Could the Large Hadron Collider Create a Black Hole That Threatens Earth?

[Orion1]

If the fundamental Planck scale is ≈ 1 TeV, LHC,
with the peak luminosity of 30 fb^−1/year will produce
over 10^7 black holes per year.

The Schwarzschild radius R_S of an (4+n)-dimensional black hole:
R_s = \frac{1}{\sqrt{\pi} M_p} \left[ \frac{M_{BH}}{M_p} \left( \frac{8 \Gamma\left( \frac{n+3}{2} \right)}{n+2} \right) \right] ^{\frac{1}{n+1}}

How do I transform this equation into Systeme International units?

Anyone here interested in examining Rossler's paper disputing Hawking Radiation?
[/Color]
Reference:
http://www.youtube.com/watch?v=M3iMX8xzofc&NR=1"
http://arxiv.org/PS_cache/hep-ph/pdf/0106/0106295v1.pdf"
http://en.wikipedia.org/wiki/Micro_black_hole"
https://www.physicsforums.com/showpost.php?p=1844504&postcount=48"
http://en.wikipedia.org/wiki/Hawking_Radiation"
http://www.wissensnavigator.ch/documents/OTTOROESSLERMINIBLACKHOLE.pdf"
http://en.wikipedia.org/wiki/Otto_R%C3%B6ssler"
http://www.youtube.com/watch?v=Kf3T4ZHnuvc"
http://www.youtube.com/watch?v=PR2OLjAr1Fc"

Leave, leave Geneva every last one of you,
Saturn will be converted from gold to iron,
RAYPOZ will exterminate all who oppose him,
Before the coming the sky will show signs.

 

[malawi_glenn]

And, by the way, I would like to suggest that if cosmic rays hitting atoms in the Earth's atmosphere are producing black holes, these holes will pass just once through the planet, and then disappear into the great unknown. Their velocity would be way beyond escape velocity.

So what have escape velocity antyhin to do with it? What matters is the directon they go and how they interact with material. Consider for example neutrinos from the sun which passes through the eart 10000000000 each second and square metre. What matters here is the interaction crossection, not the escape velocity...

 

[Almanzo]

The escape velocity seems relevant to me, because a black hole escaping from Earth (and, preferably, from the Solar System too) seems less immediately threatening than a black hole following a decaying orbit inside Earth and finally coming to rest in the center.

 

[malawi_glenn]

The escape velocity seems relevant to me, because a black hole escaping from Earth (and, preferably, from the Solar System too) seems less immediately threatening than a black hole following a decaying orbit inside Earth and finally coming to rest in the center.

Yes, if BH initial velocity is directed radial outwards, then it is a good argument. But since the vast majority of HighE-cosmic rays are directed radial inwards to earth, most of MBH's will go towards earth.. *scary* :-)

 

[Almanzo]

EDIT: ah, I think I see your argument now: you seem to think that if a BH crosses a nucleus, it "must" absorb it, no matter how small the hole. But on the BH's scale, the nucleus is not a "massive filled thing", in the same way as for a fast electron, the atom is not a massive filled thing".

What you estimated was roughly the probability of a NEUTRON to interact in matter.

You have a point. Just like the atom is made up of a nucleus and some electrons within a lot of empty space, so the nucleus is made up of protons and neutrons, which are themselves made up of up and down quarks. My expectation is that the hole would have to actually hit one of the most fundamental particles to achieve anything. Its gravity, at this stage, is much to weak to draw a particle in against the electromagnetic or the nuclear force.

However, what is the size of the most fundamental particle? If an electron is fundamental, one might try to calculate a minimum size for an electron, based on the idea that its total mass must be larger (or, at any rate, not smaller) than the mass of its electric field. This gives me a diameter of roughly 1/100.000 of the atom diameter for the electron. The quarks, being more massive, and carrying less charge, might be smaller, say 1/10.000.000 of the atom diameter. Or they might not be that small; they carry other fields, which presumably have their own contributions to their mass.

The black hole would be much smaller still; essentially point sized relative to the quarks and electrons.

