Why can't neutrinos be brought to rest?

[anorlunda]

What a great provocative question Scott.

If neutrinos were stationary so that they could be located within a nucleus or within a hadron, for an indefinite period of time, then I guessed that interactions might be much more likely. I know that interactions between free neutrons and nuclei are hugely dependent on relative velocities, why should neutrinos be different?

Since we have never seen slow neutrinos, I presume that experimental physics has no data on the interaction properties of slow neutrinos. That is why I intended my original post to be directed at theoretical physics rather than experimental physics. Photons must move at velocity c. Fermions must obey the Pauli exclusion principle. Those properties can be derived from the wave functions. I am curious to learn if there are analogous theoretical principles for neutrinos that dictate their peculiar properties.

 

[mfb]

Neutrinos are fermions. They have well-predicted (by the standard model) interactions with matter, and if they are slow their interaction cross-section is low.

 

[friend]

Neutrinos are fermions. They have well-predicted (by the standard model) interactions with matter, and if they are slow their interaction cross-section is low.

If we can't detect slow vs. fast neutrinos, then how can we tell how much of the neutrino's energy is rest mass and how much is due to velocity?

 

[mfb]

There are upper limits on the mass. Sure, the cross-section at low energies will depend on the (still unknown) mass, but as far as I know it will be small for all possible masses.

 

[reculet]

Chase it!

If neutrinos were massless, they would have to travel at c. But now we know they have mass, so they must travel at speeds less than c.

But (all?) other massive particles can be brought to rest. Why not neutrinos? Is there a theoretical reason that forbids it?

Climb into your vehicle of choice and accelerate in pursuit of the (massive) neutrino - when you catch up with it, slow down and move alongside it. Now it is at rest w.r.t. you, and you didn't even have to touch it :) [although General Relativity tells us that you could interpret what happened as the appearance of a gravitational field in your frame of reference, which brought the neutrino to rest beside you: you avoided falling by using your vehicle's power-thrusters].

Easier said than done, of course.

 

[Chronos]

We would need an experimental setup capable of isolating a single neutrino - which would be an impressive accomplishment. It's relatively easy to isolate an electron.

 

[anorlunda]

OK, I think I understand now thanks to your help. Let's see if I got it right.

The original question could have been phrased as a paradox. If neutrinos are massive, why don't we see a spectrum of non-relativistic velocities for them as we do for other massive particles? Wikipedia says that the lower limit for neutrino velocities is 0.999976 c.

The apparent answer requires two logical steps.

First, when neutrinos are emitted:

(mfb put numbers on it, and that helped me to understand.)

... A .23eV-neutrino with a kinetic energy of .10 meV moves with ~9000km/s ...

So for the sake of argument let's say that when emitted, neutrinos have a wide distribution of energy in excess of rest mass. But because the rest mass is so small, only a tiny kinetic energy is needed for relativistic speeds. Therefore, the fraction of all energies corresponding to non-relativistic speeds is tiny.

Second, after emission: Because neutrinos interact so little with other particles, they do not become thermalized. They tend to conserve whatever energy they were emitted with.

Put those two things together and we can see that it is possible to have neutrinos at any speed 0<v<c. However, non-relativistic speeds are very improbable.

The seeming paradox comes from confusing what's possible with what's probable. Secondary confusion comes from using the word possible in the ideal sense, contrasted with possible pragmatically in the laboratory.

 

[mfb]

Wikipedia says that the lower limit for neutrino velocities is 0.999976 c.

For a specific energy (here: 3 GeV). Hmm, that part of the article is outdated.

So for the sake of argument let's say that when emitted, neutrinos have a wide distribution of energy in excess of rest mass. But because the rest mass is so small, only a tiny kinetic energy is needed for relativistic speeds. Therefore, the fraction of all energies corresponding to non-relativistic speeds is tiny.

Right.

Second, after emission: Because neutrinos interact so little with other particles, they do not become thermalized. They tend to conserve whatever energy they were emitted with.

Right.

Put those two things together and we can see that it is possible to have neutrinos at any speed 0<v<c. However, non-relativistic speeds are very improbable.

Right.

 

[snorkack]

What is the shape of the tail of the beta decay?
If 100 % of the antineutrinos emitted by tritons have energy under 18 keV (because that is the total energy of the beta decay), what percentage have energy under 1800 eV? 180 eV? 18 eV et cetera?

 

[mfb]

There is a formula for the electron energy spectrum. The neutrino energy is the difference between the total energy and the electron energy.

Close to the endpoint (and neglecting the neutrino mass), the probability is quadratic with the difference to that endpoint. The fraction of neutrinos below 1800 eV is roughly 1% (guessed, should be right up to a factor of ~5), the fraction below 180 eV is roughly 0.001% and so on - every factor of 10 reduces the fraction of neutrinos by a factor of 1000.