# Some neutrino anomalies that need explanation

It is inferred that the neutrino must have mass, but beyond saying this mass is incredibly minute nobody has ever measured it. All other particles which have mass also have charge,can be slowed down,& can't travel at the speed of light. Why should the neutrino be the lone exception to these rules,& wouldn't it be better to measure its speed before claiming it has mass? If it can keep pace with a photon,then it can't have mass. The energy of a photon is electromagnetic, but what kind of energy is embodied in a neutrino?

• No need for caps in your title. Plus please make your title more specific – innisfree May 15 at 11:19

It is inferred that the neutrino must have mass,but beyond saying this mass is incredibly minute nobody has ever measured it.

While it's true that we haven't measured the absolute value of any neutrino's mass yet, we have been able to measure several related things:

• We have measured the differences in masses between the three neutrino mass eigenstates*, because these determine the outcome of neutrino flavor oscillation.
• Our measurements allow us to constrain how big the sum of the masses of all three neutrino mass eigenstates.

*There are three neutrino "flavors": electron, mu, and tau neutrinos. The reason neutrino flavor oscillation happens is because the states of definite neutrino flavor (the "flavor eigenstates") are not the same as the states of definite neutrino mass (the "mass eigenstates"). We can measure the flavor of a neutrino, and typically we use the relative abundance of the given flavors detected compared to the flavors we started with to tell us something about the mass eigenstates.

All other particles which have mass also have charge,

This isn't true. The $$Z$$ boson and Higgs boson are fundamental particles that have mass, but no charge. There are also plenty of composite particles that have mass but no charge, like the neutron and the neutral pion.

can be slowed down,& can't travel at the speed of light.

You are correct, every object with mass can't travel at the speed of light, and can be viewed from a frame where it is at rest. Getting an object with mass to be at rest in a particular frame (i.e. "slowing it down") is possible in principle, as long as you can interact with that object, but it may not be possible in practice with today's experimental equipment. This is true for neutrinos; they interact so weakly with all of our equipment that we're lucky if we even see them, let alone interact with them multiple times as would be necessary to slow them down.

Why should the neutrino be the lone exception to these rules,

It's not, because one of them isn't an actual rule that describes nature and the other is limited more by practical considerations than theoretical ones. See the above two paragraphs.

& wouldn't it be better to measure its speed before claiming it has mass?

Let's consider a typical solar neutrino. The energy spectrum of solar neutrinos from various reactions is:

As you can see, solar neutrinos typically have energies on the order of 1 MeV. Now, let's say that the neutrino has a mass of 0.3 eV/$$c^2$$ (this is actually the upper bound on the sum of all three neutrino mass eigenstates, so this is being very generous in our estimates here). We can calculate the speed of this neutrino by using $$E=\gamma mc^2$$: from this we get that the Lorentz factor $$\gamma$$ is roughly 3.3 million, which would place the neutrino's speed as

$$v\approx0.99999999999991c$$

That is indistinguishable from $$c$$ with present (and probably near future) speed-measuring equipment; as far as I know, we don't have any setup capable of measuring speed to 1 part in $$10^{13}$$ just yet.

If it can keep pace with a photon,then it can't have mass.

True, but irrelevant, because neutrinos can't keep pace with photons. In the neutrino's rest frame, you would still see photons traveling at $$c$$, because that's how special relativity works.

The energy of a photon is electromagnetic,but what kind of energy is embodied in a neutrino?

A tiny part of the typical neutrino's energy is its mass. The rest of its total energy is the kinetic energy of the neutrino.

• I was of course aware that some neutral particles,like the neutrino, are nominally chargeless,but I thought this was because they have two opposite charges which cancel each other out. – Michael Walsby May 15 at 10:40
• @MichaelWalsby It is, but as the answer mentions we also know of fundamental particles with mass and no charge such as the Z boson and the Higgs boson. – Codename 47 May 15 at 10:44
• ‘True, but irrelevant, because neutrinos can't keep pace with photons. In the neutrino's rest frame’ ... here you assume neutrinos are massive and don’t travel at $c$, but the OP is proposing a test for whether they are indeeed massive and travel at $<c$. So it rather begs the question. Agree with the rest. – innisfree May 15 at 12:17
• @innisfree Well, we know they are massive, because we've seen flavor oscillation. The OP's test would be able to measure the value of the mass, and/or confirm that they are massive. – probably_someone May 15 at 14:37
• @Codename47 Neutrinos are just as fundamental as Z bosons and Higgs bosons. They do not have two opposite charges which cancel. They are simply neutral. – G. Smith May 15 at 16:32

The problem with measuring the neutrino velocity is that the mass is so small. This means that for the sort of energies we expect neutrinos to have the speed is going to be very close to $$c$$. The velocity of neutrinos from a reactor was measured in the Opera experiment, and they found the velocity was so close to $$c$$ that they couldn't measure a difference. But then this is exactly what would be expected for neutrino masses in the 0.1 - 1 eV range.

There have been suggestions for measuring the speed of neutrinos from supernovae, but as far as I know this has not been done.

We know neutrinos must have a mass, because the neutrino oscillation data tells us the three types of neutrinos have different masses. So we know the neutrinos must travel slower than light. The problem is that the expected difference of their speed from $$c$$ is far too small to be easily measurable.