Artificial Black Holes, again

[franznietzsche]

I like your enthusiasm! That's the spirit!

All I'm saying is that the CERN scientists use the evident here-ness of solar system bodies as proof for the safety of this experiment. I'm just pointing out one not-here-ness. I don't see it as being any weaker than their arguments (especially considering that they seemed to forget about the law of conservation of momentum).


Ah, then you think it WAS a planet that broke up, versus a void orbit caused by Jupiter's gravity? Sorry, I don't see Jupiter as being capable of actually breaking a planet at that distance. Flinging it away? Maybe. But chopping it into itty bitty pieces?

Ah, then you like putting words in my mouth. You asked why, if a planet was broken by jupiter, wouldn't the asteroids be the same size. I replied to that. I was not stating that I thought a planet formed and was subsequently broken up.

Generally speaking, the non-Gallilean moons are quite small and are obviously captured asteroids, as are Mars' moons. Most have retrograde orbits. The Galilean moons orbits are only elliptical due to Laplace resonance. Where's the evidence that they are caused by Jupiter's ability to "shred it (a proposed proto-planet) into smaller bodies which could survive the tidal forces, giving rise to some of Jupiter's larger moons."

How does Io survive these amazing chopping forces of Jupiter?

Io is literally turning itself inside out because of the tidal, not chopping, forces.

I never supported the comment that captured chunks of rock gave rise to some of Jupiter's larger moons. I object to your comment that 1) Asteroids should suddenly be the same size, and 2) that jupiter's moons mostly have circular orbits.

I think this thread has been just been a progression of greater and greater crackpottery, and should simply be locked.

 

[ubavontuba]

Ah, then you like putting words in my mouth. You asked why, if a planet was broken by jupiter, wouldn't the asteroids be the same size. I replied to that. I was not stating that I thought a planet formed and was subsequently broken up.

No, I asked; "Also, why do the asteroids exist in the wide array of sizes they do then? Shouldn't they be more uniform?" in regards to an assumption that a proto-planet hadn't ever formed.

Io is literally turning itself inside out because of the tidal, not chopping, forces.

I never supported the comment that captured chunks of rock gave rise to some of Jupiter's larger moons.

Why do you think I do? That concept came from someone else (AlphaNumeric).

Aside to Alphanumeric: Why haven't the numerous smaller moons formed up into larger ones too?

I object to your comment that 1) Asteroids should suddenly be the same size, and 2) that jupiter's moons mostly have circular orbits.

Where did I write; "Asteroids should suddenly be the same size"? As for circular orbits, I was referring to the "larger" (Galilean) moons mentioned by AlphaNumeric.

I think this thread has been just been a progression of greater and greater crackpottery, and should simply be locked.

I agree. The "experts" here haven't answered any of my questions, and have resorted to crackpot rhetoric to suppress them.

 

[Rach3]

Apparently you missed the fact that we were discussing the concept of one eating a planetary core, thus embuing it with some significant mass.

Did you miss the fact, frequently repeated in this thread, that the timescale for 'eating' even a single proton is an astronomical timescale? Or the part where a 10^9 ton black hole was shown to be harmless? (It's also microscopic, if you do the math.)

That'd be nice, but what about the planetary core's own internal pressure and it's effects?

Yes, what about them? We've already mentioned that the mass density is on the order of unity that of solids at STP. I.e., insignificant.

My point exactly. Thereby belying the CERN scientists assumption that the existence of solar objects is proof that no harm can come to us by the creation of artificial nano black holes. If they form natuarally, they don't stick around long enough to cause any harm regardless.

The same argument applies equally well to accelerator-produced black holes. Their mass is SMALL compared to the energies involved, so they must invariably be highly relativistic. Not that it would make any difference.

 

[Orion1]

Classical GR cross section...


