I started with:
sqrt(1-((1/(1+120 PeV / (neutrino mass * c^2)))^2))
but it simply said "data not available". So I changed: 120 PeV to 120e15 * 1.602176634e-19 kg m^2 s^-2
neutrino mass to 1.25e-37kg
speed of light to 299792458 m/s
and finally it gave a numeric result: 0.999999999999999999999999999999999999829277971
(that's 36 nines in a row). Pasting it in Google says the value is "1", which is… not far off.If you want details about the way this is calculated, I dug up the formula from an article I'd written about particle velocities in the LHC, back in 2008[2]. For comparison, their 7 TeV protons were going at 0.999999991 × c.
[1] https://www.wolframalpha.com/input?i=sqrt%281-%28%281%2F%281...
[2] https://log.kv.io/post/2008/09/12/lhc-how-fast-do-these-prot...
Time is in seconds, length in meters, temperature in kelvin, etc. A unit of energy like a joule is then defined using these base units, so 1 joule is 1⋅kg⋅m^2⋅s^-2.
https://arstechnica.com/science/2025/02/most-energetic-neutr...
And an interesting, somewhat related, video from PBS Space Time exploring how supernovas act as particle accelerators (but don't quite explain particles like this one or the 'Oh My God' particle):
They have 1/500,000 the mass of electrons. They interact only through the super short range weak force (and gravity). Nearly 5% of fission energy is expressed in neutrinos.
And, they may be their own antiparticles, meaning they can potentially annihilate each other.
Wild that these things can carry so much energy!
Oh, but those five...
So you're saying my iPhone built-in calculator app is going to have problems....?
Time to whip out dc on the terminal.
Your Android phone's built-in calculator app, however, will not. :^)
Close, but ackshually...
Bodybuilders just oil up and pose in beauty pageants.
1 horsepower is basically one 250-pound bench press in one second. (550 foot pounds of work; the aforementioned bench press assumes a 2.2-foot stroke length.)
Most bodybuilders and serious weight lifters can do that, but they can't keep it up for long.
(To be clear, that's sustained effort over time, not just momentary. Athletically trained humans can do about 1 HP of peak momentary effort, and around 0.3 HP if sustained over time.)
From nothing, to detectable, to lethal, to big boom?
My intuition would be "detectable" but I don't know enough to do the maths.
And by the way, I am using the mass-energy, not proper mass, because the question is crazy enough not to even consider what would be the mass of a neutrino.
The probability of interaction of neutrinos with matter increases with the energy. I've asked o1 to estimate the mean free path of a 120 PeV neutrino in water and it came up with 1000km. So let's say, conservatively, that 10^-7 of the total energy gets deposited in your body when the beam goes through. The mass equivalent of a ping pong ball is about 2.5x10^14 J, which gives us 2.5x10^7 J total, or about 6kg TNT equivalent. This is only an order-of-magnitude estimate, but it would definitely not be healthy.
So BIG boom.
Since the velocity is so close to the speed of light, you can think of this like the energy released by annihilating a ping pong ball made of antimatter.
Edit: Commenter asked what would happen if they "hit", so I'm assuming a hypothetical 100% collision. But yes to stop 1/e of a neutrino beam with normal matter, you'd need a light year of lead.
Unless you get thrown back by ping pong balls normally, I think you'd be fine.
But also neutrinos don't typically collide with things very easily, they're more likely to pass through you without you ever knowing.
Not even sure if that's worth doing, either create/emit or use encode data into them as they fly by to be received by someone else
Edit: that's cool people have tried though
https://en.wikipedia.org/wiki/2011_OPERA_faster-than-light_n...
which was something that would have happened in
https://en.wikipedia.org/wiki/Steins;Gate
Funny the idea that the neutrino might be a tachyon never seems to go away. The best fit of OPERA results is within error bars of the speed of light but towards the superluminal side. Superluminal neutrinos of the energy they were generating with the kind of mass we expect wouldn't be going measurably faster than the speed of light.
I visited the site of this experiment
https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lar...
where the best fit for the squared mass was just a tiny bit negative but within bounds of zero. There is the classic 1985 Chodos paper
https://www.academia.edu/27606971/The_neutrino_as_a_tachyon?...
and people still keep writing papers about it
https://www.mdpi.com/2073-8994/14/6/1172
somebody is going to have to measure a positive mass squared to really put a stake in its heart.
Its in section 4: Jam-Resistant Underwater Communication
The drawback is the impractical size and cost of a receiver.
Doesn't need to be submerged in a body of water as large as this. The Super-Kamiokande[0] detector for instance is located in a body of water inside a mountain.