I'm not a physicist but I play one in front of my friends
September 11, 2008 6:46 PM Subscribe
Help me explain why the Large Hadron Collider doesn't spell our doom.
I know that all the doom-saying is bullshit, and that the (American) Media keeps talking about the paranoia because it's sexier than talking about the science, but my understanding of physics, while better than average, is still not authoritative. This is essentially what I've been saying to people (and all of the people I've been talking to are highly intelligent, at least enough to care about the LHC, but not really scientifically educated) who bring up the "destroy the earth" theory:
The LHC was just fired up, in a month CERN will start firing beams in the other direction. The expected result is to produce in miniature conditions similar to those at the very beginning of the universe. It is possible that such collisions will produce a microscopic black hole, which sounds bad, but even if that happens, it's not anything to worry about, because the destructive power of a black hole comes from its mass, and the mass of a few protons won't have enough gravitational power to do anything destructive to something with so, so much more mass (i.e. the earth.)
I feel like this explanation must be somewhat correct, but I've also been talking out of my ass. Can someone with better understanding help me with my argument, please?
Thank you.
I know that all the doom-saying is bullshit, and that the (American) Media keeps talking about the paranoia because it's sexier than talking about the science, but my understanding of physics, while better than average, is still not authoritative. This is essentially what I've been saying to people (and all of the people I've been talking to are highly intelligent, at least enough to care about the LHC, but not really scientifically educated) who bring up the "destroy the earth" theory:
The LHC was just fired up, in a month CERN will start firing beams in the other direction. The expected result is to produce in miniature conditions similar to those at the very beginning of the universe. It is possible that such collisions will produce a microscopic black hole, which sounds bad, but even if that happens, it's not anything to worry about, because the destructive power of a black hole comes from its mass, and the mass of a few protons won't have enough gravitational power to do anything destructive to something with so, so much more mass (i.e. the earth.)
I feel like this explanation must be somewhat correct, but I've also been talking out of my ass. Can someone with better understanding help me with my argument, please?
Thank you.
There's also a pretty good wikipedia page on the safety concerns.
posted by burnmp3s at 6:56 PM on September 11, 2008
posted by burnmp3s at 6:56 PM on September 11, 2008
Da LHC is Supa Dupa Fly
Silly, but awesome. Very very awesome to watch a music video about making mass out of energy. :)
posted by TomMelee at 6:58 PM on September 11, 2008
Silly, but awesome. Very very awesome to watch a music video about making mass out of energy. :)
posted by TomMelee at 6:58 PM on September 11, 2008
Ahh crap I forgot to add (I'm sorry), even if a black hole opens up, it won't be Armageddon style "oh crap we're gonna die in 10 hours", we'll simply cease to be instantly. We'll all be swallowed up into nothingness faster than we could possibly comprehend it. How can you be scared of your life ending painlessly, instantly, and without your awareness?
posted by TomMelee at 7:00 PM on September 11, 2008
posted by TomMelee at 7:00 PM on September 11, 2008
I can't quote chapter and verse, but I heard a very succinct explanation by Dr Karl Kruzelnickie the other day. It went something like
posted by AmbroseChapel at 7:05 PM on September 11, 2008
The theory that it could destroy the world comes from a paper published in <year>, which was disproved by a paper published in <a later year>where both years were values less than 1920.
posted by AmbroseChapel at 7:05 PM on September 11, 2008
We're not dead yet.
