B Could a Particle Accelerator Create a Black Hole That Destroys Earth?

[DaveC426913]

I expect that some portion of the Earth's mass would reach escape velocity and never be consumed.

So, we'd be safe after all!

 

[.Scott]

How much? Don't guess, calculate!

I'd be happy to. What's the formula?
The calculation for the Hawking radiation is easy. Since we are talking about a borderline case where roughly the same amount of mass is being consumed as being radiated - it's e=mc^2. Plenty enough to disturb the notion of matter simply dropping into it unobstructed.

But when stars drop into a BH, an accretion disc can formed. Sine the Earth is spinning, something like that should form around our smaller BH. In other cases, jets form along the spin axis. I don't understand the mechanism and I don't know the formulae. Educate me.

 

[.Scott]

Here some math:
Earth velocity at the surface at the equator due to rotation: Ve=460m/s
Earth radius: Re=6371 Km
BH with Earth mass radius: Rb=8.87mm
Estimated velocity due to rotation at the surface of the equator of the black hole: Vb = Ve Re/Rb

Vb = 460m/s * 6371Km / 8.87mm = 460*6371/8.87 10^6 m/s
Vb = 327.6 * 10^6 Km/s (well over c)

So there will be an accretion disk.

 

[.Scott]

So, we'd be safe after all!

Better than that, we have an up close look at some real Physics !

 

[PeterDonis]

BH with Earth mass radius: Rb=8.87mm

What does this have to do with the discussion in this thread? We're not hypothesizing a hole with the mass of the Earth. We're hypothesizing a much, much smaller hole that forms somewhere inside the Earth.

Estimated velocity due to rotation at the surface of the equator of the black hole

What does this have to do with the discussion in this thread? Nobody has hypothesized a spinning hole, much less a hole with both the mass of the Earth (see above) and the same angular velocity of rotation as the Earth (which, as you show, is impossible).

 

[PeterDonis]

Consider a homogeneous Earth. Gravitational acceleration increases with radius.

Ah, yes, you're right, I forgot to take into account the Earth's gravity as well as the hole's.

Spherical symmetry doesn't rule out spherically symmetric tangential forces (pressure).

But it does rule out tangential motion. Tangential pressure can exist, but it has to be static.

 

[.Scott]

What does this have to do with the discussion in this thread? We're not hypothesizing a hole with the mass of the Earth. We're hypothesizing a much, much smaller hole that forms somewhere inside the Earth.

What does this have to do with the discussion in this thread? Nobody has hypothesized a spinning hole, much less a hole with both the mass of the Earth (see above) and the same angular velocity of rotation as the Earth (which, as you show, is impossible).

You participated in the discussion about how atoms would feed into the black hole. In particular, I responded to your post #45. Then Nugatory asked me for some math. So I obliged.

So we were talking about what would happen when material started falling into the BH. And there I was right to assume an accretion disk. So I did as much math as I could - determining whether there was enough angular momentum for an accretion disk to form. There is - and therefore, at some point well before the BH diameter reaches 9mm, atoms are not going to simply fall into the BH.

I was also assuming that the BH started out without a spin. But it will pick up a spin - and more importantly, the material falling into it will be spinning at relativistic speeds. In any case, if you want to calculate how long we would have before dying from the tiny BH (which some posters were trying to do), these are factors that need to be considered.

 

[PeterDonis]

I responded to your post #45. Then Nugatory asked me for some math. So I obliged.

You claimed that a small BH would release a lot of energy. @Nugatory asked you to calculate how much. You haven't done that.

The point @Nugatory was trying to get you to realize is that a BH can't radiate more energy than its mass, and a tiny black hole hypothetically formed by a collision in the LHC has a tiny mass--a few TeV. So that's all the energy it can radiate, and if we're talking about possible effects on a macroscopic amount of material, that amount of energy is negligible.

we were talking about what would happen when material started falling into the BH. And there I was right to assume an accretion disk

No, you weren't, because the general conclusion of the discussion before you entered it was that, unless the BH is at least the size of a small asteroid, the radiation pressure from the hole's Hawking radiation will prevent matter from falling towards the hole at all before the hole evaporates. And since we're talking about a hypothetical hole formed somewhere inside the Earth by LHC-type collisions (or even cosmic rays), we're talking about a hole massing a few TeV, not a macroscopic hole at all.

