# Can I make a black hole with one or two atoms?

So I was watching something that said

if we compressed Earth into the size of a peanut: we would get a black hole;

if we compressed Mount Everest into a few nano-meters; we would get a black hole.

Can I make a black hole with one or two atoms? If yes, would it become larger and turn into normal-sized black hole?

• Similar question here: astronomy.stackexchange.com/questions/12466/… At the mass of a couple atoms you run into the quantum gravity problem, which is unsolved. Apr 14 '17 at 22:02
• This is a meaningless and poor question. The dynamics of atoms is described by quantum mechanics, while black holes are the prediction of a classical (non-quantum) theory. Apr 15 '17 at 18:56
• @Walter The fact that we haven't developed the theory needed to answer a question does not make that question "meaningless" or "poor". Indeed, every advance that has ever been made in theory has been made because somebody asked a question which the then current theory wasn't capable of answering. Apr 16 '17 at 15:27
• @DavidRicherby I disagree respectfully. The correct answer to this question (other than "Yes and No" :-) ) is that it's not a well-formed question. Apr 17 '17 at 13:01
• @CarlWitthoft Saying that it's not a well-formed question is fine. My objection was to saying that it's meaningless and poor just because we don't have a theory of quantum gravity. Apr 17 '17 at 13:10

There are two answers: yes and no.

Yes because every mass M has a Schwarzschild radius given by $\frac{2GM}{c^2}$ (where G is the gravitational constant (about $6.7\times10^{-11}$ and c is the speed of light (about 300 000 000 $\mathrm{m/s}$). If something is compressed to its Schwarzschild radius it becomes a black hole. You can do this for an atom. An atom of carbon (for example) has a mass of $2\times10^{-26}\mathrm{kg}$ so its Schwartzschild radius is $$\frac{2\times (6.7\times10^{-11})\times (2\times10^{-26})}{300 000 000^2}\approx 3\times10^{-53}\ \mathrm{metres}$$

So the actual answer is no as there is no feasible way of compressing an atom to this size. Of significance here is the fact that this size is so small that objects this small don't behave like small balls but as quantum mechanical objects. But a black hole is a gravitational object modeled by General Relativity, and Relativity and quantum mechanics don't work well together. In other words, we don't have a scientific model for describing how an atomic mass black hole would behave.

Stephen Hawking has shown that small black holes are unstable, so an atomic mass black hole would be very unstable, evaporating in a very short time.

• Isn't there a bit of a transitive property that applies here? In a "normal" black hole, isn't everything so compressed that the even the atoms hit the Schwarzschild radius? Apr 16 '17 at 0:21
• Hasn't Stephen Hawking in fact proposed a mechanism by which small black holes would be unstable and evaporate? One can prove that this mechanism is consistent with the theory, but that doesn't prove that it actually happens. Apr 16 '17 at 15:30
• @DavidRicherby Yes, and Einstein has proposed a mechanism by which masses are attracted to each other. It's all theory. No-one has directly observed a black hole. But Black holes and Hawking radiation are generally accepted. Apr 16 '17 at 20:27
• Since that value is roughly $10^{-18}$ of the Planck Length, that pretty much rules out the "yes" part Apr 17 '17 at 13:03

I think the answer is No.

If we try and compress these atoms, we end up (eventually) with the nuclei close enough to be forced to fuse. Fusion would mean we've formed a single nucleus.

This stage is unavoidable.

So your two atoms question now reduces to whether a single nucleus can form a black hole ?.

A nucleus is a kind of complex quark-gluon mix and if we compress it more we end up with a very dense version of that which we basically don't have physics to model properly.

It's extremely unlikely that conventional general relativity can be applied to something that will be so small it's actually smaller than we think we can apply quantum theory. And the energy density involved at that point would be so high our current theories don't make sense any more. We need a quantum theory of gravity to do this and we don't have one that works well enough. In fact we're not even sure a quantum theory of gravity would allow us to go to such small, high energy scales - even that is unknown.

So we're in uncharted waters.

So why "no" ?

Well, to force such a compression of a nucleus we'd have to apply energies to a very small region of space - smaller than we think it's possible to do, because of the consequences of the uncertainty principle. Put simplistically, beyond some point we'd not be able to simultaneously say where the nucleus is and how fast it's moving. It would be impossible to confine to a smaller region. This would happen long before we reach the Schwarzschild radius, at around the Planck length.

As you'll see from the answer by @James-K , the Schwarzschild radius is about 10−53 m, but the Planck length is 18 orders of magnitude larger at about 10−35 m.

So we could not realistically confine and compress our nucleus into a small enough space to ever reach its black hole size.

Now we can make a generic catch-all statement that a new theory might provide some loophole that lets us get around that, but it does seem unlikely as we'd expect a new theory to reproduce most of what we already know at those limits. It's hard to imagine the uncertainty principle "going away" so I don't see a way around that.

There's an unproven possibility of a yes.

A quantum theory of gravity that works might (repeat might or might not) find that gravity at that scale changes its character and allows it to form event horizons at larger sizes than we'd currently expect for such mass-energy ranges.

But we lack any evidence to support that idea, and I won't convert a "no" to a "maybe yes" simply to allow room for any wild idea. That's science fiction, not science.

• MathJax doesn't show units like that… m was formatted as a variable. Apr 16 '17 at 5:27

A small addition to the answers above (I like the Planck length answer). It was thought that it might be possible to make very small black holes at CERN, theoretically anyway, but that theory required extra dimensions to exist. Because no black holes were observed, the extra dimensions (on very small scales) theory took a hit.

Even if those black holes could be created, they are predicted to evaporate very very quickly. (billionth of a billionth of a billionth of a second), but even that rate of decay should be noticeable. None were noticed.

It's also worth asking, if CERN smashes two protons together really really fast, and, if that makes a black hole (in theory), as in, pretend it's possible . . . Would this theoretical black hole really be made up of two protons or is it made up of two protons and 14 TeV plus kinetic energy? I think it's more accurate to say that such a black hole is really created out the kinetic energy not the atoms themselves.

Some might call that splitting hairs on Schrodinger's cat, but I think it's an important point. The enormous kinetic energy of a near light speed collision, might just be able to create a micro black hole, and in that case, it's the kinetic energy that should be called the primary ingredient not the atoms.

• An interesting way of looking at it. Apr 15 '17 at 15:09
• The idea of theories with extra dimensions is that there are extra (4th, 5th etc.) space dimensions which are very small and as a consequence Gravitation is much stronger at scales smaller than the size of these extra dimensions. This brings down the Planck (energy) scale to energies accessible at colliders such as the LHC. Apr 15 '17 at 18:52