Black holes squishing Earth

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  • #76
PeterDonis
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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.
 
  • #77
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I could see possibly doing this in empty space. But inside a planet?
Produce it outside, let it fall in?
 
  • #78
PeterDonis
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Produce it outside, let it fall in?
Hm, interesting. Dr. Evil's next project? :wink:

("I will drop this black hole on the Earth unless you pay me one million dollars." "Uh, sir?" "What, what?" ...)
 
  • #79
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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.
 
  • #80
PeterDonis
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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.
 
  • #81
DaveC426913
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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.
 
  • #82
PeterDonis
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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."
 
  • #83
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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.
 
  • #84
DaveC426913
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Heh. Well, innumeracy is an epidemic...
 
  • #85
OmCheeto
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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?]
  • Schwarzchild 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)
 
  • #86
PeterDonis
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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.
 
  • #87
OmCheeto
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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!
 
  • #88
DaveC426913
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Thanks all, for letting me play Devil's Avocado for a bit.
 
  • #89
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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.
 
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  • #90
OmCheeto
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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.

2018.10.13.black.hole.maths.png

  • 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.
 

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  • #91
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A billion tonnes yields a black hole with a lifetime 200 times that of our universe.
That is right. Such a black hole could be used to power things far away from stars, e.g. interstellar spacecraft.
It would take a billion tonne equivalent energy to smoosh two protons into a black hole.
No, the Planck energy should be sufficient. It just won't last long.
 
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  • #92
The present world record for man made particle collisions is 6.5 TeV per beam @ LHC. (See Wikipedia LHC page)
This is a very small amount of energy compared to the energy of some cosmic rays hitting Earth; by a factor of 10+ million.

For a sample of ultra-energy cosmic rays see.
https://www.quantamagazine.org/ultrahigh-energy-cosmic-rays-traced-to-hotspot-20150514/

This is happening without us being aware of it. We have nothing to worry about with the LHC; there are bigger natural players in the particle collision world
 
  • #93
DaveC426913
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I suppose that makes a fine answer, if I am ever asked.

We get collisions that are 10 million times greater than the LHC produces coming from space routinely. So far, no Earth-squishing black holes.
 
  • #94
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Be careful with that number. The center of mass energy is what matters. It is still larger than the LHC energy, but the factor goes down to something like 100 (depending on which particles you consider).
 
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Consider me a layperson. There may be something you have missed. Atoms have cohesion (surface tension in water). A small black hole (on the earth's surface) will not have enough gravity to overcome that. For an atom itself there is the strong force between particles. Even more difficult for the black hole gravity to overcome. Correct me if I am wrong.
 
  • #96
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A hypothetical stable microscopic black hole wouldn't be stopped by anything. It would fly through the atoms and nuclei, with a non-zero chance to absorb a nucleon each time it passes an atomic nucleus, and a non-zero chance to absorb an electron when flying through an atom.
 
  • #97
As an average guy with an average education, I have trouble buying all of this 'embedded in matter' stuff. Black holes are dangerous because of gravitational attraction, right? Its gravity pulls things in. Without enough mass, it should neither suck matter in nor be sucked to gravitational centers. No gravity, no force. Why should being embedded in matter change that?
 
  • #98
jbriggs444
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Without enough mass, it should neither suck matter in nor be sucked to gravitational centers. No gravity, no force.
There are two problems with the idea that low mass black holes are not affected by gravity. First, if we stick to the Newtonian model, free fall acceleration is unaffected by the mass of the falling object. Decrease the mass of the object and you reduce the gravitational force, but you also reduce its inertia. The result is a wash. Second, if we adopt the idea that gravity is geometry and that freely falling objects follow geodesic paths then the mass of a falling object is largely irrelevant to the path it follows through space-time.

A small black hole dropped from rest on the surface of the Earth will fall toward the Earth's center. Being subject to negligible resistance by the Earth's crust, mantle or core, it will enter a very eccentric orbit about that center with a period of around two hours and an apogee at the Earth's surface. [At least if we hand wave away the likelihood that it will evaporate first].
 
  • #99
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As an average guy with an average education, I have trouble buying all of this 'embedded in matter' stuff. Black holes are dangerous because of gravitational attraction, right? Its gravity pulls things in. Without enough mass, it should neither suck matter in nor be sucked to gravitational centers. No gravity, no force. Why should being embedded in matter change that?
A small mass doesn't mean zero mass and a black hole can get very close to objects (there is nothing that would repel it).
 
  • #100
A small mass doesn't mean zero mass and a black hole can get very close to objects (there is nothing that would repel it).
Yeah, but aren't we talking something on a subatomic scale here? At that size, surely even something as exotic as a black hole would behave differently, perhaps even behave like subatomic particles do. Do things on that scale still react normally to gravity?
 

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