Actually that won't hold water, because what they've been doing is just low energy stuff.
posted by crapmatic at 7:28 PM on September 11, 2008
Actually that won't hold water, because what they've been doing is just low energy stuff.
posted by crapmatic at 7:28 PM on September 11, 2008
TomMelee--I don't think the LHC disaster will happen, but if it did...could a mini black hole really "instantly" swallow the entire planet? What's the event horizon diameter of a mini black hole? Even the guys who claim this will happen say it'll happen over a period of days, or a couple of weeks.
posted by zardoz at 7:31 PM on September 11, 2008
posted by zardoz at 7:31 PM on September 11, 2008
Well, to be honest, you probably won't understand why exactly it wouldn't cause a black hole. You have to have a certain amount of faith that the people who do understand these things do not want the world to end.
posted by electroboy at 7:33 PM on September 11, 2008 [2 favorites]
posted by electroboy at 7:33 PM on September 11, 2008 [2 favorites]
zardoz---there was a guy talking about it on NPR the other day, basically the idea that (if) we live in a false vacuum and (if) a mini-blackhole forms, it wouldn't stay "mini" for very long, as it would collapse in on itself exponentially. When we're talking about 10e-23 seonds here, exponential change happens....very rapidly. I mean, think about it. It light can't escape a black hole, how the ever loving hell could an atmosphere and matter escape it?
posted by TomMelee at 7:35 PM on September 11, 2008
posted by TomMelee at 7:35 PM on September 11, 2008
The simplest explanation I have heard is that the kind of collisions that will happen in the LHC happen in nature all the time; the only difference is that in the LHC we will be able to watch and analyze them. And that if "tiny black holes" are created, whether in the natural or in the artificial collisions, they are not stable and disappear almost instantly.
posted by beagle at 7:45 PM on September 11, 2008
posted by beagle at 7:45 PM on September 11, 2008
I wish I could find the source on this, but basically, the chances of the world ending due to the actions of the LHC are several orders of magnitude lower than the chances that you will dematerialize instantly while brushing your teeth.
posted by Tomorrowful at 7:46 PM on September 11, 2008
posted by Tomorrowful at 7:46 PM on September 11, 2008
Response by poster: Thank you all again, and I understand that the world isn't going to end, and that if it did (1/∞ chance) it would happen in a way in which we wouldn't even notice it happening, so what's the point of worrying about it.
I'm just looking for a way to explain (a) why this might possibly create mini-black holes; and (b) why they would be physically unstable. In kinda-sorta layman's terms, but for people who I know are smart enough to understand it if it's explained to them. "Smart people say it's nothing to worry about," isn't going to hold water here - I'm talking to law students.
My experience with learning physics (and I was always hopeless at science until taking Physics my senior year) was that things which would have seemed impenetrably complex suddenly made sense, because they had a clear explanation behind them. I don't have much understanding of black holes, but what (possibly mistaken) understanding I do have is that they occur as a result of something (generally a star) being so massive that the gravitational force of its mass becomes unstable and causes it to collapse in upon itself, creating something with the mass and gravitational force of a star to take up roughly the space of the head of a pin, and of course drawing other things, including light, into its gravitational field.
If this basic idea is correct (and again, I am willing to admit that I may be totally off-base here) than I have some trouble understanding mini-black holes at all. At the atomic or sub-atomic level - what we're seemingly talking about with the LHC - gravitational force is not only by-far the weakest of all forces involved, but essentially negligible when the mass is that of a few protons. Are the strong force, weak force, and electromagnetic force more importantly at play here? Am I missing an important aspect about density? I can't adequately understand black holes with the information I've got, and so I can't explain properly why (if this is even the case) their minute mass means that we needn't worry about them. If that's even the case.
posted by Navelgazer at 8:13 PM on September 11, 2008
I'm just looking for a way to explain (a) why this might possibly create mini-black holes; and (b) why they would be physically unstable. In kinda-sorta layman's terms, but for people who I know are smart enough to understand it if it's explained to them. "Smart people say it's nothing to worry about," isn't going to hold water here - I'm talking to law students.
My experience with learning physics (and I was always hopeless at science until taking Physics my senior year) was that things which would have seemed impenetrably complex suddenly made sense, because they had a clear explanation behind them. I don't have much understanding of black holes, but what (possibly mistaken) understanding I do have is that they occur as a result of something (generally a star) being so massive that the gravitational force of its mass becomes unstable and causes it to collapse in upon itself, creating something with the mass and gravitational force of a star to take up roughly the space of the head of a pin, and of course drawing other things, including light, into its gravitational field.
