How bad would it be if we accidentally made a black hole?
askamathematician.com
askamathematician.com
TL/DR:
1. Tiny black holes as a dark matter candidate; hundreds might pass through the earth every year
2. Difficult but not impossible to detect a black hole of 100 thousand kg passing through the earth
3. A black hole with a mass of 10 million kg at the center of the Earth would take 10^13 years to absorb the planet -- much longer than Earth will survive anyway
Newton's laws work wonderfully at human scales, but not at extremes. Similarly, the Standard Model works wonderfully on the familiar things we've tested.. but maybe the Standard Model doesn't work the same way at high energies and it doesn't explain dark matter/energy anyway..
We just don't much about what black holes are like below the Schwarzschild Radius. We haven't even detected Hawking Radiation yet.
That is 100% not true. We don't know what a black hole will do, we just guess. Until we actually measure one we have no idea if there are surprises we have not thought about - or that we simply did not have any way to know were possible since such an environment does not exist on earth.
> It's like accepting science enough to believe in cosmological constants, but not accepting science's measurements of those constants.
Is there something wrong with doing that? You have no idea if (for example) those constants are actually constant. You have no idea if those constants vary based on some local environment. Perhaps even based on some other constant that we don't even know exists because we have never been able to measure things any other way.
There are a TREMENDOUS number of assumptions baked into theories. And we try to test as many of those assumptions as possible all the time, but there could be assumptions we did not even realize we were making.
You should really look into the history of science - it will give you some humility. At every age we thought we were at the pinnacle of science, only for later generations to find out things we never realized.
There is no reason whatsoever to expect this generation to be any different.
Normally I don't ask this sort of question, but are you a practicing physicist? If you are then this point is irrelevant. But if not, then we're all laymen/women here, and it's silly to accept the mathematical "guess" that says there might be tiny black holes but reject the proposed properties, when the same math that postulates their existence describes their likely properties.
You should really look into the history of science - it will give you some humility. At every age we thought we were at the pinnacle of science, only for later generations to find out things we never realized.
No doubt. I'm not questioning that. I'm saying it's presumptuous to pick and choose elements of a hypothesis without understanding the math behind it. If any of the participants in this thread are qualified to do so (clearly I am not), I'd love a link to your work on black holes. Otherwise, I maintain my original position.
Not that the math for black holes is all that well accepted in the first place - there are many holes in the math that quite clearly scream "we don't really know". For example a charged, or rapidly spinning singularity might be "naked" which breaks all theories and clearly shows how little we know about black holes.
> but reject the proposed properties, when the same math that postulates their existence describes their likely properties.
That isn't true though. It's completely different math. And Hawking radiation has a large information theory hole which tells us to be cautious - there is a gap in the theory, we don't actually know what will happen.
Remember neither of these theories have ever been observed, it's all math and simulations, no observations. (Super massive objects have been observed, but not event horizons.)
If you are referring to the fact that radiation brings back information from the inside of the black hole, which undermines notion of black hole being "event horizon", then there is one proposal to close this hole (it had been even submitted to HN recently): computational complexity.
From what I understood this means that while in principle radiation leaks information from inside of the black hole, the computational effort needed to put that information together in its original form is too big to be possible to do in practice (at least before thermodynamical death of universe).
When it reached the center, I'd expect that its gravity well would pull the rest of Earth into the black hole, unless it somehow found itself in a vacuum large enough to not create a gravity well. That would presumably be a sphere the radius of the amount of core material that is equivalent to the mass of Mt Everest, plus whatever it accreted on its descent.
So really, the question is whether or not a black hole that we could create would be able to make it to the floor of the lab... the article sorta touches on this:
The gravitational pull of a few micrograms of matter, regardless of how it is arranged, is never dangerous; you wouldn’t get pulled inside out if you ate it. However, you wouldn’t get the chance, since any black hole that we could reasonably create would already be mid-explosion.
