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What are the circumstances in which neutrinos can harm humans or even kill them.?

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I think the only way a neutrino could harm a human was if it triggered a device intentionally built to kill the human if it detected a neutrino. –  Claudius Dec 10 '12 at 15:04
@Claudius: "neutrinos don't kill people, people kill people." –  NiftyKitty95 Dec 10 '12 at 15:17
@NickKidman And supernovae. Supernovae kill people, too. –  Claudius Dec 10 '12 at 15:20
Well, if the energy of a neutrino is hundreds of GeV or so, then such a a neutrino interacts as strongly with matter as an electron of the same energy - that's an aspect of the electroweak unification (well, the center-of-mass energy has to be hundreds of GeV to make the interaction really comparably strong, not just the lab energy). That would ionize your body and, in modest amounts, kill you. Only low-energy neutrinos are weakly interacting. –  Luboš Motl Dec 10 '12 at 16:01
Even in @LubošMotl's scenario the average energy deposition per neutrino is still only 100s or 1000s of MeV (assume DIS, but the products are necessarily heavily boosted...) rather than the full neutrino energy, so you still need a lot of them. Of course, under those circumstances you can get a lot with relatively modest sources. On the other hand, under those circumstances you can actually shield them, which you can't at MeV or GeV energies. On the gripping hand the shielding can be a hazard if it converts a lot of them to less penetrating stuff just in time to nail you. –  dmckee Dec 10 '12 at 16:11
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2 Answers

Under regular circumstances, neutrinos are absolutely harmless due to their small interaction cross section. If you hold your thumb up to the sun, about 60 billion (60 · 109) neutrinos will pass through your thumbnail per second, but you will rarely ever have any neutrino interaction in your body.

That is for 'regular' neutrino fluxes which you have from the sun. However, if you take these fluxes and increase them by several orders of magnitude, you can get into a dangerous area. Martin Beckett already mentioned supernovas, but one potentially realistic hazard comes from muon storage rings. I've found a paper that discusses this:

Muons decay into electrons and neutrinos ($\mu^- \rightarrow e^- + \bar \nu_e + \nu_\mu$), which would fly in the direction of the neutrino beam, so tangentially to the beampipe. The neutrinos eventually interact with matter, and produce harmful secondary radiation. If some day someone would build a 10 TeV muon collider, the author estimates an annual dose of 0.66 mSv in the plane of the ring, which is above the US legal off-site radiation limits (according to the linked paper). In long, straight sections of the accelerator this gets worse, since the neutrinos accumulate in a fairly small angular section.

However, this does not mean that a muon collider will produce an all-penetrating death ray in it's plane of operation. Remember, the thing that makes radiation dangerous is its energy loss in matter, and that's the same effect that makes it shieldable. You can build it further underground, tune its shape, etc., to make it less dangerous.

One small anecdote at the end: The MINOS experiment at Fermilab, one of which's goals was to study neutino oscillations, used to send a neutrino beam from the Tevatron's Main Injector through its "near detector" (at Fermilab, near Chicago) to the "far detector" (in Minnesota). They were looking for neutrino (dis-)appearance due to oscillations. When they had visitors, they used to take them on a tour of the near detector hall, even when the beam was running. Supposedly, the detector was sensitive enough (and their beam intensive enough) that if someone would stand in front of it for too long, they would leave a shadow in the detector :-). I'm not sure how long exactly they would have to stand there, though it was apparently harmless.

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The NuMI (Neutrinos from the Main Injector) beam runs in the few to few-tens of GeV energy range and emerges from it's underground trip in Manitoba. Shh! Don't tell the Canadians! –  dmckee Dec 10 '12 at 17:27
@dmckee Erratum arxiv.org/pdf/1205.6430.pdf "However we neglected the curvature of the earth"..."experiment be installed about 1.3 km above ground". That's particle physicists for you, we astronomers rarely forget the Earth is round! –  Martin Beckett Dec 10 '12 at 19:36
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Yes (probably).

Since neutrinos interact so rarely with matter (ie you) you would need an awful lot of them to have any significant effect. A supernova conveniently emits about 99% of its energy as neutrinos. So if you were standing quite close to a supernova when it went off then there could possibly be enough interactions to harm you.

If you stay a respectable distance from any exploding stars then you are OK

Just to fill in some numbers:
The Kamiokande experiment contains 3000tons of water and detected 11 neutrinos from SN1987a!
Assuming you are made of 0.06 tons of water, you would have stopped 0.00022 neutrinos.

But SN1987a was around 160,000lyr away. If you were at the distance of Earth's orbit from the star (15$\mu$ light years away) you would have received (160,000/0.000015)^2 = 10^20 as many neutrinos going through you.

I don't know what the biological effects of each neutrino interaction is (I doubt it's been the subject of many clinical trials) but having 2.5 x10^16 of them stop in your body is unlikely to be healthy.

Although it's worth pointing out that if you are standing 1 AU from a supernova this is probably the least of your worries.

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I find the 99% figure astounding. Could you give a reference? –  Niel de Beaudrap Dec 10 '12 at 15:13
I don't know who originally discovered it - but it's standard in any textbook –  Martin Beckett Dec 10 '12 at 15:15
Alright then -- being told that it's so well-known, gave me sufficient confidence to look for it on Wikipedia. "In 1966 Colgate and White calculated that neutrinos carry away most of the gravitational energy released by the collapse of massive stars, events now categorized as Type Ib and Ic and Type II supernovae.", and so on. –  Niel de Beaudrap Dec 10 '12 at 15:25
If you stay a respectable distance from any exploding stars then you are OK - This just made my day! :D –  Vilx- Dec 10 '12 at 15:35
Because the number going through decreases as the square of the distance. At some close distance there will be enough neutrinos/m^2 to have a significant interaction –  Martin Beckett Dec 10 '12 at 16:12
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