Classical GR Planck Singularity cross-section

m_{Fe} = 9.274 \cdot 10^{-26} \; \text{kg} - Iron nucleon mass (35.1% Terra composition)

m_e - Terra mass
r_e - Terra radius

\tau \sim \frac{1}{n \sigma v}

n_e = \frac{3 m_e}{4 \pi m_{Fe} r_e^3}

\sigma_c = \frac{\pi \hbar G}{c^3}

v_e = \sqrt{\frac{2 G m_e}{r_e}}

\tau_b = \frac{1}{n_e \sigma_c v_e} = \left( \frac{4 \pi m_{Fe} r_e^3}{3 m_e} \right) \left( \frac{c^3}{\pi \hbar G} \right) \left( \sqrt{\frac{r_e}{2G m_e}} \right)

Combining terms:

\tau_b = \frac{4 c^3 m_{Fe}}{3 \hbar} \sqrt{\frac{r_e^7}{2 G^3 m_e^3}}
[/Color]
Reference:
https://www.physicsforums.com/showpost.php?p=1001445&postcount=14
https://www.physicsforums.com/showpost.php?p=1002158&postcount=28

 

[vanesch]

Question for the experts - if the black hole is formed from a collision of hadrons, will it interact via the strong force? I can't imagine what qcd looks like in a black hole...

If it is a classical black hole, it can only interact through gravity. If it is not a classical black hole, then who's going to say how it interacts...

 

[vanesch]

My point exactly. Thereby belying the CERN scientists assumption that the existence of solar objects is proof that no harm can come to us by the creation of artificial nano black holes. If they form natuarally, they don't stick around long enough to cause any harm regardless.

Yes, but you're forgetting that this is only ONE of the arguments. Let's put all the arguments in a row:

- first of all, the LHC is not built to make black holes, contrary to what one sometimes might read in speculative articles. However, because the LHC is going to explore higher (a factor 10 about) per nucleon energies, new scenarios are not excluded (one of the reasons to build the machine is to explore a new region of course).

- the energies that will occur in the LHC are much lower than the highest energies occurring naturally in cosmic rays

- in the hypothetical case that black holes might form, normally they should evaporate through Hawking radiation

- in the hypothetical^2 case that Hawking radiation doesn't happen, normally they would have some remnant momentum, by far strong enough to have them escape the Earth's gravity (just as with cosmic ray generated hypothetical black holes)

- in the hypothetical^3 case where they'd form in EXACTLY the center of gravity of the collision (highly unlikely), and Hawking radiation doesn't happen, then they'd be captured by the earth, and they'd eat a proton every year or so according to classical estimations.

People figure that we're now in lala land and that we can take that risk. Others, with safety belts on their sofas, might not agree.

 

[ubavontuba]

Did you miss the fact, frequently repeated in this thread, that the timescale for 'eating' even a single proton is an astronomical timescale? Or the part where a 10^9 ton black hole was shown to be harmless? (It's also microscopic, if you do the math.)

That's right. Perhaps you missed my first post in this thread wherein I stated we're probably safe. However, that safety is relatively reliant on our theories being correct, and no one really knows that our theories hold true beyond the event horizon. I'm not saying the experiments are inherently dangerous and I'm not saying the experiments shouldn't be conducted. I'd just like the experiments to be performed in a "can't miss" secure way.

Yes, what about them (planetary core's own internal pressure and it's effects)? We've already mentioned that the mass density is on the order of unity that of solids at STP. I.e., insignificant.

Perhaps it is insignificant, perhaps not. Should the nano black hole have the ability to absorb whole particles (not known that they wouldn't), then they'd essentially become a drain in which the internal pressures can fllow into, right?

The same argument applies equally well to accelerator-produced black holes. Their mass is SMALL compared to the energies involved, so they must invariably be highly relativistic. Not that it would make any difference.

Highly relativistic in quantum scales? Don't these two theories come to odds here?

 

[ubavontuba]

Yes, but you're forgetting that this is only ONE of the arguments. Let's put all the arguments in a row:

- first of all, the LHC is not built to make black holes, contrary to what one sometimes might read in speculative articles. However, because the LHC is going to explore higher (a factor 10 about) per nucleon energies, new scenarios are not excluded (one of the reasons to build the machine is to explore a new region of course).

