**Question:** A question about the mass of neutrinos: are neutrinos actually mass-less or is that just a simplification? I ask this because neutrinos are particles from the decay of hadrons e.g. in positron-decay (and antineutrinos in beta-decay); which were predicted because a particle was need to carry away extra momentum from the decay, which the beta particle (or positron) was not carrying. Momentum = mass x velocity, so I might be being really naive here or momentum of the neutrino/velocity = mass of neutrino.
However, in reality is this a case of E=mc squared where the mass in "momentum = mass x velocity" is actually the 'mass-energy'?
p.s. I hope this question makes sense :)

Neutrinos are massive, we’ve just about estabilished this now. It’s not been easy to detect them as they intereact with other matter so infrequently, but constraints are now being placed on the size of these particles. They were originally proposed to be massless, and to a first order approximation in particle physics, they are for simplified equation balancing.

1Hi there, great question thanks!

If you think about it, photons can have momentum too – so you start to see that the equation we get taught (momentum = mass x velocity) must have some problems! Momentum, mass and energy are all related by Einsteins famous equation, but in truth, the E=mc^2 hides a lot of the truth if you just consider ‘m’ to be the rest mass of the particle.

The full energy is E= sqrt(p^2c^2 + m^2c^4)

Sorry it’s hard to write maths out like that, but the ‘^’ means to the power of and p is the momentum.

So the total energy of a particle also includes it’s momentum, whereas the E=mc^2 just talks about its “rest” mass, so is a special case where the particles aren’t moving.

You can see from that equation that if m=0, the particle can still have energy because it has momentum, like in the case of the photon and we *thought* in the case of the neutrino too.

But it turns out the neutrino also does have a tiny rest mass – though it’s not from these equations that we’ve figured that out. In fact, we figured it out by observing something really weird. If you start with one type of neutrino (say an electron neutrino) then it can change into a muon neutrino or tau neutrino, called ‘neutrino oscillations’. We know that neutrinos wouldn’t do this if they didn’t have any mass, and since we’ve observed the oscillations, we can start to guess at the tiny amount of mass they do have.

This is one of the good reasons for thinking that the ‘standard model of particle physics’ is not the whole story – because in the standard model neutrinos don’t have mass! It’s not hard to add it in, but it would be nice to really know what’s going on and what physics there is outside the standard model. Who knows, we might have to completely change our way of thinking??

1We used to think they were massless but now we know they have very little mass!

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