Neutrinos — how many are there?

How many neutrinos are there?

“Don’t be lonely, nerds! You’re surrounded by billions of neutrinos! Who will never interact with you either”

So just how many neutrinos are there in the universe?  A lot – scientific estimates say that there are about 300 per cubic centimeter in the universe.  Doesn’t sound like much?  Compare that to the density of what makes up normal matter as we know it, protons electrons and neutrons (which together are called “baryons”) – about 10-7 per cubic centimeter.  So averaged across all of space, you’ll be lucky to find a single proton in any given cubic meter of space, but you’ll find millions of neutrinos.  So what looks like empty space, once you get out past the planets and stars and deep-space outposts, is actually teeming with these little particles that we can barely detect.

Now, the size of the observable universe is a sphere about 92 billion light-years across.  So the total number of neutrinos in the observable universe is about 1.2 x 1089 !  That’s quite a lot – about a billion times the total number of baryons in the observable universe.  But, it’s interesting to point out, this is a lot less than the famous large number Googol, which is 10100.  So one Googol is more than a billion times larger than the number of neutrinos in our entire universe!

We don’t know the mass of a neutrino exactly, but a decent rough estimate of it is 0.3 eV (or 5.35 x 10-37 kg).  Scientists have indirect proof that neutrinos do have some mass, but as far as we can tell, they’re the lightest elementary particle in the universe.  So there are lots of neutrinos in the universe, but they each don’t weigh very much.  So that means in a cube of volume one Astronomical Unit on a side (where one AU is the distance from the sun to the earth, or about 93 million miles), there’s only about 600 tons worth of neutrinos!  So the mass of neutrinos in empty space millions of miles across contains less mass than the typical apartment building.

We mentioned earlier that neutrinos are passing straight through the earth, and therefore our own bodies, all the time.  Next up, we’ll figure out just how many…

Note:  huge thanks to StueyPhooey on twitter for catching a typo in this post, which originally had the radius of the universe as 46 million, not billion, light years.  What the hell was I drinking when I wrote that?  Answer:  grape juice.  Just grape juice.

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