Really? That's not what the http://www.cerncourier.com/main/article/44/9/22" says. Are they lying then?

- the energies that will occur in the LHC are much lower than the highest energies occurring naturally in cosmic rays

Sure, but why does that matter? According to CERN it doesn't matter because:

It should be stated, in conclusion, that these black holes are not dangerous and do not threaten to swallow up our already much-abused planet. The theoretical arguments and the obvious harmlessness of any black holes that, according to these models, would have to be formed from the interaction of cosmic rays with celestial bodies, mean that we can regard them with perfect equanimity.

Don't you think if conservation of momentum is considered, this argument is generally baseless?

- in the hypothetical case that black holes might form, normally they should evaporate through Hawking radiation

"Should" is not the same as "will".

- in the hypothetical^2 case that Hawking radiation doesn't happen, normally they would have some remnant momentum, by far strong enough to have them escape the Earth's gravity (just as with cosmic ray generated hypothetical black holes)

Maybe, maybe not. Remember they're intent is to make thousands at a time. Can you guarantee that none will not have escape velocity? You, yourself suggested they weaken one beam for an added measure of safety. I concurred.

- in the hypothetical^3 case where they'd form in EXACTLY the center of gravity of the collision (highly unlikely), and Hawking radiation doesn't happen, then they'd be captured by the earth, and they'd eat a proton every year or so according to classical estimations.

How can you so easily trust "classical calculations" with something that's so poorly understood?

People figure that we're now in lala land and that we can take that risk. Others, with safety belts on their sofas, might not agree.

Since the world is shared by all, shouldn't everyone's opinion count?

 

[vanesch]

Really? That's not what the http://www.cerncourier.com/main/article/44/9/22" says. Are they lying then?

It's a *hypothetical* article.

Don't you think if conservation of momentum is considered, this argument is generally baseless?

Yes, but the argument ALSO goes for production in an accelerator, because normally, there's no reason why the momentum should come out 0, as there will always be remnants.

Maybe, maybe not. Remember they're intent is to make thousands at a time. Can you guarantee that none will have not have escape velocity? You, yourself suggested they weaken one beam for an added measure of safety. I concurred.

Yes, but it is a silly argument, because the probability of having one with 0 momentum coming out with "untuned" beams is the same as for tuned beams, because no such collision will not have any remnants. So one needs the remnants to perfectly balance in order for the hole to be "at rest" in the lab frame.

How can you so easily trust "classical calculations" with something that's so poorly understood?

Well, if there are scientific arguments AT ALL to say that black holes are to be produced, and if you are using scientific arguments to say that they will eat the earth, then one is allowed to use the same kind of argument to refute it, no ?
If one can use hypothetical arguments (as of now, they ARE hypothetical) to say that black holes are going to be produced in the first place, then why can one NOT use LESS hypothetical arguments to show that they will not cause any harm ? The classical theory of black holes (on which you base yourself to even call them black holes and to even think it might eat the earth) is much more solid than the HYPOTHETICAL arguments that they might be produced (namely the necessity of the universe to be at least 10-dimensional). Hawking radiation, although hypothetical, is nevertheless based upon thermodynamics mixed with some quantum ideas and classical GR, and is as such LESS hypothetical than the theory that says that BH will form in the first place.

Since the world is shared by all, shouldn't everyone's opinion count?

No, only the opinion of people knowing what they talk about should count. Know what ? Two days ago, next to where I'm working, they opened a new research center on nanotechnology, Minatec:
http://www.minatec.com/minatec_uk/index.htm

Well, at the day of its official opening, there have been demonstations by people opposed to it for various hilarious reasons...

http://biotech.indymedia.org/or/2006/05/5127.shtml

I agree that scientists shouldn't be reckless, but one shouldn't be demonstrating against one's own ignorance either, and disrupt the work of people knowing what they are doing.

 

[ubavontuba]

It's a *hypothetical* article.

