# Neurinos are massless paricles

I've heard that it is thought that Neurinos are massless paricles, but I'm now hearing that they have kinetic energy.

Can something with no mass have kinetic energy?

Kinetic energy is a classical concept that has little use in a relativistic framework. Good quantities to use are rest energy (Lorentz invariant) and total energy (Lorentz covariant). The difference (total - rest) corresponds to the classical kinetic energy (the classical formula only picks up the lowest order term). However, since it is neither absolutely conserved nor an invariant quantity, it is not a terribly useful concept.
So the question can be restated as "Can something exist that has no rest energy?". The answer to that is yes. Such particles are required by SR to have no rest mass and to always move at the speed of light. Examples are photons and gluons, but apparently not neutrinos, since they are no longer considered massless due to observed oscillation effects.

massless particles can have momentum, so having kinetic energy is not far from it.

nrqed
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zefram_c said:
Kinetic energy is a classical concept that has little use in a relativistic framework. Good quantities to use are rest energy (Lorentz invariant) and total energy (Lorentz covariant). ....
Hi there.

Could you tell me what you mean by a quantity being "covariant"?

I thought that "covariant" made only sense when referring to an *equation*, not a quantity. An equation is covariant when the two sides transform the same way under Lorentz transformations (in SR) or general coordinate transformations (in GR). On the other hand, a quantity may be invariant or not. But I don't know what it would mean for a quantity to be "covariant". A quantity may transform as a vector, a spinor, a tensor of a certain rank, etc. In that case it is not invariant, but I have never seen (or I did not notice) the adjective "covariant" used in that context.

Pat

nrqed said:
Could you tell me what you mean by a quantity being "covariant"?

I thought that "covariant" made only sense when referring to an *equation*, not a quantity. An equation is covariant when the two sides transform the same way under Lorentz transformations (in SR) or general coordinate transformations (in GR).
Ooops, sorry. My terminology was very sloppy on that one. I meant that the four-momentum transforms as a Lorentz vector between frames of reference. This would not be true for the kinetic energy, which would transform in a more complicated manner.

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colinr said:
I've heard that it is thought that Neurinos are massless paricles, but I'm now hearing that they have kinetic energy.

Can something with no mass have kinetic energy?
Neutrinos are definitly not massless, they have a rest mass. Particles with no rest mass, for example photons, DO have energy, which can be calculated by using the equation...

$$E = h \nu$$ Where E is the energy, h is plank's canstant and $$\nu$$ is frequency of the light.