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

[mfb]

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.

 

[accel2know]

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

 

[DaveC426913]

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.

 

[mfb]

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).

 

[StandardsGuy]

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.

 

[mfb]

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.

 

[thetrellan]

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?

 

[jbriggs444]

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].

 

[mfb]

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).

 

[thetrellan]

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?

 

[jbriggs444]

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?

The model that predicts that black holes exist (i.e. General Relativity) predicts that they are affected by gravity. So yes, they do still react normally to it.

 

[PeterDonis]

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?

It depends on what "subatomic scale" theory of physics you are talking about.

Classically, everything that has energy responds to gravity. That's what our best classical theory of gravity, General Relativity, says. Black holes have energy (because they have mass), so they respond to gravity according to this theory.

If you want to bring in quantum mechanics, as your allusion to different behavior on the "subatomic scale" suggests, then we don't know the answer for sure, theoretically speaking, because we don't have a quantum theory of gravity. But all the indications we have are that the rule from classical GR will still hold: everything that has energy will respond to gravity. So even with quantum effects included, there is no reason to think that a very small black hole will not respond to gravity.

Experimentally, as far as we can tell, gravity does affect subatomic particles, or at least their energy levels:

https://www.nature.com/news/bouncing-neutrons-probe-dark-energy-on-a-table-top-1.15062

 

[thetrellan]

It depends on what "subatomic scale" theory of physics you are talking about.

Classically, everything that has energy responds to gravity. That's what our best classical theory of gravity, General Relativity, says. Black holes have energy (because they have mass), so they respond to gravity according to this theory.

If you want to bring in quantum mechanics, as your allusion to different behavior on the "subatomic scale" suggests, then we don't know the answer for sure, theoretically speaking, because we don't have a quantum theory of gravity. But all the indications we have are that the rule from classical GR will still hold: everything that has energy will respond to gravity. So even with quantum effects included, there is no reason to think that a very small black hole will not respond to gravity.

Experimentally, as far as we can tell, gravity does affect subatomic particles, or at least their energy levels:

https://www.nature.com/news/bouncing-neutrons-probe-dark-energy-on-a-table-top-1.15062

True. But why should such a thing grow, if what makes it do so is its intense gravity? There is no reason to think it would ever find the center of the planet, either, when not even light does this. The only particle I know of that can move through solid matter is the neutrino. I admit I don't know much about them, and that what I do know is pretty suspect. But they go clean through planets, don't they?

 

[thetrellan]

The model that predicts that black holes exist (i.e. General Relativity) predicts that they are affected by gravity. So yes, they do still react normally to it.

I think the operative word is "normally". Meaning it lacks to mass to grow the way a naturally formed BH would, and so would behave like any other subatomic particle. There is no event horizon, because it hasn't the mass to attract inescapably. In fact, isn't that why they dissipate? Not enough mass to sustain an event horizon?

 

[Nugatory]

I think the operative word is "normally". Meaning it lacks to mass to grow the way a naturally formed BH would, and so would behave like any other subatomic particle. There is no event horizon, because it hasn't the mass to attract inescapably. In fact, isn't that why they dissipate? Not enough mass to sustain an event horizon?

There's no such thing as not having the "mass to attract inescapably". If the mass is non-zero the Schwarzschild radius is non-zero; if that mass is all contained within the Schwarzschild radius the event horizon will form and nothing at the event horizon will be able to escape. Whether the hole evaporates or grows depends on whether it is "hotter" than its surroundings, which determines whether it loses more energy by Hawking radiation than it absorbs frames from outside.

What we don't know, because we do not have a complete theory of quantum gravity at extremely small scales, is what if any as-yet-undiscovered physics might show up at these scales. However, it is somewhat pointless to speculate without a candidate theory that will make quantitative predictions.

 

[thetrellan]

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).

How about the crust of the Earth? As stated

There's no such thing as not having the "mass to attract inescapably". If the mass is non-zero the Schwarzschild radius is non-zero; if that mass is all contained within the Schwarzschild radius the event horizon will form and nothing at the event horizon will be able to escape. Whether the hole evaporates or grows depends on whether it is "hotter" than its surroundings, which determines whether it loses more energy by Hawking radiation than it absorbs frames from outside.

What we don't know, because we do not have a complete theory of quantum gravity at extremely small scales, is what if any as-yet-undiscovered physics might show up at these scales. However, it is somewhat pointless to speculate without a candidate theory that will make quantitative predictions.

Schwarzschild radius. This is what I needed to understand. So basically any matter that collapses has an event horizon where the original diameter was, and nothing can escape crossing that. Thanks.

 

[mfb]

True. But why should such a thing grow, if what makes it do so is its intense gravity?

Once in a while matter falls in, that makes it grow. Where "it" is a hypothetical stable microscopic black hole, so we are in a science fiction scenario.

There is no reason to think it would ever find the center of the planet, either, when not even light does this.

A black hole has nothing in common with light. It would be in free-fall to a very good approximation (see above: There is nothing stopping it motion), only deviating from that when a particle falls into the black hole. This process makes it lose kinetic energy over time and it settles in the core of Earth over time.

The only particle I know of that can move through solid matter is the neutrino. I admit I don't know much about them, and that what I do know is pretty suspect. But they go clean through planets, don't they?

Neutrinos at not too high energies can go through planets, sure, but they are not the topic here.

So basically any matter that collapses has an event horizon where the original diameter was, and nothing can escape crossing that.

No, the event horizon is much smaller.

 

[OmCheeto]

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].

Interesting scenario. We should talk Kip Thorne into writing another movie.

Where "it" is a hypothetical stable microscopic black hole, so we are in a science fiction scenario.

I rest my case.

ps. Couldn't be any worse than "Bird Box"...

 

[PeterDonis]

why should such a thing grow, if what makes it do so is its intense gravity?

Have you read through the thread? This has already been discussed.

There is no reason to think it would ever find the center of the planet, either, when not even light does this.

Light can't reach the center of the Earth because the Earth is not transparent to light. The Earth is effectively transparent to a nano-sized black hole (as it is to neutrinos, which is why neutrinos can pass through the Earth). This has been discussed in the thread as well; please go back and read through it.