Sure, but obviously considered seriously.

Yes, but the argument ALSO goes for production in an accelerator, because normally, there's no reason why the momentum should come out 0, as there will always be remnants

.

Well, according to my research, the impacts have to be nearly perfect for them to obtain the hypothetical nano black hole. If they're perfect and the beams are equal, there really will be no relative momentum to the earth.

Yes, but it is a silly argument, because the probability of having one with 0 momentum coming out with "untuned" beams is the same as for tuned beams, because no such collision will not have any remnants. So one needs the remnants to perfectly balance in order for the hole to be "at rest" in the lab frame.

See above. Also, beam differentials can be sufficient to virtually gaurantee nano black hole escape velocity. That is, they can be tuned to an energy level that would not be sufficient to create nano black holes, if escape velocity is not met. However, this may reduce the energy too much to create them to begin with.

Well, if there are scientific arguments AT ALL to say that black holes are to be produced, and if you are using scientific arguments to say that they will eat the earth, then one is allowed to use the same kind of argument to refute it, no ?
If one can use hypothetical arguments (as of now, they ARE hypothetical) to say that black holes are going to be produced in the first place, then why can one NOT use LESS hypothetical arguments to show that they will not cause any harm ?

Because producing them or not isn't nearly so imporatnt as the consideration of safety. If a young kid is playing with a handgun and he told you he unloaded it, would you believe it to be safe? Assurances of safety aren't always sufficient. The gun may indeed be safe, but are you willing to take the risk?

The classical theory of black holes (on which you base yourself to even call them black holes and to even think it might eat the earth) is much more solid than the HYPOTHETICAL arguments that they might be produced (namely the necessity of the universe to be at least 10-dimensional). Hawking radiation, although hypothetical, is nevertheless based upon thermodynamics mixed with some quantum ideas and classical GR, and is as such LESS hypothetical than the theory that says that BH will form in the first place.

I'd agree wholeheartedly with this, save it's thought they've already done this at the RHIC.

No, only the opinion of people knowing what they talk about should count.

Well I live in a democracy, and in a democracy even the less astute have a say in their fate (as they should).

Know what ? Two days ago, next to where I'm working, they opened a new research center on nanotechnology, Minatec:
[URL]http://www.minatec.com/minatec_uk/index.htm[/url

Well, at the day of its official opening, there have been demonstations by people opposed to it for various hilarious reasons...

http://biotech.indymedia.org/or/2006/05/5127.shtml

Maybe they're hilarious, maybe not. However I feel it is the institution that is responsible for easing the minds of the protesters. Remember, people once thought it was stupid to protest for environmental protections too.

I agree that scientists shouldn't be reckless, but one shouldn't be demonstrating against one's own ignorance either, and disrupt the work of people knowing what they are doing.

But do they? Aren't scientists the first to state that they're conducting these experiments because they DON"T know what will happen?

 

[vanesch]

Well, according to my research, the impacts have to be nearly perfect for them to obtain the hypothetical nano black hole. If they're perfect and the beams are equal, there really will be no relative momentum to the earth.

Could you elaborate on this ? You mean it is only when there is entire coherence between the different parton interactions of the two protons that a black hole can form ? This must be a totally coherent diffractive phenomenon ?

See above. Also, beam differentials can be sufficient to virtually gaurantee nano black hole escape velocity. That is, they can be tuned to an energy level that would not be sufficient to create nano black holes, if escape velocity is not met. However, this may reduce the energy too much to create them to begin with.

Well, I have no idea of the precision by which the two beams are equal. But it would be fun if you could work out what would be the needed "untuning" for the COM.
Let's do it:
the mass of two 7 TeV protons colliding is essentally 14 TeV, or
14 TeV * 1.6 10^(-19) / c^2 = 2.5 10^(-23) kg

Giving this mass a velocity of 11200 m/s (escape velocity) comes down to a momentum of this mass of 2.78 10^-19 kg m/s, which is very non-relativistic of course. In eV units, we need to multiply by c and divide by e, to find: 522 MeV untuning is sufficient. I even wonder if they can tune the beams to such an accuracy: we're talking about 0.004% of the total beam energy here.