If this basic idea is correct (and again, I am willing to admit that I may be totally off-base here) than I have some trouble understanding mini-black holes at all. At the atomic or sub-atomic level - what we're seemingly talking about with the LHC - gravitational force is not only by-far the weakest of all forces involved, but essentially negligible when the mass is that of a few protons. Are the strong force, weak force, and electromagnetic force more importantly at play here? Am I missing an important aspect about density? I can't adequately understand black holes with the information I've got, and so I can't explain properly why (if this is even the case) their minute mass means that we needn't worry about them. If that's even the case.
posted by Navelgazer at 8:13 PM on September 11, 2008
A lady here was telling me it all depends on whether the Hawking radiation theory is true or not. She was freaking out about the world ending and I became a bit more concerned when I found out she had helped build the collider...
posted by null terminated at 8:14 PM on September 11, 2008 [2 favorites]
posted by null terminated at 8:14 PM on September 11, 2008 [2 favorites]
TomMelee, you are confusing a black hole with a vacuum metastability event. Both have been suggested as possible effects of the LHC, but only the latter is theorized to behave as you describe.
posted by DevilsAdvocate at 8:16 PM on September 11, 2008
posted by DevilsAdvocate at 8:16 PM on September 11, 2008
I don't understand it well enough to explain to you, but what you want to read about is Hawking radiation. It basically says that any black holes created will be so small that they'll evaporate instantly, so nothing to worry about right? Right, but Hawking radiation is still entirely theoretical - we haven't been able to observe it directly. I think that's the crux of the argument.
The best explanation is just, "The LHC isn't going to do anything that doesn't happen in our atmosphere all the time. All it's doing is slamming particles together at near the speed of light in an environment in which we can observe them." Also, the isn't a very good chance it's even powerful enough to create black holes.
posted by borkingchikapa at 8:17 PM on September 11, 2008 [1 favorite]
The best explanation is just, "The LHC isn't going to do anything that doesn't happen in our atmosphere all the time. All it's doing is slamming particles together at near the speed of light in an environment in which we can observe them." Also, the isn't a very good chance it's even powerful enough to create black holes.
posted by borkingchikapa at 8:17 PM on September 11, 2008 [1 favorite]
Oh, there are also strangelets, but that one's just total bullshit and your law students probably don't understand it either.
posted by borkingchikapa at 8:19 PM on September 11, 2008
posted by borkingchikapa at 8:19 PM on September 11, 2008
The best explanation of it's harmlessness I've heard is that there have been a fairly large number of recorded cosmic ray collisions in the upper atmosphere whose energy dwarfs the maximum possible energy of the LHC. (This from a physicist on an NPR show, as I recall.)
If anything bad from these experiments could happen to the Earth it would have billions of years ago already.
posted by jamjam at 8:36 PM on September 11, 2008
If anything bad from these experiments could happen to the Earth it would have billions of years ago already.
posted by jamjam at 8:36 PM on September 11, 2008
In case you overlooked it, the wikipedia page is very thorough and more importantly is also well cited - so that's another resource of articles which you can check out and cite.
posted by Solon and Thanks at 9:15 PM on September 11, 2008
posted by Solon and Thanks at 9:15 PM on September 11, 2008
In the meantime, keep updated here;
http://www.hasthelhcdestroyedtheearth.com/
posted by Effigy2000 at 11:29 PM on September 11, 2008 [1 favorite]
http://www.hasthelhcdestroyedtheearth.com/
posted by Effigy2000 at 11:29 PM on September 11, 2008 [1 favorite]
This particular site addresses the issue of creation and this world from a kabbalistic/cosmic perspective and is very informative in general.
posted by watercarrier at 5:11 AM on September 12, 2008
posted by watercarrier at 5:11 AM on September 12, 2008
Phil Plait has been all over this woo-woo nonsense. He talked about in a post titled "No the LHC Won't Destroy the Earth (link is to archives scroll down to article--for some reason the link to the article comes up blank for me).