Would swallowing an electron cause the hole to attract and devour the nucleus (and the other electrons after that)? Perhaps not. If it formed by cosmic radiation in the atmosphere, it will have relativistic speed, and may not dwell long enough in the vicinity of the other particles to draw them in. But if it formed in the LHC, at a moderate speed, if might well have enough time to do so. And otherwise it would be attracted to any nucleus it passed, increasing its effective cross section until it had neutralized its charge.

At any rate, I wonder whether a black hole could get away after swallowing just one quark. Not only would it have a partial charge, it would also have a colour charge, and be strongly attracted to the remaining quarks. I would at least expect it to take the other two quarks of the same nucleon. If this nucleon is a neutron, this might have little effect. If a proton, the hole would again have charge, and attract electrons. Eventually it would catch one, whether from the same atom or from somewhere else. It would be the electrons that moved towards it, rather than vice versa, considering that the hole is initially 10.000 times as massive at as a proton, and twenty million times as massive as an electron.

But, yes, the cross section of 1/100,000 squared might be wrong. Suppose that it is essential for the hole to hit a quark, with a cross section of 1/100,000,000 squared, and suppose that even if it does so, it only takes one nucleon mass, not an entire atom. Instead of having to pass through ten billion layers of atoms, it would have to pass through ten million billion layers of atoms, or one hundred kilometers of solid mass. On one passage through the Earth the hole would acquire roughly 100 proton masses; it would need 100 orbits to double its mass, which it would complete in a week. The growth would not be linear, because the diameter of the hole itself would slowly increase, but it might be centuries before this became noticable.

However, there would be more than one hole. The holes would be in decaying orbits, ending up in a small region, where they would eventually meet. The diameter of a black hole is proportional to its mass, not to the cube root of its mass. So the ability of a combination of holes to increase its mass would become proportional to the square of the total mass. And when the mass reaches 10³⁰ proton masses, or a few kilograms, their gravity becomes strong enough to overcome interatomic (van der Waals) forces and draw neighbouring atoms in. From there, the growth is exponential.

I expected the "dormant" stage to last a few decades, but it may actually be a hundred thousand years.

 

[mal4mac]

I'm sorry, but Martin Rees does not qualify as someone concerned about its safety...he has enthusiastically articulated his position of support.

You can be concerned about safety, but still enthusiastically support something. For instance, a sky diver might be very safety conscious but still jump.

 

[mal4mac]

Well we can always hope that people are reading the saftey reports and that we save a few. Guys who already from the beginning don't know a thing about neither physics nor how to read reports...

 

[ZapperZ]

You can be concerned about safety, but still enthusiastically support something. For instance, a sky diver might be very safety conscious but still jump.

.. which means that he HAS checked that everything is safe enough to continue to jump. If it isn't, he won't have jumped!

So if you think your analogy is correct, Martin Rees has checked that the LHC is safe and thus, will support its running. Then why are you still using his "concern" here? Via your analogy, it is SAFE. Case closed!

Zz.

 

[vanesch]

You have a point. Just like the atom is made up of a nucleus and some electrons within a lot of empty space, so the nucleus is made up of protons and neutrons, which are themselves made up of up and down quarks. My expectation is that the hole would have to actually hit one of the most fundamental particles to achieve anything. Its gravity, at this stage, is much to weak to draw a particle in against the electromagnetic or the nuclear force.

You have to get away from the "drawing in" picture. You rather have an *interaction probability* - which is in a normalized form, the so-called cross section (which, I repeat, is at this level usually not to be taken equal to any geometrical cross section, although this might give you eventually an idea of order of magnitude).

So when a MBH crosses nuclear matter - which it its scale, is a swarm of point-like quarks, gluons or eventually their constituents whatever that may be, and with each of these particles, it has a certain interaction probability, and one of the possible interactions is "eating up" (but also: scattering, or other things). This is very similar to what happens when a high-energy electron crosses a proton, only there's no "eating up" reaction, but only scattering. A high-energy electron kicks out, most of the time, just one quark. This gives then rise to a hadronic jet of the kicked-out quark, and a hadronic jet of the rest of the proton.
If we had something similar with a BH, I can imagine (although this is guesswork on my side), that something similar happens: the BH "eats" a single quark, gets colored, and a "hadronic jet" develops in which a newly created color charge will bind (strong force) to the BH, and the remnant quarks will also generate a jet. The colored BH, bound to another quark, will then maybe end up by eating up that bound quark too after some time (depends on its probability to interact with it). But a priori it will not "draw in" the other quarks of the remnant of the proton.

