# Why can't neutrinos be brought to rest?

1. ### anorlunda

678
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?

2. ### ZapperZ

30,167
Staff Emeritus
First, figure out how we bring to rest "other massive particles". Take an electron, for instance. Even assuming that we can bring it to rest (which we really can't if you think about it, but at the very least, we can confine it to a very small region of space), we capture and confine it using electromagnetic interaction. In other words, we use forces that it can interact with!

A neutrino doesn't interact with a lot of things. It has a very small mass, so its gravitational interaction is unbelievably weak. So forget about having it confined even around a very huge star. And what is left is its coupling via the weak interaction, which from its own name, is WEAK!

What you have is something that just don't bump into something else that easily and thus, can't be confined. It just won't be dragged and slowed down by everything surrounding it.

Zz.

3. ### snorkack

564
For example, take beta decay. Most of the time the energy is divided between electron and antineutrino, both getting a large share. But the shares are usually different, and electrons get a continuous spectra. Sometimes, rarely but with nonzero probability, the electrons get no energy whatsoever or only a small energy, getting stuck in a ground or excited state of the resulting atom or molecule, and the antineutrino gets all energy except for recoil of the atom. It must therefore also happen, rarely, that an electron gets almost entire energy of beta decay and the antineutrino is slow.

How would a slow neutrino behave? In particular, can a neutrino be unable to oscillate because its total energy suffices for only the lightest rest mass state but not for any others?

### Staff: Mentor

They are produced as flavor eigenstates, and those are always a superposition of the three mass eigenstates -> oscillation happens
Slow neutrinos oscillate more quickly, but it is nearly impossible to detect them as they don't have enough energy to be seen in regular neutrino detectors.

KATRIN is looking for electrons with nearly the maximal energy, but they cannot detect the corresponding "slow" neutrino.
(where "slow" is still close to c most of the time!)

5. ### snorkack

564
Does a neutrino in a flavour eigenstate possess a defined total energy?

6. ### anorlunda

678
During a type II supernova neutrinos are confined for a short time because the density of matter in the shock wave is so high that it is opaque to neutrinos. It is not clear whether those confined neutrinos are slowed or absorbed and re-emitted.

Anyhow, the supernova example shows that there is a way to make neutrinos interact strongly with matter. Can they not be slowed in that environment, at least theoretically?

### Staff: Mentor

Energy or mass?
Energy has to be well-defined, as it is a real particle.

8. ### snorkack

564
Is a real neutrino with a defined and small energy allowed to oscillate from a mass eigenstate where its rest mass is smaller than its total energy and where it possesses positive kinetic energy and real momentum into a mass eigenstate where its rest mass is bigger than the aforesaid energy and where it possesses negative kinetic energy and imaginary momentum?

### Staff: Mentor

Neutrinos do not oscillate between mass eigenstates - those are eigenstates of the Hamiltonian, the three mass eigenstates evolve independently. They oscillate between flavor eigenstates.

10. ### snorkack

564
So, if an antineutrino is emitted in a beta decay event with 1) a defined flavour at emission (electron antineutrino) and 2) a well defined energy (it is a real particle, and the beta unstable nucleus and the decay resulting nucleus were both long lived states with well defined energy) which is SMALLER than the rest energy of any mass eigenstate except the lowest - is it then also a superposition of the mass eigenstates with negative kinetic energy?

### Staff: Mentor

I don't think this is possible, at least not as pure eigenstate of the weak interaction.
Hmm... different energies for different eigenstates would not have this issue, but I don't think that is right.

12. ### kurros

387
But as you say later, flavour eigenstates are not eigenstates of the Hamiltonian, therefore they do not have energy eigenvalues right?

13. ### kurros

387
Hmm this seems relevant

He seems to argue that the uncertainty principle saves us in this situation, i.e. neutrinos are never actually produced in plane wave states, so they have some energy spread, so they oscillate. I'm not sure it answers the "in principle" question though. If we go to the extreme, say one of the neutrinos was really heavy, we'd expect the light ones don't oscillate into it. But this is probably related to the coherence length of the oscillation, which would be super short in that case. So maybe the coherence of the neutrino mixture goes away in this ultra-low energy limit.

edit: I am becoming more convinced this is the case. If you can measure the energy of the emitted (ultra-low-energy) neutrino to some fantastic accuracy (by measuring the nuclear recoil to the nano-eV or something) then you must collapse the superposition, since you just know which mass eigenstate you must have, so no oscillations.

Last edited: Aug 22, 2013
14. ### snorkack

564
At low electron chemical potential, the lowest energy beta decay processes seems to be electron capture of holmium 163, energy "3" keV, and beta decay of rhenium 187, quoted as "2,6" keV. Next seems to be tritium decay, 18,59 keV.

What if stable isotopes are SLOWLY, at a low temperature, subjected to a high chemical potential of electrons? Say, the pressure is slowly increased as matter is deposited on surface of a star, and the temperature stays low because the heat is readily radiated away from the surface where it is generated?

At which electron chemical potential would helium 3 (common in nature because copiously produced by proton fusion) spontaneously capture electrons to turn into tritium? In particular, how low would the energy of the neutrinos be at their origin (deep in the star)?

15. ### anorlunda

678
Sorry to be dense, but I'm not getting it.

A paper called Neutrino Oscillations at http://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px435/lec_oscillations.pdf says:

the eigenstates of the [neutrino] Hamiltonian are |ν1 > and |ν2 > with eigenvalues
m1 and m2 for neutrinos at rest. A neutrino of type j with momentum p is an energy eigenstate
with eigenvalues $E_{j}=\sqrt{m_{j}^{2}+p^{2}}$. ​

The quote mentions neutrinos at rest, and nothing I see in the math forbids p=0; yet the consensus seems to be that neutrinos can not be brought to rest.

### Staff: Mentor

Where?
They are just rarely discussed as all neutrinos we can measure are ultrarelativistic.

### Staff: Mentor

I think it's more a matter of it being so difficult as to border on impossible, rather than being completely impossible.

18. ### ZapperZ

30,167
Staff Emeritus
Actually, it is impossible.

We have not been able to bring an electron to a complete rest, despite the fact that it is larger than a neutrino and that it interacts more strongly than a neutrino. The HUP ensures of that. So what hope is there for a difficult-to-capture neutrino?

Zz.

### Staff: Mentor

I think everyone here knows what we mean when we say "bring to rest", and I see no reason to talk about the HUP. It just confuses the subject.

20. ### ZapperZ

30,167
Staff Emeritus
I'm not sure the OP does based on the insistence that there's nothing "in the math" that prevents p=0.

Zz.