I can see why people are buying into this crap though.
posted by IvoShandor at 6:19 AM on September 12, 2008
I can see why people are buying into this crap though.
posted by IvoShandor at 6:19 AM on September 12, 2008
the odds of a micro black hole being created by the LHC are very low, like, the odds of your component molecules all deciding to take separate vacations simultaneously.
add to that the odds that a micro black hole would have a chance absorb matter to grow in size before the hawking radiation caused it to basically evaporate are equally small.
These two events happening at the same time? while possible, are HIGHLY, HIGHLY improbable.
posted by jrishel at 6:25 AM on September 12, 2008
add to that the odds that a micro black hole would have a chance absorb matter to grow in size before the hawking radiation caused it to basically evaporate are equally small.
These two events happening at the same time? while possible, are HIGHLY, HIGHLY improbable.
posted by jrishel at 6:25 AM on September 12, 2008
Best answer: ah, I just read your comment. there are three ways to get a blackhole
1) massive star collapse (traditional model)
2) formed during the big bang (primordial blackhole)
3) acceleration of a subatomic particle to very high speeds/energy levels (micro black hole)
All three of these blackholes are continuously converting the mass that causes their singularity into hawking radiation, which appears right outside the event horizon. #1 and #2 have a lot more mass, and are usually sucking in more mass... so they stick around for billions and billions of years.
#3 is a unique case. it has enough mass to form a black hole, because relativity teaches us the that the faster you go the more massive you get. this sub atomic particle has enough mass to for a black hole, but it is still a very tiny amount of mass, in general.
this mass is then converted to hawking radiation, tada, no more tiny black hole. this happens in such a short period of time, no other matter would be able to get sucked in to feed the micro black hole to a larger size.
hawking radiation is nature's way of fixing singularities.
posted by jrishel at 6:48 AM on September 12, 2008
1) massive star collapse (traditional model)
2) formed during the big bang (primordial blackhole)
3) acceleration of a subatomic particle to very high speeds/energy levels (micro black hole)
All three of these blackholes are continuously converting the mass that causes their singularity into hawking radiation, which appears right outside the event horizon. #1 and #2 have a lot more mass, and are usually sucking in more mass... so they stick around for billions and billions of years.
#3 is a unique case. it has enough mass to form a black hole, because relativity teaches us the that the faster you go the more massive you get. this sub atomic particle has enough mass to for a black hole, but it is still a very tiny amount of mass, in general.
this mass is then converted to hawking radiation, tada, no more tiny black hole. this happens in such a short period of time, no other matter would be able to get sucked in to feed the micro black hole to a larger size.
hawking radiation is nature's way of fixing singularities.
posted by jrishel at 6:48 AM on September 12, 2008
Hawking radiation is also still entirely theoretical -- ie: yet to be observed.
I mean, think about it. It light can't escape a black hole, how the ever loving hell could an atmosphere and matter escape it?
That's not the way it works. Things don't get "sucked" into an event horizon any more than the mass of the black hole would ordinarily warrant. A mini black hole, if it doesn't evaporate away in Hawking radiation, might fall to the centre of the earth and eat it away in tiny orbits, but it wouldn't act like you describe.
jamjam has the answer you're looking for.
posted by Durn Bronzefist at 7:57 AM on September 12, 2008
I mean, think about it. It light can't escape a black hole, how the ever loving hell could an atmosphere and matter escape it?
