# I need a kilogram of neutrinos. What are the challenges?

So I am a benevolent genius that figured out that if only I had a kilo of neutrinos in a bottle, I could solve some long standing problems (climate change, rockets landing upright, world peace, the usual). What are the challenges?

So far, collecting neutrinos turned out to be... difficult. They only interact weakly (and gravitationally, I presume). The neutrinos we know of (coming from the Sun or supernovae or radioactive decay) are high energy and travel near the speed of light. My problems are

• How can I slow them down? Nuclear reactors use moderation to "cool" down fast neutrons. Can we imagine a process to cool down neutrinos? What could we bounce them off of to transfer energy? Or maybe there are cold neutrinos everywhere we just haven't detected them?

• How can I store them? Could there be some material providing a kind of electro-weak wall, like an Erlenmeyer flask for bubbly neutrino soup (probably invisible due to missing electromagnetic interaction)?

• Could I generate them already cold/slow?

• Anything else I've missed?

• You would also need to keep them at an extremely low temperature: by comparison, a flask of liquid helium would need to be kept at around 4 Kelvin.
– TLDR
Mar 6 '21 at 15:45
• On point #1, certainly there are cold neutrinos everywhere, they flood the universe from the Cosmic Neutrino Background (much like the CMB). Their exceedingly small energy already exacerbates the hard problem of detecting them. Mar 6 '21 at 22:39
• If you could collect all solar neutrinos hitting our planet, you'd have to wait over 5 to 50 years for a kg. Confining them and controlling them is your problem. Mar 6 '21 at 23:17
• In light of the comment by @CosmasZachos (which perhaps could be turned into an answer), you might make some optimistic assumptions and compute the total mass of big-bang relic neutrinos perhaps trapped in a sun-like star.
– rob
Mar 25 '21 at 19:51
• @rob Thanks for the invitation, but I'll pass... The cross-area of the earth, the flux of solar neutrinos on it, and the maximum mass of a component are pretty well estimated, and I would expect the OP to put them together. Mar 25 '21 at 20:07

Neutrinos have very little mass and react extremely weakly with just about everything.

One way to trap it is just to use gravity. Even photons can get trapped by black holes so I think it's pretty reasonable to try to collect neutrinos by placing an extremely heavy object near the sun and placing a bottle around the neutrinos that orbit it (the actual "bottle" is just for appearances and doesn't do anything, although I guess you could attach it to the black hole so something could carry the bottle around, which would move the black hole, which would cause the neutrinos to follow).

In your case you want 1kg of neutrinos in a "bottle" so having these neutrinos circling in a large orbit is not enough. But if you created a black hole that has a photon sphere (radius that photons are trapped) around the size of a bottle, then it's possible for neutrinos to be able to circle around in a bottle-sized orbit. Jupiter roughly has the mass necessary to have a "Schwarzschild radius" of $$\approx 3m$$ so if you had something around that order of magnitude, then it could be used to collect the neutrinos. (Although, in my example I work it out with light, while the orbits will be different since neutrinos have a tiny mass. Maybe someone here can do the details here more rigorously?)

Not so easy carrying around a mini-black hole with the mass of Jupiter. Also, actually collecting these neutrinos is going to be a hard task, as the crosssection of neutrinos from the sun that have bottle-sized stable orbits (that are trapped by our black hole) is probably very small. One trick that might work here is to use gravitational lensing to try to focus the neutrinos coming from the sun to a smaller area (although wikipedia is telling me that gravitational lensing isn't like optics and doesn't have a focal point so I'm not sure if this works).

Also, to add to the complications, neutrinos both famously and bizarrely oscillate between "flavors" as they propagate over long distances, which I can imagine only makes the situation more complicated.

• For a non-rotating BH, the ISCO (innermost stable circular orbit) radius for a particle with non-zero mass is $3r_s$, so twice the photon sphere radius. For a BH with high rotation, the ISCO radius can approach $r_s$. Mar 26 '21 at 8:16
• Note that gravitational trapping of neutrinos around stars is a real possibility, at least for some plausible neutrino masses -- see this answer and this follow-up question for more details. Mar 26 '21 at 11:53

Nice question! The only way, I guess, would be to invent some negative energy device that makes space(time) expand. For this, you have to create some exotic matter. The neutrinos in your bottle have a "slight" tendency to escape from it. If you put the device around the bottle, the space around it will expand towards the bottle and so the neutrinos can't escape it. Every time they think that the surface of the bottle is in reach it recedes. Maybe the bottle will break, but if you make it strong enough (which also takes a fair amount of genius), "cat in the litter box" ("kat in 't bakkie"), as the expression in Dutch goes for something "easy". You also have to make sure the space around the bottle isn't affected.
You can imagine that to do this the problem is shifted to collecting exotic matter.

So maybe it's easier to make a force field appear in the bottle. A weak force field, as this is the only force that interacts with neutrinos. You need an amount of W-bosons for that. To be bought at CERN. If you find a way to make them last long enough (they are pretty massive, so the speed of light doesn't have to be taken into consideration), bombard the bottle with the W-bosons, and the neutrinos may stay inside. I think this is the only way. Maybe putting a W-producing device around the bottle will do the trick too. The problem is shifted, however, to putting the W-particles inside a bottle, or creating a W-particle creating device (creating a weak force field producing device).

How to collect the neutrinos in the first place? Cold neutrinos travel at the speed of light and will continue with this speed after interacting with a weak force field. As said in a comment, it takes a five-year wait to see an amount of 5 kilograms neutrinos pass the Earth. So put devices around the Sun to direct all the outgoing neutrinos towards the Earth (though a five-year wait shouldn't be too long for saving the world from human-induced disaster, as is presently slowly unfolding). The device should produce W-particles as these are the only means for interacting (Z-particles will do too, though). You can use the same device to redirect the neutrinos that would otherwise pass through the Earth. Once you have redirected (focused) them towards your bottle, then you can make them move in small circles by bombarding them with well-adjusted W-particles and subsequently place them (again with W-particles) inside your bottle. This device will have to be in operation constantly because otherwise, the neutrinos will escape. You can, for security, put the space expanding device around the bottle, though maybe the Earth will not survive this. I'm not sure if you can apply space expansion locally.

The second option As you know, one neutrino is produced when two protons fuse. For one kilogram of neutrinos to appear, how many protons are needed? Then you need to know the mass of one neutrino. For the lightest neutrino, this is $$1.25 \cdot 10^{-37}(kg)$$. So for one kilo we need about $$10^{37}$$ neutrinos and we need twice as many protons. Knowing that the mass of one proton is $$1.8\cdot 10^{-27}(kg)$$, we need about $$3.6 \cdot 10^{10}(kg)$$. In words, about thirty-six billion kilograms. That's a high pile of protons, but managable. To make them fuse is manageable too. The best way (I think) is to put a two spherical shell around your bottle, and let the fusion reaction take place between them. So the production of neutrinos has been taken care of. How to let them stay in the bottle? You always have to include gravity or the week force to do this. I'll use W-particles (or Z's). Place an array of W- and Z- particle guns near your bottle and direct them towards it. If the guns sends three (six, two parallel planes for each direction) perpendicular showers of the particles around the bottle, the neutrinos might stay in the bottle. The problem will be that this can only be applied after you have filled the bottle. The bottle itself isn't actually needed to make the neutrinos stay in a small region of space.

To answer your question, your problems would be huge, to say the least. But if you succeed, the pay-off will be considerable.