Black holes and the LHC

[smoker]

Hi all,

 

My question relates to the size of any possible black hole that could possibly be created by the LHC. Please bear in mind that my interest stems from trying to explain the minute scale of the actual interaction to a non scientist.

 

What I'm trying to achieve is an explanation that while not being 100% accurate, is sufficient to allay fears. To this end I have decided to concentrate on the size of the particles involved and possibly the energy.

 

Here's what I've got so far :

Assumptions -

• a proton can be said to have a "size" of approx. 1.0 x 10^{-13} mm
  
• a human hair can be said to have a diameter of about 2.0 x 10^{-1} mm
  
• the distance between atoms (in silicon, don't know about carbon) is 2.22 x 10^{-17} mm
  
• the black hole doesn't move and therefore can only "feed" on anything already within the event horizon.
  
• The mass is so tiny as to be unable to gravitationally attract any other particles outside the event horizon.
  

 

My Hypothesis -

In forming a black hole the protons would be compressed into a volume approaching Planck length, which is many many times smaller than the distance between atoms.

The Event Horizon radius of such a black hole would be so small as to not affect any neighbouring atoms. Nothing would get "sucked in".

 

So if there were such a black hole resident in the centre of a human hair, you could hold the hair in your hand to no ill effect. It would not destroy the earth. It would not even destroy the hair.

 

The second aspect, that the energy used in the collisions is minute. And the public don't realise how small 1 trillion eV is.

For example, 1.2 TeV = 1.92261175 × 10-7 joules

A typical electric fence for containing animals produces 10 joules.

It is the concentration of the miniscule amount of energy in a miniscule space that gives us the relative power, but that is not earth shattering power.

 

Am I so far off as to be misrepresenting the situation, or would this be "good enough" for the general public ?

 

Cheers

 

Alan

[ydoaPs]

That post made me think of:

[smoker]

Heh, thanks ydoaPs.

 

Unfortunately that image doesn't help explain things, it just says "you're stupid". The public like car analogies and as a car exists on a vastly bigger scale than a hair, I thought it would be useful to have an explanation I could demo in the pub.

 

I must admit to not having studied physics since 1982, and that was at the end of high school. But I do possess a certain amount of logical ability, and it is that which provoked my post.

 

What I'm really looking for is some kind of expert assurance that my statement,

So if there were such a black hole resident in the centre of a human hair, you could hold the hair in your hand to no ill effect. It would not destroy the earth. It would not even destroy the hair.

bears some resemblance to reality. Or am I way off here ?

Cheers

Alan

[timo]

a proton can be said to have a "size" of approx. 1.0 x 10^{-13} mm

More like 10^{-12} mm, I think.

 

a human hair can be said to have a diameter of about 2.0 x 10^{-1} mm

Dunno. Sounds somewhat reasonable, though.

 

the distance between atoms (in silicon, don't know about carbon) is 2.22 x 10^{-17} mm

Orders of magnitude smaller than the size of a proton? I don't think that is true. About 10^{-7} would seem reasonable so maybe that just was a typo of yours.

 

the black hole doesn't move and therefore can only "feed" on anything already within the event horizon.

Why would a created black hole not move?

 

The mass is so tiny as to be unable to gravitationally attract any other particles outside the event horizon.

It might be "effectively unable to have any influence". But to make this statement you'd need a scenario and a scale from which you can tell effectively irrelevant contributions from relevant contributions. I don't think you should throw around such strong statements without a context. As an analogy: One often hears that the gravitational force is much weaker than the electromagnetic force. In all generality that is crap, of course (think the motion of planets around the sun which is exclusively determined by gravity) but often stated in a context where it is true and the scale/scenario is obvious (e.g. chemical bonds in standard laboratory conditions). And these statements can then be backed up with rough calculations (e.g. by calculating the electromagnetic force and the gravitational force between two protons at 1 nm distance).

 

 

In forming a black hole the protons would be compressed into a volume approaching Planck length, which is many many times smaller than the distance between atoms.

The Event Horizon radius of such a black hole would be so small as to not affect any neighbouring atoms. Nothing would get "sucked in".

It would probably be better to give an estimate of how big the radius of the event horizon actually is (just assume a standard black hole; the radius as a function of the mass can be found on Wikipedia, for example). Note that the gravitational attraction of a black hole does not end at the event horizon.

 

So if there were such a black hole in the centre of a human hair, you could hold the hair in your hand to no ill effect. It would not destroy the earth.

Even assuming the BH was not moving: What if something flies in due to random thermal motion? Wouldn't that cause the BH to grow over time? Such qualitative statements have the problem that you do not know how much stuff is flying in in what time (not to mention that BHs are expected to radiate off).

 

The second aspect, that the energy used in the collisions is minute. And the public don't realise how small 1 trillion eV is.

