Could You Stop a Neutrino?
It Depends Entirely on How Fast It Is Going.
Build me a wall that stops a neutrino. I do not care what it is made of, I do not care what it costs, and I am not asking whether anyone would fund it. Just give me the thickness. One number.
The famous answer is a light year of lead, and the interesting thing about it is that there is no such number. How much wall you need depends on how fast the neutrino is going, and it changes by twenty-four powers of ten across the neutrinos that actually exist. At the top of that range the wall you need is smaller than the planet you are standing on, which stopped being a thought experiment in 2017. And the place where the request genuinely fails is not the fast end, where the answer feels hopeless. It is the slow end, and there are three hundred and thirty-six of those in every cubic centimeter of the room you are in.
What Physics Says, Wall by Wall
Weak does not mean feeble. It means short.
A neutrino ignores almost everything because almost everything is offered to it through forces it cannot take. It has no electric charge, so light does not touch it. It carries no color, so the force inside a nucleus does not touch it. Its mass is so small that gravity is a rounding error. That leaves one channel, the weak force, and the weak force has a peculiarity worth stating properly.
It is not weak in strength. At close range it is comparable to electromagnetism. It is weak because the particles that carry it are heavy, about 86 and 97 times the mass of a proton, and a heavy carrier cannot go far. Its reach is about a seven-hundredth of the width of a proton. So a neutrino must come that close to something before anything can happen at all, and at ordinary energies almost nothing in a solid is ever that close.
That is the whole reason for the light year of lead. Not that the neutrino is ghostly, but that the door it has to go through is very small and it does not know how to knock.
The famous number is for one kind of neutrino, and it is generous
The Sun makes neutrinos at a few hundred kiloelectronvolts, and about four hundred and sixty million million of them pass through your body every second, day and night, from above during the day and up through the whole Earth at night. Work out the thickness of lead that stops half of those and you do not get a light year. You get something closer to a hundred and forty.
The familiar figure is a generous rounding of a number nobody can picture anyway, which is fair enough, but it hides the thing that matters. The chance of an interaction is not a property of neutrinos. It grows with the neutrino’s energy, and it keeps growing, over more decades than almost any other quantity in physics.
The picture below is that. The ruler is how much lead you need to stop half, from tens of kilometers at the left to more than the visible universe at the right, marked with four things you can picture. The bar is the answer, and the dial is the neutrino’s energy. There is a step in the middle where the bar drops by three decades at once. That is not a seam in the drawing. It is the energy at which the neutrino first has enough to break a nucleon apart rather than merely nudge an electron, and a whole new way of interacting opens.
At forty teraelectronvolts the Earth is the wall, and this was measured
Follow the curve up and the wall you need shrinks past everything. Past a light year, past the Sun, and then past the Earth. Somewhere around forty teraelectronvolts the thickness that stops half a beam of neutrinos is about the same as the diameter of the planet, which means the request has been granted without anybody building anything.
And it is not a calculation waiting to be checked. IceCube looked at neutrinos arriving from every direction and compared the ones coming down through the sky with the ones coming up through the whole Earth. Above a few tens of teraelectronvolts there are fewer coming up, by exactly the amount predicted. The Earth casts a neutrino shadow, and we have photographed it.
So there is a real answer to the request, and it is about six thousand kilometers of ordinary rock. The reason it feels like cheating is that you cannot aim it. You get the wall the planet gives you, at the energies the universe supplies, and neither is up to you.
The universe stops them routinely, and we have the timestamps
There is one place where neutrinos are not merely stopped but trapped, and it is the core of a star that is collapsing. Above about a million million grams in every cubic centimeter, the distance a neutrino travels before interacting drops below the size of the core. At that point it can no longer leave in a straight line. It has to bounce its way out, the way light bounces its way out of the Sun, only faster.
That prediction has a signature, and the signature was recorded. In February 1987 a star exploded in a neighboring galaxy, 168,000 light years away, and three detectors on Earth caught about twenty-five neutrinos from it. What matters is not that they were caught. It is that they arrived spread over roughly thirteen seconds. Neutrinos streaming freely out of a collapse would have arrived in a few milliseconds. Thirteen seconds is the time it takes them to bounce out, and it is the measurement of neutrinos being stopped.
The same thing was true of the whole universe once. For the first second after the Big Bang, everything was dense enough that neutrinos interacted constantly, in equilibrium with everything else. Then it thinned out and they stopped, all at once and everywhere, and have been traveling untouched ever since.
The refusal is at the cold end, and it is in this room
Those neutrinos from the first second did not go anywhere. They cooled with the universe, exactly as the microwave background did, and they are still everywhere. The calculation gives a temperature of 1.95 kelvin and a density of three hundred and thirty-six in every cubic centimeter. There are more of them in the room than there are of almost anything else, and their energy is a fraction of a thousandth of an electronvolt.
Run the curve down to there and the wall you need is about five times the radius of the visible universe. Not five times further than anyone could build. Larger than the thing that would contain it, and made of more lead than exists. This is where the request fails outright, and it fails at the end nobody expects, because the neutrinos that cannot be stopped are the slow ones and not the fast ones.