But do they? Aren't scientists the first to state that they're conducting these experiments because they DON"T know what will happen?

Well, there's a difference between expecting eventually some new stuff to happen, and totally out-of-the-blue catastrophe scenarios, which are on one side BASED upon speculative, and less speculative theories in order to even make the catastrophe scenario initially potentially plausible, but then DENYING the same theories which are then used to show that the catastrophe will not happen, finally.

Why not putting up scenarios for ultrasound ripping apart the spacetime continuum, so that sudden singularities will open up a corridor that enables space invaders to take over earth, and feed on humans ?
I would propose, based upon that, to ban immedately any research on piezo-electric sound transducers...

Honestly, both scenarios sound just as crazy.

 

[AlphaNumeric]

Right, but with little or no relative momentum to the Earth's center of mass.

They are moving at 99.9999% the speed of light, while the Earth is moving at ~0.00001% the speed of light. Is that a big enough different for you? They have LOADS of momentum (for an subatomic object) when taken in the Earth's reference frame! If they didn't, the particle accelerator would be useless, it'd not be accelerating anything!

Remember, momentum is conserved.

No, really? So that was what I should have remembered for my quantum field theory exam last Thursday

If you'd just apply basic Newtonian Mechanics to what you are writing, you'd see that regardless of the odds of one forming, the odds of one sticking around are virtually zero. Therefore, this argument is meaningless.

So is your about the black holes perhaps to be had at CERN, they've shedloads of momentum to move through the Earth. Even if the colliding beams are untuned by 0.0001% the resultant black hole would sail through the Earth without thinking twice.

Aside to Alphanumeric: Why haven't the numerous smaller moons formed up into larger ones too?

Why would they?

But do they? Aren't scientists the first to state that they're conducting these experiments because they DON"T know what will happen?

That's what experiments are for, to check what we hope will happen will happen. Are you saying any kind of electronic research should be stopped incase the energy involved triggers a castestropic black hole or sends out a signal aliens hear and then come to invade us?

Won't someone think of the children!

 

[Rach3]

Highly relativistic in quantum scales? Don't these two theories come to odds here?

No, SR is not in conflict with QM.

Well, according to my research, the impacts have to be nearly perfect for them to obtain the hypothetical nano black hole. If they're perfect and the beams are equal, there really will be no relative momentum to the earth.

You claim to be doing research in string theory...

 

[SpaceTiger]

SpaceTiger, I attempted to setup your equation in post #28, however I obtain a large value for \tau_b?

You're using the conventional Planck length for the horizon radius. TeV mass black holes only appear in theories with extra dimensions that modify the Planck quantities. See here:

https://www.physicsforums.com/showpost.php?p=1001445&postcount=14"

 

[Orion1]

Classical GR Terra micro-singularity cross-section:

m_{Fe} = 9.274 \cdot 10^{-26} \; \text{kg} - Iron nucleon mass (35.1% Terra composition)

m_e - Terra mass
r_e - Terra radius
E_b - 1 Tev energy

\tau \sim \frac{1}{n \sigma v}

n_e = \frac{3 m_e}{4 \pi m_{Fe} r_e^3}

r_h = \frac{\hbar c}{E_b}

\sigma_c = \pi \left( \frac{\hbar c}{E_b} \right)^2

v_e = \sqrt{\frac{2 G m_e}{r_e}}

\tau_b = \frac{1}{n_e \sigma_c v_e} = \left( \frac{4 \pi m_{Fe} r_e^3}{3 m_e} \right) \left[ \frac{1}{\pi} \left( \frac{E_b}{\hbar c} \right)^2 \right] \left( \sqrt{\frac{r_e}{2G m_e}} \right)

Combining terms:

\tau_b = \frac{4 m_{Fe}}{3} \left(\frac{E_b}{\hbar c} \right)^2 \sqrt{\frac{r_e^7}{2 G m_e^3}}