However, what is the size of the most fundamental particle? If an electron is fundamental, one might try to calculate a minimum size for an electron, based on the idea that its total mass must be larger (or, at any rate, not smaller) than the mass of its electric field. This gives me a diameter of roughly 1/100.000 of the atom diameter for the electron.

For sure not. 1/100 000 of an atom diameter is about the size of a nucleus. We know that electrons are way way smaller, given that we use it as a probe inside the proton. In fact, in the standard model, we consider the electron to be point-like.
But again, you cannot really use geometrical arguments to derive interaction probabilities. There is no "touching" at this scale.

But if it formed in the LHC, at a moderate speed, if might well have enough time to do so. And otherwise it would be attracted to any nucleus it passed, increasing its effective cross section until it had neutralized its charge.

You have to understand that far most interactions at the LHC are also not in the center of gravity of the two protons, but rather in the center of gravity of the two interacting quarks, which have wildly different momenta.

At any rate, I wonder whether a black hole could get away after swallowing just one quark. Not only would it have a partial charge, it would also have a colour charge, and be strongly attracted to the remaining quarks.

My guess is that it would end up in a bound state (under the strong force) with a complementary quark.

But, yes, the cross section of 1/100,000 squared might be wrong. Suppose that it is essential for the hole to hit a quark, with a cross section of 1/100,000,000 squared, and suppose that even if it does so, it only takes one nucleon mass, not an entire atom. Instead of having to pass through ten billion layers of atoms, it would have to pass through ten million billion layers of atoms, or one hundred kilometers of solid mass. On one passage through the Earth the hole would acquire roughly 100 proton masses; it would need 100 orbits to double its mass, which it would complete in a week. The growth would not be linear, because the diameter of the hole itself would slowly increase, but it might be centuries before this became noticable.

As I said somewhere else jokingly, we might already have produced a lot of such black holes at the Tevatron, which are just starting to eat out the Earth from inside.

 

[mal4mac]

.. which means that he HAS checked that everything is safe enough to continue to jump. If it isn't, he won't have jumped!

So if you think your analogy is correct, Martin Rees has checked that the LHC is safe and thus, will support its running. Then why are you still using his "concern" here? Via your analogy, it is SAFE. Case closed!

Zz.

Martin Rees might still jump, given his safety analysis, but others might decide, on the same analysis, that it is too risky for them. So the case is never closed, because people will always have different subjective preferences.

 

[Almanzo]

If we had something similar with a BH, I can imagine (although this is guesswork on my side), that something similar happens: the BH "eats" a single quark, gets colored, and a "hadronic jet" develops in which a newly created color charge will bind (strong force) to the BH, and the remnant quarks will also generate a jet. The colored BH, bound to another quark, will then maybe end up by eating up that bound quark too after some time (depends on its probability to interact with it). But a priori it will not "draw in" the other quarks of the remnant of the proton.

Would it be fair to say that after "eating" a quark, a micro black hole would behave like a quark, although an unusually massive one? In that case, micro black holes, formed by cosmic radiation or whatever, might be found inside some "protons" and account for some of the Dark Matter. That would be interesting, because such "heavy protons" might be harvested from space, and manipulated by means of chemistry. Superdense materials might be created.

Once confined inside an elementary particle, the micro black hole would probably be harmless. (Unless too many of them existed within a small space, and the treshold for formation of a black hole would be exceeded once more. But on second thought, an atom containing a 10.000 proton mass black hole would have merely 10.000 times the density of normal matter, while neutronium has 10¹⁵ times that density. If neutron stars can be kilometer-sized, confined micro black holes would not quickly become dangerous.)

For sure not. 1/100 000 of an atom diameter is about the size of a nucleus. We know that electrons are way way smaller, given that we use it as a probe inside the proton. In fact, in the standard model, we consider the electron to be point-like.
But again, you cannot really use geometrical arguments to derive interaction probabilities. There is no "touching" at this scale.