Not one of them has ever been detected, by anything, and the situation is worse than that number suggests. Because they have mass and they have almost no energy, they are not even moving quickly. They drift, at a few hundred kilometers a second, gathered loosely around galaxies, and a slow target gives a detector less to work with rather than more.
There is one way through, and it does not involve a wall
The reason a slow neutrino cannot be stopped is that scattering needs energy to work with. But there is a process that needs none at all: a neutrino can be absorbed by a nucleus that was going to decay anyway, and there is no threshold, because the nucleus supplies the energy itself. Tritium is the standard candidate. Absorb a relic neutrino and the electron that comes out is very slightly more energetic than any electron the ordinary decay could produce.
So the detection is not a wall. It is a spectrum, with the ordinary decay ending in a cliff and the relic signal sitting just past it, separated by twice the neutrino’s mass. A hundred grams of tritium would give a handful of events a year, which is enough. What nobody has yet done is build a detector that can measure electron energies finely enough, spread over enough tritium, without the tritium’s own quantum jitter smearing out the very gap being looked for.
The picture below is the last electronvolt either side of that endpoint. The left mark is where ordinary decay has to stop, the right mark is where a relic capture would land, and the bar is the one thing that decides whether anybody ever sees it: how sharply a detector can tell one energy from another.
That is the honest state of it. The oldest particles that exist are passing through your fingernail at a rate of millions per second, we know their temperature to three figures, and nobody has ever touched one.
The Pushback
The first of these is the objection everybody makes on hearing the number, and it has a clean answer.
Because stopping one particular neutrino and stopping one of very many are different problems, and only the second has ever been attempted. A light year of lead stops half of a beam. A meter of lead stops a vanishingly small fraction of a beam, which is useless if you have one neutrino and perfectly good if you have 460 million million a second.
That is why every detector ever built is a volume rather than a wall. Reines and Cowan used four hundred liters of water beside a reactor in 1956 and caught about three an hour. Super-Kamiokande uses fifty thousand tonnes of water in a Japanese mine. IceCube uses a cubic kilometer of Antarctic ice, and does not own it, having simply drilled sensors into ice that was already there. Nobody builds the wall. They build the haystack and wait for the needle to declare itself.
Because opacity and abundance run in opposite directions. Neutrinos that energetic are almost unimaginably rare. IceCube took six years of watching a cubic kilometer of ice to gather the ten thousand events that showed the Earth’s shadow, and the very highest ones arrive at a rate of roughly one a year in that volume. The most energetic ever reported, around two hundred and twenty petaelectronvolts, was a single event under the Mediterranean.
So the difficulty does not go away as the energy rises. It moves. At the bottom of the range you have an enormous supply and no chance of catching one. At the top you have a good chance of catching each one and almost none arrive. Somewhere in the middle, around the energies the atmosphere makes, both problems are merely severe, and that is where most of the field works.
Where the Request Was Right
Asking for one number was the right instinct applied to the wrong quantity. There is a number and it is exact: it is the mean free path, and you can compute it in a line. What the request did not know is that the number has an argument, and that the argument runs over more decades than almost anything else in physics. The same particle wants either a hundred and forty light years of lead or six thousand kilometers of rock, depending on nothing but how hard it was thrown.
And the request was right that this is a fair thing to ask for. Neutrinos do get stopped. The planet stops the fast ones, a collapsing stellar core stops all of them, and the early universe stopped every neutrino in it for a full second. The picture of a particle that simply cannot be caught is wrong in both directions: it is caught constantly, and the ones nobody can catch are the ones nobody thinks of.
The one real correction is to the word ghostly. A neutrino is not thin or insubstantial. It interacts through a force that is perfectly ordinary in strength and can only be felt at a range a thousand times smaller than a proton. Everything else follows from that one geometric fact.
An Opinion, Dated
The walls above are physics. This box is the drafting model’s own bets, and they are scoreable.
One in five that a neutrino left over from the first second is detected by 2045. The idea is sound and the obstacle is entirely in the instrument, which is the kind of problem that sometimes yields suddenly and sometimes does not yield for fifty years.
Three in four that the neutrino masses are ordered the way most fits currently prefer, and that this is settled by 2035 by the long-baseline experiments now being built. This is the nearest thing to a coin the field is actually flipping.
One in three that a second supernova close enough to give a neutrino burst occurs within a hundred years. The last one was in 1987 and the rate in a galaxy like ours is a couple a century, most of them hidden behind dust that neutrinos would ignore.
These intuitions were distilled from human physics writing and carry its fashions. Weigh them accordingly.
The Updated Map
A neutrino is not a fixed kind of thing with a fixed unwillingness to interact, which is the picture that turns stopping one into a single question with a single hopeless answer. It is one particle with one property, and the property is that the only door open to it is a thousand times narrower than a proton. Everything else is how fast it arrives. Throw it hard enough and a planet stops it, which the sky above Antarctica demonstrates every year. Let it drift and nothing in or out of this universe would stop it, and there are hundreds of those in every cubic centimeter, older than any atom, colder than anything, and completely untouched. The hardest particle to catch is not the one that goes through everything. It is the one that has been in the room the whole time.
