LHC Black Holes

A microscopic black hole, if such a thing could exist, would radiate itself away via Hawking radiation before it had much of a chance to do anything.

Granted, we don't actually know if the laws of the universe are anything like static and consistent over either long timescales, or at size scales approaching the Planck length.

In fact, there are good reasons to argue that they aren't. You can neatly solve a bunch of problems in cosmology and grand unification by assuming that the universal constants and equations of relativity and quantum mechanics only apply in constrained domains, not the whole universe.

What does the earth have to do with it?

The key point about a tiny black hole created by the LHC is that it would be /tiny/. Really, really, /really/ tiny. So small that even bacteria would need a bacteria microscope to see it, as one of my kids used to say.

The collisions in the LHC are at 13 TeV. That's about 14 K atomic masses - the weight of 1000 nitrogen atoms. So even assuming the entire collision energy goes into making a black hole, it is not a very big one. It is 2.3e-23 kg, with an event horizon radius of about 3.4e-50 m. For comparison, a proton is about 0.9e-15 m in radius, and the Planck length is 1.6 e-35 m.

So if and when a hydrogen nucleus, a proton, touches this black hole,

temperature, atomic vibrations will be moving the proton in the region of 10e-11 m at about 10e13 Hz, with RMS speeds of about 2200 m/s.

These numbers are all simplistic, because they are based on a "billiard balls" model of the particles. But I think the numbers speak for themselves - the black hole would be so tiny, with such a low mass, that it would have totally negligible influence on anything around it. It would simply pass through matter (the earth included) without affecting it measurably, in the same way that neutrinos do, continuing in a path determined by its initial direction and speed when it was created. If it were at rest relative to the earth, then it would immediately fall to the centre of the earth, pass through to the other side, and oscillate almost endlessly. While it /could/ get lucky and see direct hits from particles that gradually increase its mass, the universe would have passed away in heat death long before the growing black hole could have any noticeable effect on the earth.

Taking a bit more quantum mechanics and detailed physics into account,

the CERN folks would love to increase their power by a factor of a million million million, but I suspect budget considerations would rule that out - the tunnel would have to be approximately the same circumference as the Milky Way.

Also note that cosmic rays are hitting us continuously, many with energies far above 14 TeV. The highest measured energy was about 20 million times as high as the LHC can make, and it did not result in a world-destroying black hole.

Kind of like this?

Marvellous sci-fi, but not /exactly/ as it would happen in reality!

There are a great many reasons why it won't happen, or be as graphic as fiction would like to depict:

- The energy level is some 12 to 38 orders of magnitude too low.

- A uBH will decay extremely quickly. For any energy levels we can observe right now (in the EeV range, including cosmic rays), the size and lifetime of such a state will be below the Planck length and time, respectively. It might as well not exist at all, because there's no meaningful way to express something that fine (much as there's no meaningful way to say that radio waves, of finite wavelength, might come from an instantaneous point source: how can you even know?).

- A uBH will be extraordinarily luminous. Besides radiating away all its mass-energy within a proportionally small time scale, the intensity of that radiation is the highest possible in the universe. Accretion is limited by radiation pressure:

For a uBH, presumably its intensity is so great that its accretion is negative -- it literally costs energy to try and stuff more into it!

- A small BH isn't actually scary. If one were to fly through our solar system, and happened to intersect the Earth, it would be travelling faster than escape velocity, so it can't come to a rest unless it absorbs enough reaction mass to balance out. It will tend to carry right on through!

But because it's small (and any infalling matter becomes very quickly heated as it micro-accretes, and mind this is assuming the BH is cool enough to accrete room-temperature matter by its own gravity, without blowing it away by its radiation), it doesn't consume much if any, as it passes.

- A BH big enough to threaten the Earth, must be of planetary scale, so that it can, say, be captured into orbit, using other planets or moons as reaction mass. An orbit inside of the Moon would eventually decay (fairly quickly?) due to the larger tidal forces. (Although, Earth's spin carries quite a bit of energy too, which is why the Moon is actually gaining altitude. Or, if this thing entered a retrograde orbit, the spin would make things worse.)

A planetary-size BH will be fairly cool, and not terribly big. If Earth's mass were crushed to "zero" size, it would have an event horizon of about

1.5cm diameter, and would be cosmically stable -- cooler than the cosmic microwave background. It would have no problem (eventually) devouring planets, though again, it will be rate limited, not instantaneous.

I want to say xkcd did a calculation of that, but I don't see it offhand. Give it a search, maybe.