That is strange. I will try to recalculate the minimum radius for the electron. The idea is that the electric field E = Q/4*pi*epsilon*r² had an energy density U = epsilon*E²/2, and therefore a mass density U/c². Which can be integrated over the space outside the electron to yield a mass proportional to 1/R, where R is the radius of the electron. In using the electron as a probe, would it be the size of the electron (at rest) that matters, or rather the wavelength of the (moving) electron's de Broglie wave?

 

[vanesch]

That is strange. I will try to recalculate the minimum radius for the electron. The idea is that the electric field E = Q/4*pi*epsilon*r² had an energy density U = epsilon*E²/2, and therefore a mass density U/c². Which can be integrated over the space outside the electron to yield a mass proportional to 1/R, where R is the radius of the electron.

If you do that, you will find the "classical electron radius" http://en.wikipedia.org/wiki/Classical_electron_radius or the Thomson scattering length.

But that's not the "size" of the electron as a "bullet".

 

[vanesch]

Once confined inside an elementary particle, the micro black hole would probably be harmless.

Not really, because it would interact sooner or later with its partner and "eat it". Just like positronium (a bound state of a positron and an electron) can sooner or later annihilate.

 

[Sakha]

How much time does it takes to the protons to reach 99.999% of c in the LHC?

 

[gendou2]

Good question. There are several stages in the acceleration of the beams. See this video for some more info:

 

[humanino]

How much time does it takes to the protons to reach 99.999% of c in the LHC?

In which referential frame ?

 

[Sakha]

In the detectors referential frame.

 

[gendou2]

The Schwarzschild radius R_S of an (4+n)-dimensional black hole:
R_s = \frac{1}{\sqrt{\pi} M_p} \left[ \frac{M_{BH}}{M_p} \left( \frac{8 \Gamma\left( \frac{n+3}{2} \right)}{n+2} \right) \right] ^{\frac{1}{n+1}}
How do I transform this equation into Systeme International units?

First of all, let's stick to 4 dimensions for simplicity where:

R_s = \frac{2Gm}{c^2}

Solving for the smallest black hole having 1 Planck mass:

R_s = 3.23123546 * 10^-35 meters

References:
http://en.wikipedia.org/wiki/Schwarzschild_radius
http://en.wikipedia.org/wiki/Planck_mass

 

[humanino]

In the detectors referential frame.

I thought we had the convention that smileys indicate a joke

R_s = 3.23123546 * 10^-35 meters

Can we use this to set up an upper bound on the cross section for MBH matter accretion ?

 

[gendou2]

Sure, but I'm not sure how to do that.
Using the same math as my other post, I calculate the evaporation time of a black hole this size to be 1.38 * 10^-40 seconds.
This small size and evaporation time suggests to me that the energy density required for accretion of such a black hole is unimaginably enormous.
In other words, I subscribe to the general statement that present day micro black holes are unstable. Period.

 

[humanino]

In other words, I subscribe to the general statement that present day micro black holes are unstable. Period.

If you think that I question that, you must have read very few pages of this discussion.

Sure, but I'm not sure how to do that.

My question is : how is the geometrical cross section related to the Schwarzschild radius ? It's a simple and elementary question. Which classical radius should I use to set up an absolute upper bound on any possible quantum cross section ? The even horizon, the acoustic horizon, the apparent horizon (...?) ?

 

[gendou2]

If you think that I question that, you must have read very few pages of this discussion.

Please understand, I did not mean to question you at all.

How is the geometrical cross section related to the Schwarzschild radius? It's a simple and elementary question. Which classical radius should I use to set up an absolute upper bound on any possible quantum cross section? The even horizon, the acoustic horizon, the apparent horizon?

Oh, sorry I misunderstood your question. As I understand, R_s is the radius of the event horizon, which is the surface of the black hole. So, the quantum cross section should have a radius of R_s.

It is reasonable to consider the semiclassical cross sections with form
factors greater than unity as loose upper bounds on the black hole cross sections, which may increase by a factor of a few as the trapped-surface cross sections increase.

- From http://arxiv.org/abs/hep-ph/0609055

 

[humanino]

I found this article: http://arxiv.org/abs/hep-ph/0609055
Might be helpful.

