# Is there any cosmological evidence that neutrinos travel at a speed other than c?

I've been looking into neutrinos. One thing I'm puzzled about is how fast they travel.

See the Wikipedia SN1987A article where you can read this: “approximately two to three hours before the visible light from SN1987A reached Earth, a burst of neutrinos was observed at three separate neutrino observatories”. Some reports describe an initial burst of neutrinos which arrived 7.7 hours before the light. It's thought that the neutrinos were emitted before the light because of the way stars collapse, wherein photons take longer to get out. I don't have much of an issue with that. But what's interesting is that in 168,000 years travelling through space, the photons didn’t overtake the neutrinos. That suggests to me that neutrinos are massless, which ties in with what Fermi said in section VII of his 1934 paper. He plotted three curves and noted that the μ=0 curve matched the empirical curves. He concluded that “the rest mass of the neutrino is either zero, or, in any case, very small in comparison to the mass of the electron”.

The thing is that if neutrinos travel at exactly c they have no mass at all. And I can't find any evidence that they don't. I can find plenty of evidence for electrons travelling at speeds less than c. The neutrino is said to be a fermion like an electron. But I can't find any evidence of neutrinos travelling at speeds less than c.

Can anybody give me a reference to any cosmological evidence that neutrinos travel at less than c? Or any other hard scientific evidence? By evidence I don't mean an inference such as "neutrinos go missing so they must oscillate therefore they must have mass therefore they must travel at less than c". I mean evidence.

• Would you like evidence specifically tied to astronomy, or would something drawing on other fields be valid (in which case this might be better for Physics)? – HDE 226868 Sep 4 '17 at 22:05
• It doesn't indicate that neutrinos are massless of course. It indicates that there is an upper limit to their mass - an upper limit that is not especially interesting compared to other constraints. – Rob Jeffries Sep 4 '17 at 22:58
• Fermi was right. Neutrino masses are less than eV or so. As you know. – Rob Jeffries Sep 4 '17 at 23:00
• Almost identical to physics.stackexchange.com/questions/295004/… – Rob Jeffries Sep 4 '17 at 23:10
• @HDE 226868 : I was asking for cosmological evidence because I previously asked the question on Physics stack exchange and only got one answer saying there's no direct evidence. I was referred to a duplicate which said "your question is equivalent to asking what the absolute mass of the neutrinos is". What I'm after is evidence for neutrinos travelling at less than c. Rob Jeffries gave an answer referring to the Wie paper but didn't get much attention, even from me. I've learned something about GRBs since then and will look at that afresh. – John Duffield Sep 5 '17 at 18:06

A paper by Wie et al. (2016) uses the coincidence between gamma rays from Gamma ray bursts and individual 3-30 TeV neutrinos to estimate the difference in propagation speed between neutrinos and photons.

They find $$\frac{|v-c|}{c} < 2.5 \times 10^{-18}$$

They say this is about 7 orders of magnitude more precise than any previously published limit. However, it does rely on the genuine coincidencce between the GRBs and these individual neutrino events, which does seem to be in question or even doubtful in some cases.

The mass limit this places on the neutrinos appears to be a rather uninteresting $<6.8$ keV, but it is a direct measurement of speed rather than an extrapolation of the speed from a mass limit and special relativity.

• Thanks for this Rob. I've recently done some digging around on GRBs, so this is particularly interesting. Sorry I didn't notice it last year. – John Duffield Sep 5 '17 at 18:25

I can find plenty of evidence for electrons travelling at speeds less than c. The neutrino is said to be a fermion like an electron. But I can't find any evidence of neutrinos travelling at speeds less than c.

This seems to be the core of your doubt.

I'd really suggest you read the answers to questions on this subject on Physics SE, but a few notes on this specific point.

• A fermion can be massless (Weyl and Majorana types can be).
• Experiment suggests neutrinos may have a very small mass (order of a few eV). This is often pointed to as evidence suggesting the standard model is not complete.
• There is no absolute agreement on the mass (or lack of) of neutrinos. It's a good way to get particle physicists arguing. :-)

So your confusion is understandable : so is everyone else.

By evidence I don't mean an inference such as "neutrinos go missing so they must oscillate therefore they must have mass therefore they must travel at less than c". I mean evidence.

That is evidence. :-)

One of the problems with what you're asking for is that it presumes that neutrinos don't oscillate. If someone gets an experimental result apparently demonstrating they do, you should not ignore it.

I don't know how familiar you are with the theory of neutrino oscillation and why it's so important, but I've linked to Wikipedia's page on the subject as a starting point just in case.

[Regarding SN1987] I don't have much of an issue with that. But what's interesting is that in 168,000 years travelling through space, the photons didn’t overtake the neutrinos.

This simply places an upper limit on the mass of neutrinos. Wikipedia's article quotes this as 16 eV from that experimental data and I've no reason to argue with that.

But the failure to overtake doesn't say any more than this.

That suggests to me that neutrinos are massless, which ties in with what Fermi said in section VII of his 1934 paper.

To give Fermi his due, note this quote from that paper (well, the translation of it) :

Hence we conclude that the rest mass of the neutrino is either zero, or, in any case, very small in comparison to the mass of the electron.

Well the current values place the upper limit at around 1/30,000 th of the electron mass. That's "very small" in my book. So Fermi had it nailed pretty good : good scientist, that lad. :-)

Just a few items of importance show how much has changed :

So you do need to factor in the new physical models for the neutrino into your thinking about them.

• Thanks for answer Stepehen The "core of my doubt" is that the neutrino was predicted in 1930 and we still haven't seen one going slower than c. Try as I might I can find no actual evidence for this. I've read the Physics SE answers but they to tend to give the oscillation inference or "suggestion" rather than the direct evidence of neutrino speed. PS: I quoted Fermi saying "or, in any case, very small". And as for new physical models for the neutrino, I'm not sure there's even an old one. – John Duffield Sep 5 '17 at 18:20