That's not the way it works. Things don't get "sucked" into an event horizon any more than the mass of the black hole would ordinarily warrant. A mini black hole, if it doesn't evaporate away in Hawking radiation, might fall to the centre of the earth and eat it away in tiny orbits, but it wouldn't act like you describe.
jamjam has the answer you're looking for.
posted by Durn Bronzefist at 7:57 AM on September 12, 2008
IANAPhysicist, but :
supposing that micro black holes are actually generated in a collision (which is a fairly improbable, but not impossible event), they are of incredibly small mass - subatomic mass.
As pointed out before, cosmic rays are in fact protons of extremely high energy, some of them several orders of magnitude larger than the energies they'll ever reach in the LHC, so way more likely to create micro black holes.
An incredible number of those clashes with the upper atmosphere (and that's where the ~10,000 muons that shower every square metre of the earth every second come from).
Many cosmic rays cross the upper atmosphere and some of those cross (est. about a dozen) you every second: the entire universe has been engulfed in such particles since, well, forever, stars are way larger and denser than the Earth (so much more capable of attracting a mbh), and despite this (a) no "star destroying micro black hole" event has ever been observed.
(b) Now, let's rule out Hawking radiation, and say that micro black holes are permanent (which, to my understanding, is plausibly although not demonstratedly false, since the Hawking radiation is a theory): a black hole of such dimensions and mass would simply pass through matter as a stone in the air, and having a speed close to the speed of light, 4 orders of magnitude above earth's escape velocity (which is a measly 11km/s at the earth surface) it would leavethe earth on a tangent in nanoseconds, before even having had the opportunity of interacting with anything. So, we have a rogue micro black hole in space, and we are back to point (a): no planet or star has ever been observed being swallowed by such a thing.
As previously posted, this thread on SA is a good read.
posted by _dario at 8:35 AM on September 12, 2008
supposing that micro black holes are actually generated in a collision (which is a fairly improbable, but not impossible event), they are of incredibly small mass - subatomic mass.
As pointed out before, cosmic rays are in fact protons of extremely high energy, some of them several orders of magnitude larger than the energies they'll ever reach in the LHC, so way more likely to create micro black holes.
An incredible number of those clashes with the upper atmosphere (and that's where the ~10,000 muons that shower every square metre of the earth every second come from).
Many cosmic rays cross the upper atmosphere and some of those cross (est. about a dozen) you every second: the entire universe has been engulfed in such particles since, well, forever, stars are way larger and denser than the Earth (so much more capable of attracting a mbh), and despite this (a) no "star destroying micro black hole" event has ever been observed.
(b) Now, let's rule out Hawking radiation, and say that micro black holes are permanent (which, to my understanding, is plausibly although not demonstratedly false, since the Hawking radiation is a theory): a black hole of such dimensions and mass would simply pass through matter as a stone in the air, and having a speed close to the speed of light, 4 orders of magnitude above earth's escape velocity (which is a measly 11km/s at the earth surface) it would leavethe earth on a tangent in nanoseconds, before even having had the opportunity of interacting with anything. So, we have a rogue micro black hole in space, and we are back to point (a): no planet or star has ever been observed being swallowed by such a thing.
As previously posted, this thread on SA is a good read.
posted by _dario at 8:35 AM on September 12, 2008
"#1 and #2 have a lot more mass, and are usually sucking in more mass... so they stick around for billions and billions of years."
Certainly in the case of 1, and depending on just how big 2 is, they could quite happily never consume any mass again and last for such a long time that billions and billions of years would seem like the blink of an eye.
The luminosity of a black hole is inversely proportional to the square of the mass. You'd have to wait about ten times the lifetime of the universe for a stellar mass black hole to lose as much as a hydrogen atom in weight. It's just ridiculously slow even by cosmological standards.
An LHC collision has about 1053 times less energy than a stellar mass of matter though, so a black hole originating from it would radiates about 10106 times more brightly at a minimum. In other words, it radiates for its brief lifetime at a power level of around 1077W. To put this in perspective, the sun has a power output about as many times greater than a lightbulb as this black hole would be against an entire universe of stars. It doesn't take long to radiate a few TeV at that level. It's just ridiculously fast, even by subatomic standards.
posted by edd at 8:47 AM on September 12, 2008 [2 favorites]
Certainly in the case of 1, and depending on just how big 2 is, they could quite happily never consume any mass again and last for such a long time that billions and billions of years would seem like the blink of an eye.