Thanks for the link. After reading the beginning, I realize that my question is moot. If one is after a cross section upper bound estimate for safety purposes, a factor 3, 4 or even 10 is irrelevant. The upper bound must provide safety with plenty orders of magnitude anyway. Still, the article discusses this, and other aspects as well.

 

[gendou2]

Yeah, that trapped surface cross section stuff is a little over my head. Sorry for the initial confusion.

 

[malawi_glenn]

How much time does it takes to the protons to reach 99.999% of c in the LHC?

that is just 220GeV.. not so long time. It depends on what you mean-> starting a single proton bunch at 0 to 99.999c or when LHC will start running protons at that energy?

 

[Nick666]

LHC live cam.

http://www.cyriak.co.uk/lhc/lhc-webcams.html

 

[Almanzo]

Humanino: Assuming that the initial mass of the micro black hole would be equal to ten thousand proton masses, I calculate a Schwarzschild Radius of 1.2 * 10^-50 meter. The impact parameter would not be appreciably larger, because the force of gravity is 10⁴⁰ times weaker than the electromagnetic force, so the hole would not be able to draw anything in by its gravity. Neither would it be able to polarize or damage anything by its tidal force.

R= GM/c², where G = 6.67 * 10^-11 m³/kg*s², c = 3.00 * 10⁸ m/s, and M = 1.67 * 10^-23 kg.

 

[Vanadium 50]

that is just 220GeV.. not so long time. It depends on what you mean-> starting a single proton bunch at 0 to 99.999c or when LHC will start running protons at that energy?

220 GeV is below injection energy for the LHC.

 

[Hans Dorn]

Since the postulated minature black holes are so incredibly small, wouldn't they just pass through protons or neutrons unaffected?

Hadrons are composite particles after all.

 

[Orion1]

(4+n)-dimensional black hole...


The Schwarzschild radius R_s of an (4+n)-dimensional black hole: (ref. 2)
R_s = \frac{1}{\sqrt{\pi} M_p} \left[ \frac{M_{BH}}{M_p} \left( \frac{8 \Gamma\left(\frac{n+3}{2} \right)}{n+2} \right) \right] ^{\frac{1}{n+1}}

The Schwarzschild radius R_s of an (4+n)-dimensional black hole: (ref. 3)
R_s = \frac{1}{M_p} \left[ \frac{M_{BH}}{M_p} \left( 2^3 \sqrt{\pi}^{(-n-1)} \frac{\Gamma \left(\frac{n+3}{2} \right)}{n+2} \right) \right]^{\frac{1}{n+1}}

Why does the second equation solution dimensionally act upon \sqrt{\pi}, however the first equation solution does not?

Theorists have thus suggested that there could be extra spatial dimensions below this scale, curled up into tiny loops. Gravity could then be much stronger than we have measured, but with most of it being absorbed into the "invisible" extra dimensions. Stronger gravity corresponds to a smaller Planck mass, lowering the predicted Higgs mass and thus solving the hierarchy problem.

It is plausible that extra dimensional micro-black holes can quantum-gravitationally interact with normal matter equivalent to the strong nuclear force via Strong Gravitation.

Strong Gravitation: (1 Tev)
(Quantum BH strong nuclear reaction with a proton)
\boxed{t_p = \frac{4 E_b^2}{3} \sqrt{\frac{m_p r_p^7}{2 (\hbar c)^5}}}
\boxed{t_p = 3.362 \cdot 10^{-16} \; \text{s}}
[/Color]
Reference:
http://www.youtube.com/watch?v=kVsZdgz5oFM"
http://arxiv.org/PS_cache/hep-ph/pdf/0106/0106295v1.pdf"
http://arxiv.org/PS_cache/hep-ph/pdf/0609/0609055v2.pdf"
http://www.wissensnavigator.ch/documents/OTTOROESSLERMINIBLACKHOLE.pdf"
http://physicsworld.com/cws/article/print/26016"

Leave, leave Geneva every last one of you,
Saturn will be converted from gold to iron,
RAYPOZ will exterminate all who oppose him,
Before the coming the sky will show signs.