For example, 1.2 TeV = 1.92261175 × 10-7 joules

A typical electric fence for containing animals produces 10 joules.

It is the concentration of the miniscule amount of energy in a miniscule space that gives us the relative power, but that is not earth shattering power.

While it is true that the energies are negligible, the worry is that the BH starts to suck in other stuff and due to this process becomes large enough to have an impact.

 

Am I so far off as to be misrepresenting the situation, or would this be "good enough" for the general public ?

No, I think it misses the point. If you assume LHC forms a BH but that BHs do not evaporate (and I think the actual point is that forming and evaporation are tightly tied) then you do have a stable object that should grow over time. The only way you could argue that the growth is negligible is by actually doing calculations, i.e. integrating the attraction of the BH on other particles over the thermal averages of the particles in the surrounding and then deducting a growth rate from that. This then can be insignificant but there's no way to tell that without at least rough numbers.

 

EDIT: Seeing ajb's post: Right, comparing to situations already known is an alternative (say "experimental") approach to the question. In fact -the problem that you should better convince yourself that the situations are comparable aside- it should probably be regarded the more reliable one. Scientific theories and calculations might just be wrong; nature is expected to always behave exactly like nature behaves .

Edited November 22, 2009 by timo

[ajb]

Mirco-black holes are probably being produced all the time in cosmic rays. Such small black holes will evaporate very quickly due to their Hawking radiation. Notice, that these have not destroyed the earth yet.

 

In collides they will appear as short-lived exotic particles.

[Sisyphus]

Your explanation is not entirely correct (a hypothetical black hole would certainly move, for example, but more importantly it would evaporate essentially instantly), but the most important point is that the LHC is not doing anything novel. It will recreate natural phenomena, specifically cosmic rays colliding with the upper atmosphere, with more energy than the LHC is capable of. Yet the Earth is still here.

 

Here's a link from CERN addressing safety concerns in layman's terms:

 

http://public.web.cern.ch/Public/en/LHC/Safety-en.html

[swansont]

Unfortunately that image doesn't help explain things, it just says "you're stupid". The public like car analogies and as a car exists on a vastly bigger scale than a hair, I thought it would be useful to have an explanation I could demo in the pub.

 

No, it really doesn't say that. The image mocks ignorance, and more specifically, willful ignorance. Stupidity and ignorance aren't the same thing; ignorance can be reduced by learning something. You can't fix stupid.

 

But here's a car analogy for you: Ranting about how the LHC is going to destroy the world is analogous to insisting that your auto mechanic change the spark plugs on your diesel engine. Except in that case, there aren't bloggers and reporters who do exposés on how the mechanic is disreputable because he refuses to do necessary work on your car, and how this makes the car unsafe and it's a conspiracy to destroy the car prematurely so you'll have to buy another one.

Edited November 22, 2009 by swansont
typo

[Fuzzwood]

For ppl who dont get the car analogy: a diesel engine doesnt need sparkplugs.

[smoker]

Wow, I didn't expect so many relevant replies.

I'm used to slashdot, where most replies are flames.

 

Anyway, my aim is not to be perfectly accurate, but to demonstrate the futility of worrying about any black hole the LHC may produce.

 

Specifically replying to timo,

 

All my dimensions were googled, I assumed the black hole didn't move because that would bring other factors into the calculations which weren't relevant to a picosecond event and who in the *real world* cares anyway, the point of mentioning the event horizon is to demonstrate that anything beyond that radius is not inescapably drawn into the BH, I am not allowing for foreign objects, as this is technically a laboratory experiment where external influences are immaterial, and finally please bear in mind this is not a Phd thesis, it is a way of starting the extremely ignorant on the path to being less ignorant.

 

As for the other comments, yes - I agree.

I am a trained car mechanic if that helps.

 

swansont - it does say "you're stupid" if the person you are talking to is stupid. Anybody with a brain wouldn't take it so harshly, but the people I'm aiming at would. It's not my fault...

 

Thanks for your time anyway

 

Alan

[A Tripolation]

For ppl who dont get the car analogy: a diesel engine doesnt need sparkplugs.

 

Another person trying to cover up the truth with LIES.

Haven't you ever heard of glow-plugs?

 

That's another analogy about the whole LHC mess. People misconstrue what the experts say...namely because they don't understand the experts. Here, glow-plugs [math]\ne[/math] spark plugs, even though they are similar. Same with black holes and micro black holes.

 

Sorry if this just made everything more confusing, or that I'm completely wrong.

Edited November 23, 2009 by A Tripolation

[ydoaPs]

Another person trying to cover up the truth with LIES.

Haven't you ever heard of glow-plugs?

What did I tell you about trolling? Don't do it until you stop failing.