# The neutron star teaspoon example

Reading through the recent black hole/neutron star threads reminded me of the usual example cited in order to illustrate the incredible density of these things.

The example points out that a single teaspoon of the stuff would weigh an incredible amount. Wiki says: “mass over 5.5×1012 kg, about 900 times the mass of the Great Pyramid of Giza.”

So I started thinking, what WOULD actually happen if I were to hold in my hand a teaspoon carrying neutron star soup. Let’s forget about the issue of getting the stuff and transporting it here to Earth for a moment. Right now, I’m holding the spoon. I’m standing in, let’s say the middle of central park, NYC. What happens exactly?

My guess is that the stuff would be so heavy, my arm is ripped right off, or maybe I just drop the spoon and that leaves a crater. But I’m also thinking that without the tremendous gravitational forces of the neutron star, the soup in the teaspoon will quickly and violently expand (i.e explode).

So experts, what would happen exactly? Would I die, and if so how? What would happen to central park and the poor animals at the nearby zoo?

(Maybe I should change the title to need answers quick…)

It shouldn’t “explode” if for no other reason that its gravity will keep it together.

So long as it remains “intact” or at least ‘compact’, won’t it fall to the centre of the Earth since nothing in or on the Earth is strong enough to hold it up. (Now, whether it oscillates, I won’t comment. That is, when it falls toward the center, it will pick up momentum and overshoot the centre eventually, only to fall back toward the centre from the other side).

I think.

I’m not sure about that. Earth’s mass is 6e24 kg, and radius is 6e6 meters, so if the teaspoon of neutrons is 1 cm in radius (and I didn’t screw up the math), the gravity at the surface of the teaspoon of neutrons is about 3 million times Earth’s gravity. Which is enough to destroy the spoon itself by flattening it against the neutrons, but I don’t think is enough to hold all the neutrons together. So I suspect the result would be “KABOOOM!” (don’t know if it would be Earth-shattering or not).

By the way, if it didn’t go boom, thanks to a magic force field, your hand would be ripped off of your body as gravity pulled it into the neutrons, but your torso would only get about one Earth gravity of pull from the neutrons, because the gravity falls off as the square of the distance. The teaspoon would also fall to the ground, and I think what would happen is that it would quickly attract a surrounding layer of rock smooshed flat against the neutrons and held there. The whole thing would be pulled down through the bedrock, I suspect reaching some equilibrium, where the layer of rock gravitationally bound to the neutrons would spread the weight enough to be supported by bedrock (and/or magma if it got that far down).

First of all, yes, the teaspoon would explode violently, kill you instantly, and leave a crater. I’ll let someone less lazy than myself try to calculate how large a crater. At the very least, without the tremendous pressure of the neutron star to keep it dense, the stuff would expand violently into 5.5×10^12 kg worth of ionized hydrogen, helium, and metals (I don’t think we know enough to say what proportion). At the very least the crater would be larger than NYC.

Second of all, the stuff is so dense that your arm would be put under tremendous force from its gravitational pull. If you held the teaspoon at arm’s length, my rough calculation says that your head, for example, would be subjected to approximately 500 pounds of force. Your fingers would experience over a million pounds of force. So if the stuff didn’t explode as I described above, you would be violently sucked into the teaspoon, and eventually the earth would get eaten up too.

Crap!

Don’t worry guys I’m calling off the experiment. At least until I can convince someone else to hold the spoon.

The mass of the Earth is 12 magnitudes larger than a teaspoon of neutron star. While there would be serious surface damage, the Earth as a whole wouldn’t be eaten up.

Edit - looking at the earlier thread, a teaspoon of neutron star has about the same mass as the meditterenean sea, so “serious surface damage” might be putting it mildly. I’m guessing this might be an extinction level event.

Maybe try a spork?

Oh yes, I was about to opine it would be only on the order of magnitude of a nuclear bomb, but that was assuming that a nuclear bomb’s worth of neutron star material were teleported. That would still be a big explosion, since the gravitational binding energy in a neutron star is quite high.