 

[mfb]

But it does rule out tangential motion. Tangential pressure can exist, but it has to be static.

No one was talking about tangential motion (well, now .Scott started it, but that is a separate discussion). Pressure is just another name for the forces discussed.

You claimed that a small BH would release a lot of energy.

I'm quite sure the claim was that infalling matter would release a lot of energy in the process of falling in. For a rotating Earth that is certainly the case - most of the matter has too much angular momentum to fall in directly. We get an accretion disk, we get radiation from this disk, the radiation pressure will slow further collapse. The accretion disk has to get rid of angular momentum for more matter to fall into the black hole. The calculation to show that has been done.

A black hole with nearly maximum spin is highly efficient in converting infalling matter to radiation - something like 20-30% if I remember correctly. Earth's gravitational binding energy is just 2*10³² J, or 4*10^-10 times its total energy. Something like a billionth of the mass falling into the black hole could release sufficient radiation to evaporate the rest of Earth.

 

[PeterDonis]

I'm quite sure the claim was that infalling matter would release a lot of energy in the process of falling in.

The claim was that infalling matter would form an accretion disk, thereby releasing a lot of energy. But in order to form such a disk, first, the hole would have to be spinning; and second, the matter would have to get close enough to the hole's horizon to form such a disk and convert an appreciable fraction of its rest mass to energy.

For a hole formed by particle collisions, I would expect its spin to be small. But that's not really the major issue.

The major issue is that, for holes that could possibly be formed by any kind of particle collision process, their Hawking radiation pressure will, by many orders of magnitude, keep any matter from getting anywhere near close enough to their horizon to form an accretion disk and start radiating energy, before the hole itself evaporates. That's what the discussion that's already been had in this thread shows.

For a hole with the mass of a small asteroid or larger, yes, it might be possible for matter to get close enough, without Hawking radiation pressure blowing it away, to form an accretion disk (and for the hole to acquire enough spin to make the energy conversion rate non-negligible) and start radiating energy. But such a hole is not going to form inside another body like the Earth by any conceivable process.

 

[mfb]

The major issue is that, for holes that could possibly be formed by any kind of particle collision process, their Hawking radiation pressure will, by many orders of magnitude, keep any matter from getting anywhere near close enough to their horizon to form an accretion disk and start radiating energy, before the hole itself evaporates. That's what the discussion that's already been had in this thread shows.

Yes, we discussed this already.
Here we have a new scenario: What if the black hole is large already, so large that Hawking radiation doesn't play a role.

 

[PeterDonis]

Here we have a new scenario: What if the black hole is large already, so large that Hawking radiation doesn't play a role.

As I said, such a hole cannot form inside a body like the Earth by any conceivable process.

 

[mfb]

Not naturally. We might be able to create one in the very distant future, e.g. with gamma ray lasers.

 

[PeterDonis]

We might be able to create one in the very distant future, e.g. with gamma ray lasers.

I could see possibly doing this in empty space. But inside a planet?

 

[Justin Hunt]

Do we even know how gravity works at the quantum level?? We have Newtonian and Relativity, but my understanding is that neither is valid at the quantum level. In addition, gravity is the weakest of the four forces and only overpowers the electromagnetic force at the macro level due to charge not matting for gravity. what does Quantum physics say about Black Holes?

 

[PeterDonis]

Do we even know how gravity works at the quantum level??

We don't have a good complete theory of quantum gravity. We do have a lot of heuristic work that has been ongoing for decades to figure out what we can say about quantum gravity, in the absence of a complete theory, based on the fact that it has to reduce to the familiar gravity behavior we observe in the domain we have observed it in.

what does Quantum physics say about Black Holes?