\tau_b = 12331.540 \; \text{s} = 3.425 hrs.

m_p - Proton mass
m_{\odot} - Sol mass
r_{\odot} - Sol radius

Classical GR Sol micro-singularity cross-section:
\tau_b = \frac{4 m_p}{3} \left(\frac{E_b}{\hbar c} \right)^2 \sqrt{\frac{r_{\odot}^7}{2 G m_{\odot}^3}}

\tau_b = 15.722 \; \text{s}

Oh no!, micro-singularity radiation has seeded the Earth and the Sun with some black-holes!, we must all evacuate this solar system immediately!

[/Color]
Reference:
https://www.physicsforums.com/showpost.php?p=1001445&postcount=14
https://www.physicsforums.com/showpost.php?p=1002158&postcount=28
https://www.physicsforums.com/showpost.php?p=1004506&postcount=64

 

[vanesch]

r_h = \frac{\hbar c}{E_b}

Didn't check everything, but this is weird: the hole radius DECREASES with increasing energy ??

 

[Orion1]

Didn't check everything, but this is weird: the hole radius DECREASES with increasing energy ??

Affirmative, setting the threshold energy equivalent to the Planck Energy results in a Planck Radius:

r_h = \frac{\hbar c}{E_b}

E_b = E_p

E_b = \sqrt{\frac{\hbar c^5}{G}}

r_h = \hbar c \sqrt{\frac{G}{\hbar c^5}} = \sqrt{\frac{\hbar G}{c^3}}

r_h = r_p

r_h = \sqrt{\frac{\hbar G}{c^3}}

This is called a 'quantum black hole'.

According to my research, the Planck Mass is the maximum producible mass of a 'quantum black hole'. Meaning that any particle accelerator or cosmic event within this quantum threshold is not capable of generating a more massive quantum singularity, except by spherical absorption or accretion.

Interesting to note, that if 'quantum black holes' can exist as naked singularities, then a Planck Mass can also exist as a naked singularity.
[/Color]

 

[vanesch]

Affirmative, setting the threshold energy equivalent to the Planck Energy results in a Planck Radius:

Ah, yes, understood ; you adapt G in the classical formula of a BH in order for the Planck energy to come out equal to 1 TeV. Yes, then the schwarzschild radius is indeed the Planck radius (up to a factor 2 I think).

Next point, your tau_b is the time constant needed to EAT ONE SINGLE IRON NUCLEUS, right ? So this BH eats one single iron atom every 3 hours, if I'm not mistaking ? (and on the sun, one proton every 15 seconds).

Not so worrysome, right ?

 

[rcgldr]

Why don't neutrons or protons behave like mini black holes? Can matter get even denser than a single neutron or proton?

 

[jarvis]

This is a very entertaining thread, in the funny nothing of consequence sort of way! It has been like daytime television. I can read page one, then come back later and read page 6, and I have not missed a beat! Anecdotal arguments, lucky for us, are not sufficient to cease all fundamental high energy physics in the world. It reminds me of the people who thought we would set the Earth's atmosphere on fire by detonating a nuclear device. By the way, when the great name of "string theory" is invoked, which of the five mathematically self consistent versions are you referring to? The one that we have a chance at doing experiments to support? Wait, that doesn't answer the question does it, still left with five.

This is all in good fun of course, no offense is intended towards anyone!

 

[tehno]

Why don't neutrons or protons behave like mini black holes? Can matter get even denser than a single neutron or proton?

electrons/positrons are "denser".

 

[rcgldr]

electrons/positrons are "denser".

OK, can a single electron exhibit the behaviour of a very tiny black hole? Hmm, they do capture and release photons.

 

[Orion1]

\tau_b is the 'mean time' interval for nuclear reaction occurence or the time required to absorb 1 particle. This is the amount of time required for a single quantum black hole to reaction with a single iron nucleus or with a single proton.

The 'particle reaction rate' is the reciprocal of the 'mean time'.