Since the proposed method of creating the hole is to collide particles in an accelerator, we would expect the hole, when formed, to be moving the way particles created in an accelerator move, i.e., at close to the speed of light. So the hole would fly off into space, since it would be moving much, much faster than escape velocity. (Also, as the article notes, the hole would explode due to Hawking radiation soon after it was created.)
> unless it somehow found itself in a vacuum large enough to not create a gravity well
Not sure what you mean by this. The "gravity well" of the hole is the same whether it's surrounded by vacuum or matter. The only difference is what can possibly fall in.
And....wouldn't it interact with everything along it's path?
I mean..it wouldn't be quantum tunneling correct? (I've only taken rudimentary physics related to standard mechanics and electricity/magnetism).
But it seems to me, since the LHC is underground, it would have a decent probability of hitting something along it's path to space, or am I way off?
I guess it depends on the length of the "drill hole", the mass of the original black hole before it left the vacuum in the lab, the size of the event horizon and the original velocity?
[1] Technically I suppose it has some momentum due to the rotation of the Earth but I assume that's not significant. If it were significant, it would just mean that there's are "good" and "bad" directions for the escape so a worse case scenario could only get slightly worse, not better.
The mass would increase (unless the hawking radiation is fast enough to counteract the mass it is absorbing, which I don't know), so unless something had other forces on it, it would slow down somewhat... but unless some stuff outside of it has momentum significantly changed, I would think that the momentum would stay the same?
(assume a frame of reference where the matter it is passing through has roughly no momentum to start with)
Momentum is mass times speed, the momentum would stay the same, but since the mass is going up the speed has to go down.
It would stop pretty quickly actually.
"Friction" type interactions with matter it did not eat would also bleed energy.
Only in the non-relativistic limit. We're talking about a hole that starts out with ultrarelativistic velocity, so its momentum is not mv, it's gamma * mv, where gamma = 1 / sqrt(1 - v^2). For v close to 1 (meaning the speed of light), gamma can easily be a thousand or a million, meaning the actual momentum of the object is a thousand to a million times what the non-relativistic formula would make you think.
> It would stop pretty quickly actually.
I think you need to show some calculations. If the hole starts out moving at the typical velocities of particles in an accelerator experiment, it would need to absorb thousands or millions of times its starting mass to be slowed down to less than Earth escape velocity, let alone to be stopped. And at its starting speed it would take less than a twentieth of a second to pass through the entire Earth.
That's only if use non-relativistic mass which you should not be doing anyway. In any case it's still proportional to mass and velocity - the gamma factor does not change that.
> meaning the actual momentum of the object is a thousand to a million times what the non-relativistic formula would make you think.
You are missing parts of the interaction. Say it eats an atom - it has to accelerate that atom to the same relativistic velocity - meaning that new atom now has EXACTLY the same gamma as the black hole, and steals just as much momentum as if gamma was 1.
Or in other words the gamma factor is completely irrelevant for these calculations, it cancels out.
> it would need to absorb thousands or millions of times its starting mass to be slowed down to less than Earth escape velocity
As I've shown you, this is incorrect. It only needs to absorb mass similar to its own rest mass.
> And at its starting speed it would take less than a twentieth of a second to pass through the entire Earth.
That is also irrelevant. The only thing that matters is its "width", i.e. how many of the particles it interacts with does it eat.
Because otherwise you could say anything is proportional to velocity, but with another term which counteracts that factor?
Also, I thought the view was shifting to using rest mass instead of relativistic mass but I might have that backwards.
Yes. At ultrarelativistic velocities, momentum can change a lot for a very, very small change in velocity, so the behavior is highly nonlinear.
Not quite the same, but almost, yes. The final velocity of the hole after it eats the atom will be equal to the velocity of the center of mass of the hole + atom before the atom is eaten. But if the hole has the rest mass of Mount Everest, the motion of the center of mass of the system will be almost the same as the motion of the hole, since the rest mass of Mount Everest is probably about 40 orders of magnitude larger than the rest mass of an atom.
