# Do we have any evidence of slower-than-light neutrinos? [duplicate]

I'm writing a piece on the electron neutrino. There's plenty of excellent material out there, but I'm struggling to find anything definitive about their speed. There is for example evidence from SN1987A:

Approximately two to three hours before the visible light from SN 1987A reached Earth, a burst of neutrinos was observed at three separate neutrino observatories. This is likely due to neutrino emission, which occurs simultaneously with core collapse, but preceding the emission of visible light.

Some reports mention an earlier burst which preceded the visible light by 7.7 hours. There are no reports that I know about described any neutrino lag. There's also the infamous OPERA faster than light neutrinos incident of 2011:

In 2011, the OPERA experiment mistakenly observed neutrinos appearing to travel faster than light. Even before the mistake was discovered, the result was considered anomalous because speeds higher than that of light in a vacuum are generally thought to violate special relativity, a cornerstone of the modern understanding of physics for over a century.

I didn't have much of an issue with this myself, and would point out that they didn't measure neutrinos to be going slower than light. And yet one can find assertions that cosmic neutrinos slow down. But is there any evidence of this? Do we have any evidence of slower-than-light neutrinos?

Edit: my question is different to speed of neutrinos where the accepted answer is 6 years old, and says your question is equivalent to asking what the absolute mass of the neutrinos is. I'm definitely not asking that. I'm asking if we've ever seen a neutrino going slower than light. If the answer is no, because neutrinos can never go slower than light, this means that a neutrino is more like a photon than an electron. And that despite the claims associated with neutrino oscillation, that it doesn't have any mass at all.

I think there's not any direct evidence for, or against, the existence of slower-than-light neutrinos. There's just not any data with the requisite precision. Here's why.

The upper limit on the mass of the heaviest neutrino species is about $\rm2\,eV$. Laboratory neutrinos are generated by beta decay, either of radioisotopes at rest or of beams of unstable particles in flight. The average energies involved in these decays are typically millions of eV, and for beams the relativistic boost adds the beam energy to the neutrino energy. So neutrinos produced for laboratory experiments have typical relativistic factors $\gamma \geq 10^6$. While the phase space for these decays certainly includes low-energy neutrinos, the probability of selecting $\gamma \lesssim 10$, for which you could measure a difference between neutrino speed at $c$ and some slower speed, is vanishingly small.

Then you have the problem of detecting such a low-energy neutrino. The processes that we use to observe neutrinos are also weak nuclear interaction processes with typical energies of millions of eV. They're typically threshold interactions, which turn off completely below some critical neutrino energy. That's why, for instance, our observations of solar neutrinos explore some side-branch of the solar fusion process (perhaps boron decay? I have forgotten) rather than $\rm pp\to d$, where most of the power comes from. The fusion processes that produce most of the Sun's power make neutrinos whose energy is too low to be visible in our detectors. For a neutrino with kinetic energy of a few eV, there's just no hope at all.

The KATRIN experiment will be able to set an improved limit on the neutrino rest mass by looking at the electron energy spectrum in the especially low-energy decay of tritium to helium-3. But the low-energy neutrinos will go unobserved — KATRIN is an electron spectrometer.

• You are correct that there is no direct evidence. Neutrino oscillations need massive neutrinos, but it is an indirect measurement. The existence of the neutrino itself was proposed using momentum and energy conservation. I worked for years on bubble chamber experiments with antineutrino beams, those were direct interactions but the accuracy of measurement was way higher than any mass in the input vector. – anna v Dec 20 '16 at 17:55
• Thanks for answering Rob. Surely OPERA offered direct evidence of neutrino speed? – John Duffield Dec 20 '16 at 17:56
• @JohnDuffield Consistent with $c$, as predicted. The beam of neutrinos observed by OPERA was, if I recall correctly, produced by decay of a relativistic muon beam. Almost certainly the spread in the beam energy was larger than the upper limit on the neutrino mass, so a mass measurement would be impossible there. – rob Dec 21 '16 at 2:13
• Given current estimates of neutrino mass based on oscillation mass differences and caps on the total mass of neutrinos from cosmology, you'd need to measure neutrinos with kinetic energies on the order of 0.01 eV to 0.001 eV or less to directly confirm or refute the hypothesis from special relativity and neutrino oscillation experiments. – ohwilleke Jan 30 '17 at 3:37