multiplied by the ULTIMATE LOSS(it is infinite to us!) is unacceptable:

I beseech you to write an OPEN LETTER to the Director of CERN, copying to President Sarkozy and other heads of state, colleagues etc.(9)

COLLIDER MODE SHOULD BE DISABLED until INCONTROVERTIBLE EVIDENCE of HAWKING RADIATION is found in beams striking STATIONARY TARGETS, just like cosmic ray impacts(and so just as safe), and in the COSMIC RAY DATA itself.

In the last century, Einstein's General Relativity theory predicted twice the bending of light passing the Sun that Newton's theory predicted. That factor of two made it possible for Eddington and to verify Einstein's prediction in 1919 during a Solar Eclipse.

Today we have competing ideas, whose particular expressions predict wildly different orders of magnitude.......and NO EXPERIMENTAL DATA to help us DECIDE WHICH IS EVEN REMOTELY CLOSE TO THE TRUTH.

CERN might try to jump the gun, and launch before the expected date. If HAWKING RADIATION IS OBSERVED, beyond any doubt, then we could be safe until they dream up the next way to endanger the Earth. Banishment of the whole show to a distant asteroid should be contemplated, if we are to avoid becoming an exemplar for the FERMI PARADOX.(10)

But if NO HAWKING RADIATION is observed, dont expect contrition: We were wrong. Micro black holes could be accreting exponentially in the heart of the Earth. We could be safe, or we could be doomed. WE SIMPLY DONT KNOW. Instead expect an arrogant we told you it was safe.

Then we would see a dreadful hurry, like the rush of the GADARENE SWINE, to do more powerful experiments, like COLLIDING LEAD NUCLEI at 10 ^ 6GeV.

All the above betrays a heart of darkness. But it is not just a scientific elites suicidal hubris. It is potentially the worst, most murderous, folly ever contemplated, and we are all hostages to this madness.

Cass St John



CERN still cite this:
Note the scathing dismissal of mBH production:

Do mBHs radiate? Is HR fast enough?

Note the UNQUESTIONED ASSUMPTION that HR will save us:

(3) (4) (5)
Note the repetition of the false analogies, and the CULT LIKE BELIEF that HR will save us:


Again the FAITH that HR will occur, and will be rapid enough to save us. More worried about careers and Noble Prizes!


Really awful FAITH in linear growth:
Do people who associate themselves with CERN get loans from Swiss banks that charge 5 cents a year interest on 1 Euro, and still only charge 5 cents a year interest on 1billion Euros, or a trillion, or 10^20, or the number of nucleons in the Earth, 3.6 x 10 ^ 51?

(7)If we look at initial rate of absorption as the mBH slows and grows, and consider the Classical case:

The mBH is effectively flying through free space, since most of an atom is empty space.

An mBH with an initial mass Mo, initial velocity Vo that absorbs a nucleus mass m:

By conservation of momentum if M = Mo + m

M x V = Mo x Vo


V = Mo x Vo / M

Expressing everything in atomic terms of nucleons

V = No x Vo / N

V is inversely proportional to N.

Number of nucleons absorbed per unit time is proportional to Volume swept out by mBH:

dN/dt = Const x pi x R ^ 2 x V

Where R = 2GM/c ^ 2, the Schwarzschild radius.

Gathering constants and noting that R proportional to N, and V inversely proportional to N

dN/dt = k x N ^ 2 / N

Gives us

dN/dt =kN

Integration gives us

N = No e ^ kt

A very slow mBH will just fall through the floor of the Collider to the centre of the Earth, with an acceleration at any point R from the centre of

a = -[G(4/3)pi D R ^ 3]/ R ^ 2

Where the square bracket represents the mass of Earth inside the radius R, and D is the density.

So the acceleration is

a = -[4/3)pi G D] R


The angular velocity w is given by

w ^ 2 = (4/3) pi G D = (4 pi ^ 2)/T ^ 2

The period T = (3pi/GD) ^ is therefore 1.4 hours, taking 0.7 hours for a single traverse of the Earths diameter.

T is constant, irrespective of the fact that the amplitude Rmax decreases directly as the velocity, and hence inversely as the mass. Thus when the mBH absorbs 50 nucleons, Rmax is only reduced by 1%, as is Vmax(at the centre of the Earth).

The diameter of the Earth is 1.27 x 10 ^ 7 meters, so taking it as 10 ^ 7, a rough order of magnitude calculation for the VOLUME CUT OUT BY THE mBH:

[ (10 ^ - 19) ^ 2] x 10 ^ 7

Thats 10 ^ - 31 meters cubed.

Iron atoms are pretty small, in the order of [(10 ^ -10 ) ^ 3] or 10 ^ - 30.

So about ten traverses of the earth does the business, taking 7 hours.

If we round everything to an order of magnitude:

One complete atom, typically iron in the Earth, gobbled every 10 hours, 56 nucleons per first 10 hours, roughly 5 nucleons per hour. Even when the mBH has doubled in mass, and is executing SHM with only half the amplitude(but the period is still 1.4 hours), it is oscillating in the much denser, iron rich region of the Earths bulk, and it is relentlessly growing in diameter.

In the last 20 doublings, the mBH goes from being one millionth the Earths mass to gobbling it up. 2 ^ 20 = approx 10 ^ 6.

In the last 10 x T2, the mBH gobbles the last 999/1000 of the Earth.

Survival time is insensitive to initial number of mBHs absorbed in a short time, if belated prudence sets in and the machine is switched off. Thus a thousand mBHs shorten the life by about 10 x T2, say from 6400 to 6000 or with the revised accretion figure, 12.8 years to 12, since 2 ^ 10 = 1024, or approx a thousand. So PERVERSELY, even a single mBH is almost as dangerous as a whole lot of them. It just gains us a little extra time towards the end.

Survival time is of course proportional to the typical or average doubling time T2, which could be longer than a month, or a year, or 40 years, but is wildly uncertain.

A closed letter would be thrown into the bin, or would disappear into a bureaucratic black hole!
Or some secretary who doesnt know a hadron from a haddock would keep it on file until after the LHC is fully operational, so as not to upset the boss

Perhaps all civilizations in the Galaxy are like us, and find it easier to switch on a LHC in collider mode, before they have self-sufficient space colonies which would allow them to avoid total extinction. Hence the answer to the question, where the hell are they?

Update to timeline of Wagner/Sancho vs. US DOE, NSF and CERN

August 5, 2008 -- Wagner/Sancho file for permanent injunction versus CERN
August 11, 2008 -- Wagner/Sancho refile with additional signatures
August 13, 2008 -- Sheldon Glashow, Frank Wilczek and Richard Wilson decide that this is too much fun to pass up and file legal papers


Update 2. Swiss ambassador claims service on CERN by Swiss legal system is illegal and patiently explains the correct process. This would invalidate the service on CERN and the court clerk's entry of default.

Okay, it's July 2nd and nothin's happening. >:P