> meaning that new atom now has EXACTLY the same gamma as the black hole
Yes. But this gamma will be slightly less than the gamma of the hole before it ate the atom.
> and steals just as much momentum as if gamma was 1.
I see what you're thinking, but it's still wrong; you haven't calculated the effect correctly. See below.
> It only needs to absorb mass similar to its own rest mass.
No. Say the hole starts out with rest mass M, and is moving at velocity v, where v is almost 1 (the speed of light), so the gamma factor is, say, 1000. Then the total momentum is about 1000M.
Now the hole absorbs enough atoms to have rest mass 2M, and each atom is at rest before it's absorbed, so each atom contributes zero momentum to the total, so the total momentum is still 1000M after all the atoms are absorbed. That means the gamma factor is now (to a very good approximation) 500 (rest mass 2M times gamma of 500 times v approximately 1 gives momentum 1000M), which still corresponds to an ultrarelativistic velocity.
For the velocity to be less than Earth escape velocity, the total momentum of 1000M would have to be carried by a hole with a rest mass of about 3 million M, since Earth escape velocity is about 1/3000 of the speed of light (11.2 km/s vs. 300,000 km/s)--i.e., we would have rest mass 3 million M times gamma of approximately 1 times v of 1/3000, to give total momentum 1000M.
> That is also irrelevant. The only thing that matters is its "width", i.e. how many of the particles it interacts with does it eat.
The cross section (what you are calling "width"--what fraction of particles encountered does the hole eat) will depend on the speed of the hole; the faster the hole is traveling, the lower the cross section will be.
OK, I see your point. At those speeds a tremendous reduction in speed-energy (AKA relativistic mass) is only a small reduction in speed.
> the faster the hole is traveling, the lower the cross section will be.
At these masses gravitational attraction (that could pull in matter if given some time) is basically nil. I am assuming direct front-end collisions between the black hole and matter, so the speed doesn't make much difference.
Although thinking about it, I suspect the cross section (event horizon radius) of a proton massed black hole would be smaller than a neutrino.
Ah, ok; yes, in this approximation (which I agree is a pretty good one--there is another subthread on this that I've been posting in), the number of particles eaten is basically the number of atoms that can be lined up end to end across the diameter of the Earth (in the worst case scenario where the hole flies straight down through the Earth). That number is about 10^17, which is many, many orders of magnitude less than the number of atoms in Mount Everest (the very rough back-of-the envelope number I come up with for that is 10^40).
> I suspect the cross section (event horizon radius) of a proton massed black hole would be smaller than a neutrino.
I thought the hole's mass was assumed to be about that of Mount Everest, at least for this discussion. The horizon radius of such a hole would be about 1.5 x 10^-14 meters, or about the size of a large atomic nucleus. I'm not sure we have a good number for the "size" of a neutrino.
There were two discussions at once - Mount Everest, and a particle from the LHC.
That depends on the initial size of the hole; if it starts out small enough, it would radiate away mass fast enough that it would evaporate before it had a chance to travel far.
> unless some stuff outside of it has momentum significantly changed
Which it would.
Highly unlikely. If the hole starts out moving at nearly the speed of light, it will spend less than a twentieth of a second passing through the Earth. That's not enough time for it to absorb much matter, and it would have to absorb many times its starting mass (quite possibly thousands or even millions of times) to be slowed down from nearly the speed of light to less than escape velocity.
That's exactly it -- if the gravity well is a vacuum, then by definition there is nothing to fall into it, and thus nothing to increase the mass, and so the black hole would not grow.
Not quite. The proposed method involves rotating two [sets of] particles in opposite directions, and then ramming them together. Yes, both sets of particles have super-high velocities- but if they were rammed together, the resulting net velocity should be zero-ish (plus or minus experimental error).
Not necessarily. This is how current accelerator experiments work, and the particles coming out of those do not have zero velocity.