Right now, I think the key things that are accepted about black holes in a quantum context are:

The entropy of a black hole is 1/4 of the area of its horizon in Planck units. We don't know exactly what microscopic states underlie this entropy, although there are a number of proposals.

Black holes emit Hawking radiation, and will eventually evaporate if their Hawking radiation temperature is higher than the temperature of their surroundings. (Note that, for black holes we can observe, i.e., stellar mass or larger, their Hawking radiation temperature is orders of magnitude lower than the temperature of their surroundings, which is at least 2.7K, the CMBR temperature, so none of them will be losing mass on net to evaporation any time soon.) We don't know exactly what will be left behind when a black hole evaporates; that's part of the black hole information paradox, which I don't think can be considered solved, although a number of physicists have made claims that it is, since we have no way of verifying any of the proposed models experimentally.

 

[mfb]

I could see possibly doing this in empty space. But inside a planet?

Produce it outside, let it fall in?

 

[PeterDonis]

Produce it outside, let it fall in?

Hm, interesting. Dr. Evil's next project?

("I will drop this black hole on the Earth unless you pay me one million dollars." "Uh, sir?" "What, what?" ...)

 

[Justin Hunt]

Also, I am not sure if hawking radiation can really be used to explain this when we have no proof for it. My understanding of hawking radiation is that particle pairs by chance can form near the EH with one going into the hole and one escaping. My problem with this explanation is I don't see how anti-matter versus matter would have the preference for being absorb by the hole and the other being ejected otherwise the net change should average zero.

My intuition, is that Black holes less than a 3 solar masses are just unstable and that the equation for hawking radiation may be a good equation for determining how long such a hole would last. The mechanism, however, is probably unknown.

 

[PeterDonis]

I am not sure if hawking radiation can really be used to explain this when we have no proof for it.

We don't have any experimental verification of Hawking radiation (because for black holes we can observe, i.e., stellar mass or larger, it is much too faint for us to detect). However, the theoretical reasons for expecting it to be there are pretty strong.

My understanding of hawking radiation is that particle pairs by chance can form near the EH with one going into the hole and one escaping.

This is only a rough heuristic picture and has many limitations. The actual underlying theory is quite different.

I don't see how anti-matter versus matter would have the preference for being absorb by the hole

There is no preference for anti-matter vs. matter being absorbed by the hole. The hole is expected to radiate particles and antiparticles in equal quantities.

otherwise the net change should average zero

No, it shouldn't. Both particles and antiparticles radiated away will have positive energy.

If you want to ask further questions about this, you should start a separate thread, it's off topic for this discussion. (But first you should search the forums as there are plenty of previous threads on the topic of Hawking radiation.) Also, it should not be a "B" level thread as the mechanism of Hawking radiation is at least an "I" level, if not an "A" level, topic.

My intuition, is that...

Please review the PF rules on personal speculation.

 

[DaveC426913]

Not naturally. We might be able to create one in the very distant future, e.g. with gamma ray lasers.

That is playing directly into the fears of laypeople.

What you are saying is tantamount to: "We're sure that the low amount of energy we are using now can't create a BH that will eat the Earth, but once we reach higher energies, we'll be off to the races..."

To which the laypeople would say " So, it's really just a matter of degree then. How will we know when enough is enough? Is today's amount enough? Are you sure?"

Which is exactly what I was hoping to establish not to be the case with this thread.

 

[PeterDonis]

Which is exactly what I was hoping to establish not to be the case with this thread.

If you're looking for a guarantee that the laws of physics will always and forever be able to prevent intelligent beings from creating black holes and doing possibly unpleasant things with them, there isn't one.

@mfb said "might" and "the very distant future", and the relative orders of magnitude have already been given, roughly (and roughly is quite enough for this purpose), in this thread. So the proper answer to some layperson asking this:

" So, it's really just a matter of degree then. How will we know when enough is enough? Is today's amount enough? Are you sure?"