\lambda_b = \frac{1}{\tau_b} = \frac{dn}{dt}

\lambda_b = \frac{dn}{dt} = \frac{3}{4 m_{Fe}} \left(\frac{\hbar c}{E_b} \right)^2 \sqrt{\frac{2 G m_e^3}{r_e^7}}

Based upon this particle rate, and presuming this rate is constant, how much time would be required for a single quantum black hole to consume 1 m^3 of Terra?

t_a = \frac{n_e}{\lambda_b} = \frac{1}{\sigma_c v_e} = \frac{1}{\pi} \left( \frac{E_b}{\hbar c} \right)^2 \sqrt{\frac{r_e}{2 G m_e}}

t_a = \frac{1}{\pi} \left( \frac{E_b}{\hbar c} \right)^2 \sqrt{\frac{r_e}{2 G m_e}}

t_a = 7.309 \cdot 10^{32} \; \text{s m}^{-3} - 2.317*10^25 years*m^-3

Based upon this particle rate, and presuming this rate is constant, how much time would be required for a single quantum black hole to consume Terra?

n_t = \frac{m_e}{m_{Fe}}

t_e = \frac{n_t}{\lambda_b} = \left( \frac{m_e}{m_{Fe}} \right) \frac{1}{\lambda_b}

t_e = 7.951 \cdot 10^{53} \; \text{s} - 2.521*10^46 years

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Reference:
https://www.physicsforums.com/showpost.php?p=1005179&postcount=75

 

[vanesch]

\tau_b is the 'mean time' interval for nuclear reaction occurence or the time required to absorb 1 kg.

This is then a strange notation, because:

(density x sigma x velocity) is normally the rate, per unit of time, of ONE SINGLE INTERACTION (of which there are "density" items per unit of volume).

 

[Orion1]

your tau_b is the time constant needed to EAT ONE SINGLE IRON NUCLEUS, right ? So this BH eats one single iron atom every 3 hours, if I'm not mistaking ? (and on the sun, one proton every 15 seconds).

(density x sigma x velocity) is normally the rate, per unit of time, of ONE SINGLE INTERACTION (of which there are "density" items per unit of volume).

Affirmative, that is correct.
\lambda = n \sigma v

t_e = \frac{4}{3} \left(\frac{E_b}{\hbar c} \right)^2 \sqrt{\frac{r_e^7}{2 G m_e}}

t_e = 7.951 \cdot 10^{53} \; \text{s} - 2.521*10^46 years

[/Color]
Reference:
https://www.physicsforums.com/showpost.php?p=1005179&postcount=75

 

[Orion1]

The Planck mass...

However, the multiple dimensions postulated by string theory would make gravity many orders of magnitude stronger at small distances. This has led some string theorists to predict micro black hole production at upcoming colliders.

Current predictions for the behavior of a black hole with a mass less than Planck mass are inconsistent and incomplete.

I am enquiring as to what the string theory predicted 'orders of magnitude stronger' value is for G at small distances?

m_p - Proton mass

Gravitational Coupling Constant:
\alpha_g = \frac{G m_p^2}{\hbar c}

Gravitational 'Constant':
G = \frac{\hbar c \alpha_g}{m_p^2}

Strong Gravitational Coupling Constant:
\alpha_g = 1

Strong Gravitation:
G_s = \frac{\hbar c}{m_p^2} = 1.130 \cdot 10^{28} \; \text{Nm}^2 \text{kg}^{-2}
t_e = \frac{4}{3} \left(\frac{E_b}{\hbar c} \right)^2 \sqrt{\frac{r_e^7}{2 G_s m_e}}
t_e = 6.110 \cdot 10^{34} \; \text{s} - 1.937*10^27 years

Combining terms:
t_e = \frac{4 m_p E_b^2}{3} \sqrt{\frac{r_e^7}{2 m_e (\hbar c)^5}}
[/Color]
Reference:
http://en.wikipedia.org/wiki/Quantum_black_hole
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/couple.html

 

[IMP]

If they were able to make a small black hole, and it got "loose" and fell to the center of the Earth, the pressures at the Earths core would force material into it so fast that even a very small one would gobble us up very fast. I am not sure what the exact pressure is at the Earths core but it could force material through even a very small "hole" very quickly. I do agree that once it gobbled up the Earth, it would just continue to orbit the Sun, and the Moon would still orbit the black hole as if it were the Earth...

