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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.

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John Duffield
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    well, we have evidence of the fact that neutrinos are massive, right? – AccidentalFourierTransform Nov 26 '16 at 18:13
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    Various existing questions covering bits of the same ground: http://physics.stackexchange.com/q/139 http://physics.stackexchange.com/q/245615 http://physics.stackexchange.com/q/15320 http://physics.stackexchange.com/q/274050 http://physics.stackexchange.com/q/258883 – dmckee --- ex-moderator kitten Nov 26 '16 at 18:36
  • There is a proposed direct measurement of the beta decay end-point energy using RF circulation of the recoiling electron in a strong external magnetic field that could—assuming they can suppress their background as well as they expect—constrain $\langle m_{\nu_e}\rangle$ much better (and sooner) than current mixing based investigation. – dmckee --- ex-moderator kitten Nov 26 '16 at 18:47
  • @AccidentalFourierTransform : I don't think we do actually. We have a model of oscillation that suggests the neutrino has a small mass, but AFAIK we have no actual evidence. In similar vein we don't seem to have any evidence of any neutrinos ever moving at less than c. Which suggests to me that the neutrino is massless. – John Duffield Nov 27 '16 at 13:10
  • If neutrino oscillation happens then, if neutrinos travel at $c$, relativity must fail (SR and with it GR). So if there is good evidence for oscillations, then the question is actually 'do we think relativity is correct?' I'm not in touch with the experimental situation at all, but I think that there is good evidence for oscillation and relativity is correct, hence neutrinos must travel slower than $c$ (or anyway not at $c$). –  Dec 12 '16 at 20:39
  • @tfb : noted. The point is that I'm struggling to find any evidence of neutrinos travelling slower than c. As is everybody else, it would seem. – John Duffield Dec 13 '16 at 19:15
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    @JohnDuffield Evidece other than oscillations you mean, I guess, which is extremely convincing evidence. –  Dec 13 '16 at 21:06
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    @tfb : neutrino oscillations aren't actually evidence for a speed slower than c. That's an inference based upon a hypothesis. I'm looking for some actual evidence of neutrino speeds less than c, and I can't find it. – John Duffield Dec 14 '16 at 16:36
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    @JohnDuffield: Indeed, the hypothesis being 'that special relativity is correct'. I give up. –  Dec 14 '16 at 17:37
  • @tfb : that isn't the hypothesis at all. – John Duffield Dec 15 '16 at 16:21
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    The answer is no, that there are no measurements showing that neutrinos travel slower than the speed of light. There are also no measurements showing that neutrinos travel at exactly the speed of light. The existing measurements are perfectly consistent with current limits on the neutrino mass, as explained in answers to the the duplicate. – ProfRob Dec 22 '16 at 15:07
  • @Rob Jeffries : I'm afraid I draw a different conclusion. The neutrino was proposed by Pauli in 1930, and confirmed by Cowan and Reines 22 years later in 1952. That was 64 years ago, and in all that time we have never seen a neutrino going slower than c. Knowing what I do, and paying particular attention to E=mc², I conclude that like the photon, the neutrino has no charge, and it has no mass either. – John Duffield Dec 22 '16 at 15:15
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    My conclusion is and was "The existing measurements are perfectly consistent with current limits on the neutrino mass" and that is simply a fact. Your "conclusion" is an opinion and you appear not to be interested in measurements or evidence, but in pushing your own non-mainstream ideas (again). Rob's answer perfectly explains why detecting low-energy neutrinos is difficult and the fact they were discovered in 1952 is really irrelevant to that. And $E = (p^2c^2 +m^2c^4)^{1/2}$; that's the problem. – ProfRob Dec 22 '16 at 15:32
  • @Rob Jeffries : Neither E=mc² nor conservation of energy is some opinion of mine, and I'm extremely interested in evidence. If there is no evidence to support some 48-year-old hypothesis, then I will point this out. Or if somebody else does, you won't find me dismissing what they say. That's because I care about physics and the scientific method, not for peddling some evidence-free hypothesis as the definitive answer and dismissing all others as "non-mainstream". – John Duffield Dec 22 '16 at 15:50
  • There is evidence that neutrinos have mass and the very link you provide briefly summarises the Nobel-prize winning (2015, “for the discovery of neutrino oscillations, which shows that neutrinos have mass”) evidence that supports the 48-year old hypothesis. What evidence do you think there is that neutrinos travel at exactly the speed of light (which they must if massless). There is zero evidence to contradict the 48 year old hypothesis. – ProfRob Dec 22 '16 at 16:19

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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.

rob
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    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 02:13
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    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 03:37