The luminosity of a black hole is inversely proportional to the square of the mass. You'd have to wait about ten times the lifetime of the universe for a stellar mass black hole to lose as much as a hydrogen atom in weight. It's just ridiculously slow even by cosmological standards.
An LHC collision has about 1053 times less energy than a stellar mass of matter though, so a black hole originating from it would radiates about 10106 times more brightly at a minimum. In other words, it radiates for its brief lifetime at a power level of around 1077W. To put this in perspective, the sun has a power output about as many times greater than a lightbulb as this black hole would be against an entire universe of stars. It doesn't take long to radiate a few TeV at that level. It's just ridiculously fast, even by subatomic standards.
posted by edd at 8:47 AM on September 12, 2008 [2 favorites]
Take heart! Even if the LHC manages to produce a micro black hole that doesn't evaporate instantly, you still have nothing to worry about. It's gonna take many many many lifetimes to eat us. At least, according to this guy at Cornell U.
posted by greenland at 10:13 AM on September 12, 2008
posted by greenland at 10:13 AM on September 12, 2008
I am not a scientist. Nonetheless my understanding is that the LHC has far too little power to make a black hole The only way it's possible would be for some very odd versions of string theory to be correct. I won't pretend to understand them very well, but I do know they are a minority viewpoint.
But were one to be formed, there wouldn't be any time for it to cause damage. Firstly, if one were created, it would be moving at just under the speed of light. (That's what the LHC does- smash particles together at 99% of C.) The black hole would zip through or past Earth in a second. Also, the black hole would be so tiny that it would likely move through atoms; 99% of atomic volume is empty space. The singularity would, I read, be very unstable. Finally, it would also be so small (about the Planck size) that it would probably evaporate via Hawking radiation very quickly.
posted by spaltavian at 2:07 PM on September 12, 2008
But were one to be formed, there wouldn't be any time for it to cause damage. Firstly, if one were created, it would be moving at just under the speed of light. (That's what the LHC does- smash particles together at 99% of C.) The black hole would zip through or past Earth in a second. Also, the black hole would be so tiny that it would likely move through atoms; 99% of atomic volume is empty space. The singularity would, I read, be very unstable. Finally, it would also be so small (about the Planck size) that it would probably evaporate via Hawking radiation very quickly.
posted by spaltavian at 2:07 PM on September 12, 2008
I'll tell you what confuses me:
1) It is claimed in the media quite often that LHC will create "energies not seen since the Big Bang."
2) It is also claimed in the media that "gamma rays magnitudes of order more powerful strike the earth constantly."
So which is it? It seems to me those two statements contradict each other. If the former is true, how does the 2nd one jive with the first? If the first is true, why shouldn't we be concerned, unless the second is true, in which case, isn't the first statement false?
Someone please help me understand this!
posted by PigAlien at 9:17 AM on September 13, 2008
1) It is claimed in the media quite often that LHC will create "energies not seen since the Big Bang."
2) It is also claimed in the media that "gamma rays magnitudes of order more powerful strike the earth constantly."
So which is it? It seems to me those two statements contradict each other. If the former is true, how does the 2nd one jive with the first? If the first is true, why shouldn't we be concerned, unless the second is true, in which case, isn't the first statement false?
Someone please help me understand this!
posted by PigAlien at 9:17 AM on September 13, 2008
I can only assume that 2) refers to the fact that observations of the cosmic rays are somewhat less direct than you get in the LHC.
