Why does the neutrino have momentum?

[ChrisHarvey]

Why does the neutrino, which used to be assumed massless, have momentum? I know the answer to this has something to do with special relativity, but I'm not overly familiar with the theory.

Thanks,
Chris

 

[tavi_boada]

According to quantum mechanics photons, which are also massless, have momentum given by the de Broglie relation. This is routinely corroborated experimentally by, for example, the photoelectric effect in any undergraduate quantum mechanics lab course. Momentum is not only associated to massive particles. Even fields in classical mechanics can have momentum, like the magnetic field.

In fact, the first person to speak of the possible existence of neutrinos, Pauli, guessed its existence because momentum and energy were not conserved in a certain decay process. Therefore, the neutrino, if it exists, does have momentum or on the contrary conservation laws hold in all physical processes except this particular decay, which isn't likely.

 

[mathman]

Neutrinos, which come in 3 varieties, have mass, although very small. The masses are different for the different varieties.

 

[tavi_boada]

Neutrinos, which come in 3 varieties, have mass, although very small. The masses are different for the different varieties.

I didn't know that, but if they were massless they still have momentum,right?

 

[selfAdjoint]

Yes. When they were not thought to have mass, they still needed to have momentum and kinetic energy because they were originally thought up to explain two problems with beta decay, in which a neuron emits an electron and becomes a proton. First of all you and spin 1/2 (electron) subtracted from spin 1/2 (neutron) and that should have given you a unit spin, but the proton again has spin 1/2. And the other problem was that the energy of the emitted electron varied all over the lot.

Pauli saw you could solve both problems at once by positing a light neutral fermion that was part of the interaction but undetected because of its neutrality and small mass (it wasn't till later that they considered the neutrino to be massless). The energy in the electron+neutrino system would be constant, but depending on the angles the two particles came out at, the part of the energy carried by the electron could vary. And since the new particle was to be a fermion, with spin 1/2, there would be a balancing of the books: an odd number of spin 1/2 in (1 neutron), and an odd number out (proton + electron + neutrino).