 

[vanesch]

If they were able to make a small black hole, and it got "loose" and fell to the center of the Earth, the pressures at the Earths core would force material into it so fast that even a very small one would gobble us up very fast. I am not sure what the exact pressure is at the Earths core but it could force material through even a very small "hole" very quickly. I do agree that once it gobbled up the Earth, it would just continue to orbit the Sun, and the Moon would still orbit the black hole as if it were the Earth...

No, you should read this thread.

First of all, a black hole that falls to the center of the earth, wouldn't stop there, but would continue falling up on the other side, just to plunge in again, and on and on, because there's no "friction" on the black hole.

Second, there have been posted in this thread a lot of calculations of the speed at which it would gobble up matter.
Don't forget that the black hole we're talking about here IS MUCH MUCH SMALLER THAN A PROTON. As such, pressures on *atomic* level (such as in the center of the earth) matter little: the black hole travels most of the time in the empty space between nucleae.
A way to calculate the probability of hitting a nucleus (and somehow imagining that it would gobble up the entire nucleus, which is MUCH MUCH bigger than the black hole itself - which is a worst-case scenario) is done by calculating the "cross section" of the black hole and its probability to cross a nucleus on its voyages through the earth. We know its speed (just falling), and knowing the cross section and the density of nucleae, we can estimate how many nucleae it could eat per unit of time.

For a classical black hole, the calculation is done in the link provided by Pervect in this post:
https://www.physicsforums.com/showpost.php?p=1001414&postcount=12

for a MUCH LARGER black hole, about the size of a proton, weighting a billion tons (figure that! A black hole *the size of a proton* weights a billion tonnes ; we're talking here about black holes that weight 10 TeV or 10^(-24) kg - go figure how small it is !)

For more exotic calculations which are more severe, orion made some, and arrived at a time to eat the Earth ~ 10^46 years.

All this in the following rather un-natural hypotheses:
- no Hawking radiation (which would make the black hole evaporate almost immediately)
- production of black hole EXACTLY IN THE CENTER OF GRAVITY of the collision (no remnant particles)
- very high production rate, producing billions of black holes per second.

 

[MelissaSweet]

Hi guys. Just a few quick questions:

Your calculations seem to be based on a constant rate of absorption, is this right? Wouldn't the absorption rate increase exponentially? In your cross section, are you looking only at the Schwarzschild radius? Doesn't gravity extend far beyond? Someone mentioned that the scientists failed to mention the effect that conservation of momentum has on nanoblackholes. Is that right? If they missed this very basic concept what else might they be missing?

 

[Orion1]

Current predictions for the behavior of a black hole with a mass less than Planck mass are inconsistent and incomplete.

One problem with calculating a constant rate of absorption, is the fact that a quantum black hole's horizon radius decreases with increasing mass. Therefore the horizon radius becomes a function of its mass:

r_h(E_b) = \frac{\hbar c}{E_b}

This means that the cross section and reaction rate decreases as the quantum black hole mass increases.

However, I can determine what the upper limit of my equation is:

E_b = E_e = m_e c^2

r_h = \frac{\hbar}{m_e c}

t_e = \frac{4m_p}{3} \sqrt{\frac{(m_e c)^3 r_e^7}{2 \hbar^5}}

t_e = 6.874 \cdot 10^{131} \; \text{s} - 2.180*10^124 years

An exponentially decreasing reaction rate should be even longer than this.

An equation demonstrating an exponentially decreasing cross section and reaction rate would probably show that the time required to absorb the Earth is infinite.

Is this infinite?, close enough...
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