I'd say the first statement is maybe misleading. The second statement, if you substitute 'cosmic ray' for 'gamma ray' would be fine.
posted by edd at 4:26 PM on September 13, 2008
I'd say the first statement is maybe misleading. The second statement, if you substitute 'cosmic ray' for 'gamma ray' would be fine.
posted by edd at 4:26 PM on September 13, 2008
It's not energies since the big bang, but conditions not seen since the big bang. Nothing has ever happened that can approach the energy of that event.
posted by spaltavian at 12:22 PM on September 14, 2008
posted by spaltavian at 12:22 PM on September 14, 2008
You might find this useful. It's an interview with Professor Brian Cox on why we've nothing to worry about and also everything else you'd need to know about the LHC.
posted by feelinglistless at 1:32 PM on September 14, 2008
posted by feelinglistless at 1:32 PM on September 14, 2008
The luminosity of a black hole is inversely proportional to the square of the mass. ...
An LHC collision has about 10^53 times less energy than a stellar mass of matter though, so a black hole originating from it would radiates about 10^106 times more brightly at a minimum. In other words, it radiates for its brief lifetime at a power level of around 10^77W. To put this in perspective, the sun has a power output about as many times greater than a lightbulb as this black hole would be against an entire universe of stars. It doesn't take long to radiate a few TeV at that level. It's just ridiculously fast, even by subatomic standards.
It strikes me, edd, that these considerations could be a basis for arguing that there is a minimum size below which black holes cannot exist.
As follows: if Hawking radiation is exclusively photons, then the evaporating black hole must emit at least one photon during its exceedingly brief lifetime. That would seem to require that the frequency of the emitted photon be at least 1/(lifetime of black hole), since otherwise the black hole would not have existed long enough to complete the process of emitting that single photon.
And that means a minimal photon of higher and higher frequency the smaller the initial size of the black hole; indeed, the frequency of the photon would approach infinity as the initial mass of the black hole gos to zero. Which is a paradox, because the energy of that minimal photon would also go to infinity, and that would be a violation of conservation of energy, which requires that the energy of all emitted photons be no greater than the initial energy of the black hole.
Such a paradox could be resolved by saying that the smallest black hole which can exist is the one where the two curves intersect; where the energy of the black hole just equals the energy of the photon whose frequency is 1/(lifetime of black hole)-- that is, if i haven't made some blunder and there is a paradox in the first place.
posted by jamjam at 3:31 PM on September 14, 2008
An LHC collision has about 10^53 times less energy than a stellar mass of matter though, so a black hole originating from it would radiates about 10^106 times more brightly at a minimum. In other words, it radiates for its brief lifetime at a power level of around 10^77W. To put this in perspective, the sun has a power output about as many times greater than a lightbulb as this black hole would be against an entire universe of stars. It doesn't take long to radiate a few TeV at that level. It's just ridiculously fast, even by subatomic standards.
It strikes me, edd, that these considerations could be a basis for arguing that there is a minimum size below which black holes cannot exist.
As follows: if Hawking radiation is exclusively photons, then the evaporating black hole must emit at least one photon during its exceedingly brief lifetime. That would seem to require that the frequency of the emitted photon be at least 1/(lifetime of black hole), since otherwise the black hole would not have existed long enough to complete the process of emitting that single photon.
And that means a minimal photon of higher and higher frequency the smaller the initial size of the black hole; indeed, the frequency of the photon would approach infinity as the initial mass of the black hole gos to zero. Which is a paradox, because the energy of that minimal photon would also go to infinity, and that would be a violation of conservation of energy, which requires that the energy of all emitted photons be no greater than the initial energy of the black hole.
Such a paradox could be resolved by saying that the smallest black hole which can exist is the one where the two curves intersect; where the energy of the black hole just equals the energy of the photon whose frequency is 1/(lifetime of black hole)-- that is, if i haven't made some blunder and there is a paradox in the first place.
posted by jamjam at 3:31 PM on September 14, 2008
This thread is closed to new comments.
posted by Dumsnill at 6:55 PM on September 11, 2008