However, it is true that there is a key difference between current experiments and a hypothetical experiment that forms a black hole. The rest mass of the particles formed in current experiments is fixed, so any energy pumped into the particles over and above that becomes kinetic energy. But the rest mass of a black hole is not fixed, so it would be possible for all of the energy pumped in to become rest mass of the hole, instead of kinetic energy. (Possible, but still not guaranteed, as far as I can see; but since nobody really has a detailed theory of how all this would work, it's all speculation anyway.)
As a layperson, I don't understand this. Are you suggesting it would somehow pull in nearby mass and increase the density of that mass somehow? How would it keep adding mass while sustaining the necessary high density?
Any additional mass that enter the event horizon falls to the center and the density is still infinity.
(The event horizon get bigger when you add mass. You can image the black hole as a big sphere that is almost empty, except for a few things that are quickly falling to the center. And you have at the center all the remainder mass gathered at one point.)
That would depend on how it was formed and what its state of motion was. If it were moving fast enough (where "fast enough" means anything above escape velocity at the Earth's surface, 11.2 km/s--and objects created in our particle accelerators travel at close to the speed of light), it would just fly off into space.
> wouldn't the earth fall into it?
Not any more quickly than the Earth would fall into the existing Mount Everest. If such a hole were sitting at the center of the Earth, it would gradually accrete matter from the Earth, yes, but it wouldn't just swallow the Earth all at once.
The net momentum of a collision in the LHC is 0 relative to the Earth.
Of course it would happen more quickly. Everest is kept separate from the rest of the Earth by atomic bonds. But an Everest-mass black hole, created at rest on the Earth's surface, would fall through the ground to the center of the Earth very quickly (a few minutes of travel time), gobbling up all the matter within at least a few atoms distance of it's path. Then it would shoot past the center, sailing up toward the other side of the Earth. It would oscillate back and forth, effectively in a damped orbit about the center of the Earth, accreting more and more matter.
Since the accretion rate is probably proportional to the cross-sectional area of the black hole, and the area is proportional to the mass, the black hole size would grow roughly exponentially, at least until it came to rest at the center of the Earth. At this point, it would start accreting as fast as the liquid iron or whatever can get pushed into, which I imagine becomes very fast very quickly.
Actually, no, it would take about 45 minutes--half the time it would take to make one orbit of the Earth at approximately the radius of the Earth. That's assuming that the hole's motion is approximately equivalent to free-fall motion, which is what you're basically assuming--no inter-atomic forces exerted on the hole.
> gobbling up all the matter within at least a few atoms distance of it's path.
Not necessarily. Even though there are no inter-atomic forces preventing atoms from falling into the hole, the hole's gravity is still very small, so the force drawing atoms into the hole is very small. The hole's passage will disrupt the forces between atoms in the horizontal direction, but those forces are negligible anyway; the main force exerted on an atom that's part of the Earth is in the vertical direction. So the atoms just to the side of the hole's passage will start out at rest, and they will only fall into the hole if the hole's gravity is enough to pull them sideways into the hole in the time the hole passes.
Just to run some numbers, suppose the hole's mass is 10 trillion kg (my rough back of the envelope estimate of the mass of Mount Everest). Its horizon radius will then be about 1.5 times 10^-14 meters, or about the size of a large atomic nucleus. A typical atom is about 10,000 times larger, or about 10^-10 meters in radius. Using standard formulas for black holes, the time it takes for an object to be pulled into the hole from rest at 10^-10 meters away is sqrt(r^3 c^2/2GM), which works out to about 10^-8 seconds for r = 10^-10 meters and M = 10 trillion kg. But the time it will take the hole to cover 10^-10 meters, and thereby move out of the way of an atom being pulled in from the side, is only 10^-10 seconds at a slow speed of 1 meter/second (which the hole will achieve a tenth of a second after it starts to fall), and about 4 x 10^-14 seconds at the speed it will have at the center of the Earth (about 8000 meters/second, the same as low Earth orbital velocity). So pretty much the only atoms the hole will eat are the atoms directly in its path; its gravity will be too small to pull in atoms from the side quickly enough.
