How can individual neutrinos have different amounts of energy?

Question

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?

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, Commented Nov 22, 2018 at 16:34
High energy neutrinos simply have more kinetic energy than low energy neutrinos. — PM 2Ring, Commented Nov 22, 2018 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 --- ex-moderator kitten, Commented Nov 22, 2018 at 16:47
Neutrinos can have any velocity less than the speed of light, it all depends on how they are produced — Triatticus, Commented Nov 22, 2018 at 17:06

G. Smith · Accepted Answer · 2018-11-22 18:51:06Z

2

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

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

answered Nov 22, 2018 at 18:51

G. Smith

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$\begingroup$ 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). $\endgroup$
– anna v
Commented Nov 23, 2018 at 5:38

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