Is "Yes, we're sure that today's amount is not only not enough, it's many, many orders of magnitude short of being enough. It's not even close. It's not worth worrying about."

 

[mfb]

You would need at least the mass equivalent of about a billion tonnes in gamma rays. That is 34 orders of magnitude beyond the LHC energy.
Yes, if you can increase the energy by a factor 10000000000000000000000000000000000 you can see new effects. That shouldn't be surprising.

 

[DaveC426913]

Heh. Well, innumeracy is an epidemic...

 

[OmCheeto]

You would need at least the mass equivalent of about a billion tonnes in gamma rays. That is 34 orders of magnitude beyond the LHC energy.
Yes, if you can increase the energy by a factor 10000000000000000000000000000000000 you can see new effects. That shouldn't be surprising.

Is there a reason you chose a billion tonnes of gamma rays?

I've worked through 20 different masses, from 2 protons through the sun, calculating:

• time to evaporate (sec) [1 second is about as much as an obese blue whale]
• time to evaporate (aou = age of the universe) [13.8 billion years yields 173 billion kg. More than a fat blue whale, but less than Mt. Everest.]
• Schwarzschild radius (meters) [1 meter is about 100 Earth masses]
• temp (Kelvin) [a mass of about half the moon yields the CMB temperature, where black holes stop evaporating]
• energy (e=mc^2 in joules) [the mass of my truck(1400 kg) or 1/4 global annual energy consumption or power output of our sun]
• power over lifetime (watts) [good grief! A Mt. Everest black hole(1e15 kg) would radiate 1000 watts for 200 billion times the age of our universe?]
• Schwarzschild surface area (m²) [came in handy, when I couldn't comprehend the power output of a 2 proton mass black hole. My always suspicious maths says that black holes have a luminosity of 0.8 watts at the Bohr radius. Someone may want to check that.]
• et al.

and a billion tonnes doesn't stand out on my graph.

ps. does a billion tonnes of gamma rays weigh as much as a billion tonnes of feathers? (asking for a friend)

 

[PeterDonis]

Is there a reason you chose a billion tonnes of gamma rays?

Because that's an applicable rough threshold that comes out of the discussions and calculations that have been done in this thread. Please read them.

 

[OmCheeto]

Because that's an applicable rough threshold that comes out of the discussions and calculations that have been done in this thread. Please read them.

Ok. I read them. Still nothing.
So I'm guessing that means this discussion is too far over my head, so, I'll just unsubscribe from the thread.
Ciao!

 

[DaveC426913]

Thanks all, for letting me play Devil's Avocado for a bit.

 

[mfb]

Is there a reason you chose a billion tonnes of gamma rays?

It gives a Schwarzschild radius of 1.5 fm, which means you have a chance to focus gamma rays into a region roughly that size.

 

[OmCheeto]

It gives a Schwarzschild radius of 1.5 fm, which means you have a chance to focus gamma rays into a region roughly that size.

Thanks! Not sure how I missed that. I think I was focusing more on my spreadsheet that the discussion.

• blue: evaporate too fast to be a hazard
• orange: human timescale
• green: my confusion zone (Guessing had I not switched from "number" to "scientific" notation, I would have seen it.)
  
• pink: evaporate too slowly(or not at all) to be interesting

My previous interpretation: A billion tonnes yields a black hole with a lifetime 200 times that of our universe. That's kind of overkill.
My new guess: It would take a billion tonne equivalent energy to smoosh two protons into a black hole. Which is kind of underkill, as that poor hole would evaporate rather quickly.

ps. Fun problem. But, as I said, I do not understand any of this, so, I'll just go back to watching, if that's ok.
pps. On a linear scale, those numbers create the worlds most boring graph I've ever seen. Kind of "head scratchy" on a log-log scale though.
ppps. As always, I will not be offended if anyone deletes this post if my spreadsheet has any errors, or if anyone thinks I'm just adding noise to the discussion.