At the center of the earth, since its the gravitational locus of the planet, we wouldn't even notice it - while stuff would be falling in, the planet would still weigh the same and thus have the same surface gravity, and most of the planets material would resisit falling in by pressure against itself.
Remember anything which doesn't land on the event horizon is going to spiralling around and deflecting anything trying too.
This is why blackholes glow in the X-ray in space and it would apply here too.
Sure, matter will stream in at a constant rate - but there are real mechanical limits.
Not as cool as a black hole, but a pretty neat engineering challenge.
http://spectrum.ieee.org/aerospace/astrophysics/cern-to-star...
And a comparison of graphite vs. water schemes here: http://tesla.desy.de/new_pages/TESLA_Reports/2001/pdf_files/...
A hypothetical red giant that swallowed a neutron star, which sinks into the center and replaces the giant's core. Even at such a scale, the star is relatively stable (i.e., it doesn't go all kaboom immediately) because the matter falling into the neutron core is heated to such a degree that it can balance the inward pressure from gravity.
Now I'm imagining astronomers going "Where's the kaboom? There was supposed to be a star-shattering kaboom!"
http://www.askamathematician.com/2012/04/q-will-cern-awaken-...
>>> Astronomers have certainly discovered thousands of massive compact objects, which are considered as black hole candidates. In a strict sense, no one can detect a black hole as "not even light can escape" from it. They are at the best quasi-black holes. My research (Journal Mathematical Physics, 2009) has shown that true black holes have zero (gravitational mass) which means their positive mass-energy is neutralized by negative gravitational interaction energy . Thus no massive body can be a true black hole. In addition, my parallel research has independently corroborated this fact that true black holes have M=0! And such M=0 black holes can form only asymptotically, implying they never quite form. And only approximate and quasi-black holes can be formed.
Some reports say NASA has confirmed your idea that the so-called black holes are balls of fire. But you say that's not exactly ...
Yes. The NASA report does not mention my research and admits that `Black Holes are not Black Holes'. But the NASA research certainly bolsters my findings because eruption of corona from a black hole is not understood, as admitted in the NASA report. On the other hand, it gets most naturally explained by the MECO paradigm by which the socalled black holes are balls of ultra-magnetized fire (plasma) -something like the Sun.
My research has shown that there cannot be any true black hole. It is just a point and all vacuum with an imaginary boundary Event Horizon from which even light cannot escape. So if the corona (charged particles) have been inferred to be ejected from Black Hole, it means it is not a true Black Hole as claimed in 15 peer reviewed papers by me and collaborators. We also showed that as a star would get hotter and hotter during Black Hole formation, there will be a stage when the radiation pressure of the star material would counter the pull of gravity. This is a quasi-static state and the hot star material would be plasma.
What's your take on Stephen Hawking? Hawking has been trying to resolve Black Hole Information Paradox (created by himself in 1976). Failing to do so, from 2004, he has been making noises that "there may not be exact EH" (2004), and "there cannot be any true black hole " (2014) from some vague Quantum Gravity argument which nobody understands, not even those who believe in black holes . In contrast, my proof is exact, comple te and supported by observations, and based on simple general relativity, no unspecified quantum gravity nonsense. Many Nobel laureates too have been struggling to resolve this paradox, but they want to keep black holes alive. Nobody wants to kill the goose, which has been laying golden eggs. In contrast, only my research resolves it meaningfully , by showing there is no black hole, no EH. Hence, there is no paradox in the first place. You see, black hole is one of the biggest physics paradigms for almost 100 years with thousands of celebrity professors, researchers, Nobel Laureates having personal stake. Who would like to set their own Lanka on fire? <<<
0: http://timesofindia.indiatimes.com/home/science/There-are-no...