But a Mediterranean Sea’s worth of neutron star material, whose gravitational binding energy per kilogram is only a couple orders of magnitude lower than the energy released by a nuclear bomb (by my wild-ass guess)? Yes, the kaboom would be earth-shattering in all but the most literal sense.

If you do the calculation, you’ll find that the acceleration at the surface of the teaspoon is large enough to start eating up the earth. It’s a matter of density, not total mass. Similarly, a rather tiny black hole could eat up the earth. It’s all about density here. Of course it’s moot anyways, since the damn thing will explode before any of this speculation would be applicable.

Yeah, but then again, I’ve got worms in my garden that can start to eat up the Earth. The question isn’t whether it can start, but whether it can finish.

And the energy per mass of neutron-star material is going to be significantly greater than that of a fusion bomb, by over an order of magnitude.

Hmmm, I knew that the gravity well was certainly this large – it stands to reason because neutron stars are close to becoming black holes, so their escape velocity must be relativistic. But I had assumed that most of the energy would be radiated away rather than used to pack the particles closer together.

Looking at the thread, I think the Mediterranean Sea mass was for a cubic meter of neutronium. A teaspoon is (at 5 ml) about 200,000 times less.

Again, if we could make a stable object that size and density, the gravity right at the surface is ferocious, but just six meters away it’s only about one earth gravity, and 50 meters away it’s undetectible without very sensitive scientific equipment.

So if it teleports to a teaspoon in your hand, you’re about to become a smear of compressed goo wrapped around the magic pea of contained neutronium; the person across the room will suddenly feel like she’s standing on a 45 degree slope. The guy across the building won’t notice (assuming the building doesn’t collapse when the magic pea falls through the floor, taking some of the floor with it.)

The only reason it wouldn’t be able to continue eating up the earth indefinitely is if the process of eating up the earth sufficiently reduced the density of the stuff. A valid point. But I was assuming, for the sake of argument, that the stuff wouldn’t explode. If it magically doesn’t explode, and I assume there is no extreme fine-tuning of forces, then I think it is reasonable to assume it will it will crush the earth it “eats” to it’s own density, allowing the process to continue indefinitely. But this is not necessarily so, so I’ll let it go. This is a pretty silly argument we’ve started here btw

Just to further clarify: if we start with the premise that the surface of the teaspoonful has enough attractive force to bind the nuclei together, unless there is fine tuning, then infinitesimally above the surface there is also enough attractive force to bind nuclei together. Therefore the “eating” process would continue indefinitely.

Thanks, was a hurried edit on my part after skimming the other thread.

I think there is some confusion over the thought experiment here. I’m assuming that once the tea-spoonful of neutron star has been magically teleported here, the magic stops. In that version, I think “blow up” is the right answer. In the version where the matter is magically bound together, I think accretion is the right answer.

Thought experiments like this help give me a better idea of the holy fuck batman ™ forces involved.

If we’re assuming that the spoonful of neutronium is bound together somehow, it must be by forces other than its own gravitation, since it takes a whole star’s worth of gravitation to do the job.

The thread that made me realize this board was for me, we were going into the effect of the Heisenberg uncertainty principle for Galileo’s hammer and feather experiment. This thread still has a ways to go, I think.

Just to be clear, I was doing a thought experiment where the teaspoon-sized lump of neutronium is not gravitationally powerful enough to keep itself together (which is I believe is in fact true), but we have some kind of magic force field applied that will keep it together and stable, with only gravity escaping. In that case, the person holding it gets sucked in and smooshed, then the lump drops into the earth and coats itself with rock and dirt (and a layer of what used to be the person holding it). I don’t think the rock coating would be nearly as dense as the netronium; rock can stand pretty high pressures without compacting very much, so you’d end up with a big rough 3-meter cube of rock that is really, really, heavy, but has only mild gravity on the outside.

Fair enough. In case anyone is interested in how much pressure the rock would be subjected to at the boundary between it and the teaspoon, here is my rough calculation assuming the teaspoon to be ~1 cm in diameter and a 10 kg rock being tugged against it:

10kg*(6*10^12kg)G/(.01m)^2/(.01 m)^2 = 400 GPa

That’s about the same pressure that rocks experience at the center of the earth.

Ha! I don’t want to try to compete with that