Tim

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"rickman"  wrote in message  
news:nou6ss$1qu$1@dont-email.me... 
>I was explaining black holes to a friend who asked about the LHC and  
>thought about what might happen if a tiny black hole were created. 
> 
> I believe matter falling into a microscopic black hole would still enter  
> it in a similar manner to large black holes elsewhere in the universe by  
> orbiting the tiny black hole while being accelerated causing energy to be  
> emitted before crossing the event horizon. 
> 
> The black hole would immediately be pulled by gravity toward the center of  
> the earth.  It would pick up matter as it fell.  Unlike an object falling  
> in an evacuated tube it would not have enough momentum to rise on the  
> other side back to the surface of the earth.  The matter picked up on the  
> way down would have less momentum on reaching the center. Then as it rises  
> up the other side it picks up more matter that continues to slow the speed  
> of the black hole before it reverses direction at an even lesser distance  
> from the center of the earth.  The result would be diminishing  
> oscillations until it appears to be stationary at the center. 
> 
> While falling and on reaching the center I believe the theoretically  
> liquid core would fall into the black hole.  However, the energy released  
> by falling into the black hole would create pressure that limits the rate  
> of matter entering the black hole.  I have no idea how fast or slow this  
> would be.  The earth might be stable like this for many, many years as the  
> earth's core falls into the black hole while being repelled by the energy  
> released.  Or the entire earth might collapse into the black hole as fast  
> as it can fall. 
> 
> --  
> 
> Rick C

It's called a "strangelet" by those who've already considered this possibility and if your analysis of the damped oscillation is correct, then it's hard to see how we wouldn't be instantly (or more or less instantly) destroyed. Fortunately the experts reckon they can create strangelets with no adverse consequences. :-)

If such a thing as Hawking radiation exists.

There's still a lot we don't know about the border of relativity and quantum mechanics, and it's on that border where Hawking radiation is described. Most physicists _think_ that black holes evaporate, but no one's observed it, and if our existing models are true then there ought to be small black holes left over from the Big Bang, evaporating away with an obvious radiation signature -- but we have seen no such signature.

--
Tim Wescott 
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The whole "black holes in the LHC" thing came about because _if_ string theory is correct, and _if_ some of the rolled-up dimensions are big enough, then a black hole can form at LHC energies, and be detectable. Such a black hole would decay rapidly, due to Hawking radiation.

If the standard model applies, then see David Brown's discussion.

There were no black hole events seen at the LHC, which puts an upper limit on the size of any rolled-up dimensions in any higher-order models of particle physics (like string theory).

--
Tim Wescott 
Control systems, embedded software and circuit design 
I'm looking for work!  See my website if you're interested 
http://www.wescottdesign.com

IIRC Hawking radiation mostly follows from thermo-dynamics. It's like black body radiation... Black holes have some temperature. (Finding the temperature of a black hole is the hard part... :^)

George H.

I'm not sure that is a valid way to look at it. Everything that makes up a black hole is on the other side of the event horizon. It may well have a temperature, but we'll never feel any effect from it as nothing can cross back through the event horizon. In a sense, the event horizon

radiation from the space around the black hole, but nothing from the black hole itself.

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Rick C

It kind of has to, or else what we think we know about quantum field theory must be pretty much wrong

The main question is not whether Hawking radiation exists, but what happens to the information.

I don't understand your thinking. How is it definite that we would be instantly destroyed? The gravitational attraction of the black hole is only as strong as the matter inside it. Initially that would be very little. As some have pointed out, it would most likely be far too small to even interact with other matter in any short time and would likely evaporate before it does.

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Rick C

o

Ahh, Rick I understand you are a smart guy. There are plenty of other smar t guys out there. I think the best (clearest) explanation I've seen/ read (and it's been a while) was in a set of video lectures by Leonard Susskind. Googling he's got a bunch... I don't recall which ones. Advanced stat. me ch. or maybe QM.

Black holes have a temperature. That's pretty cool. (NPI) Here's wiki...(I only looked at the first few paragraphs.)

George H.

Trouble is all of this is speculation and none is proven. I like a nice mechanical explanation. Saying matter leaves a black hole by it swallowing matter is not a very good argument. That's what Hawking Radiation says.

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Rick C

Read Hawking's "A Brief History of Time". Computing Hawking radiation from the amount of curvature of space and computing it from the ratio of entropy to total surface area gives the same answers. At the time this was a fall-on-the-floor astonishing result, and one that gave a lot of credence to the result.

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com 

I'm looking for work -- see my website!

Well, true, and it probably does, but it hasn't been observed yet.

Quantum field theory doesn't predict either dark energy or dark matter, yet astronomical measurements say they must exist. So quantum field theory is kind of behind the 8-ball right now on explaining how the universe works.

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com 

I'm looking for work -- see my website!

Hawking radiation is caused by half of a virtual particle-antiparticle pair falling into the event horizon and the other half escaping.

CHeers

Phil Hobbs

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hobbs at electrooptical dot net 
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I never read that book. I think this is the susskind video I watched,

Black holes don't start till ~55 minutes. (The beginning is all good stat. mech. stuff...)

It might be a similar argument.

George H.

Hmm.. Tim, this may not be correct, but I think QM field theory does predict dark energy. ... it just gets it wrong by 60 orders of magnitude.. or some number like that.... it's like the zero point motion of virtual particle in the vacuum. (see link below) Dark matter (presumably) is just some particle(s) that you have to add to the theory... QM theory doesn't predict the electron for instance.

I was reading this at home...

George H.