# How can individual neutrinos have different amounts of energy?

Photons have no mass, travel at the speed of light, and their energy is related to their frequency.

Neutrinos have a very small mass, travel at almost the speed of light; what is their energy related to?

Do high energy neutrinos have a slightly higher mass or a slightly higher speed?

• The mass of an elementary particle is fixed. – probably_someone Nov 22 '18 at 16:31
• Are you talking about relativistic mass when you ask "Do high energy neutrinos have a slightly higher mass"? That's just confusing; it's usually easier to deal only with rest masses. – user191954 Nov 22 '18 at 16:34
• High energy neutrinos simply have more kinetic energy than low energy neutrinos. – PM 2Ring Nov 22 '18 at 16:44
• The smart-alec (but not necessarily helpful) answer is the neutrino energy depends on the frequency exactly as much as the photon energy does. At the underlying quantum level they are described by a theory with wave-like character as much as particle-like character. Trying to make a distinction of type here is a losing battle. – dmckee Nov 22 '18 at 16:47
• Neutrinos can have any velocity less than the speed of light, it all depends on how they are produced – Triatticus Nov 22 '18 at 17:06

## 1 Answer

For any particle with invariant mass $$m$$, its energy depends on how fast it is moving:

$$E=\frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}.$$

Since neutrinos have mass, this formula applies to them.

An alternate formula in terms of momentum rather than speed is

$$E=\sqrt{(m c^2)^2+(p c)^2}.$$

• one should add that it is the second form widely used and useful for particle physics (useful because velocity is not a conserved quantity in Lorenz transformtions, energy and momentum are). – anna v Nov 23 '18 at 5:38