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I have read these questions:

Do neutrinos change speed in neutrino oscillations?

Neutrinos always travel at same speed?

Neutrinos always travel at same speed?

Where are all the slow neutrinos?

Neutrino Oscillations and Conservation of Momentum

There are a lot of questions on this site about neutrino speed and mass, but none of them answer my question.

The neutrino is the lightest known massive particle, and for a while its rest mass (or if it is massless) was a debate. Today we do know that the neutrino does have a rest mass.

A neutrino (/nuːˈtriːnoʊ/ or /njuːˈtriːnoʊ/) (denoted by the Greek letter ν) is a fermion (an elementary particle with spin of 1 / 2 ) that interacts only via the weak subatomic force and gravity.[2][3] The neutrino is so named because it is electrically neutral and because its rest mass is so small (-ino) that it was long thought to be zero. The mass of the neutrino is much smaller than that of the other known elementary particles.[1]

https://en.wikipedia.org/wiki/Neutrino

I have read this question:

Which is the lightest thing in this universe? Is that a photon or neutrino?

Where rob says:

There are three flavors of neutrino and they all have different masses. Therefore at least two of them are massive; whether the lightest neutrino is massless is an open question.

This information is from several years ago, there might be new information (I did not find any) on this.

So it could be that the neutrino is oscillating between flavors in flight, and these flavors are superpositions of massive and massless states, and this could mean too that it is oscillating between the speed of light and a slower speed, but because of this, it can never slow down (on average when measured over a long distance) from the vicinity of the speed of light.

Question:

  1. Do neutrinos really have a massless state?
Árpád Szendrei
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    Its spatial speed is as close as we can get to the speed of light. Why do you think that? With enough energy, any massive object can get arbitrarily close to $c$. – G. Smith Feb 17 '20 at 18:15
  • @G.Smith I do understand you are correct, but in any experiment, as far as we can tell, what I have found is that the neutrino seems to be the fastest. But I will edit. – Árpád Szendrei Feb 17 '20 at 18:17
  • I don’t think you can have oscillations between massive and massless states, but I could be wrong about this. And I think that in principle massive neutrinos can be brought to rest. There is of course an inertial frame in which they are already at rest, but I mean at rest relative to us. – G. Smith Feb 17 '20 at 18:22
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    In short, I do not believe that you can have a particle which travels slower than light which cannot be further slowed down, to zero speed. – G. Smith Feb 17 '20 at 18:24
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    One difficulty with this question is that neutrinos are notoriously hard to detect. IIRC, our best neutrino detectors investigating solar neutrinos only detect about one per billion of the neutrinos that pass through them. Obviously, slower neutrinos have less energy, and generally lower energy implies a smaller cross-section for interaction, and hence detection; see http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/neutrino3.html Theoretically, the cosmic neutrino background contains extremely redshifted neutrinos, and current technology cannot detect such slow neutrinos. – PM 2Ring Feb 17 '20 at 18:48
  • I can't find a good ref for the neutrino detection rate, but https://en.wikipedia.org/wiki/Neutrino_astronomy#Detection_methods says "the enormous flux of solar neutrinos racing through the Earth is sufficient to produce only 1 interaction for 10³⁶ target atoms" – PM 2Ring Feb 17 '20 at 19:05
  • @G.Smith can you please elaborate on what you mean by slow down any massive particle to zero speed, that is to rest (not absorb or scatter), just simply slow them down? I thought no one has ever seen an electron for example at rest. – Árpád Szendrei Feb 18 '20 at 03:53
  • I don’t know what experimentalists are able to do. But there is no theoretical reason why you can’t have an electron with zero momentum. You can slow down, stop, and reverse a beam of electron with nothing more than an electric field. Quantum-mechanically, as its momentum becomes zero and thus certain, its position becomes uncertain, but we’re not talking about position. – G. Smith Feb 18 '20 at 04:54
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    " oscillating between massive and massless states in flight ..." that kind of oscillation does not obey energy-momentum conversation. Also, relic neutrinos are probably ultimately slow, but it is almost impossible to catch them. – bulmust Feb 18 '20 at 07:06
  • @CosmasZachos correct, though, do you agree that one of the masses might be 0? – Árpád Szendrei Feb 18 '20 at 17:42
  • @CosmasZachos thank you i edited. – Árpád Szendrei Feb 18 '20 at 17:45
  • The quote by rob seems to answer your question already explicitly (one of the flavours might be massless, but it's an open question). What do you want to know here that is not already answered by what you quote? Also, let me point out to you again that it is completely irrelevant to other users to list all the questions you have read, unless you explain what they have to do without your question specifically and why they didn't answer your question. – ACuriousMind Feb 18 '20 at 17:46
  • @ACuriousMind that was several years ago, is there any (I could not find any) new information on this? – Árpád Szendrei Feb 18 '20 at 17:48
  • The way to ask for updated information on a question is to offer a bounty on that question, not to duplicate it. – ACuriousMind Feb 18 '20 at 17:48
  • @ACuriousMind that question is asking whether the photon or the neutrino is the lightest. I am not asking about the photon. All i am trying to figure out is whether there is a massless state of the neutrino, and if this has any effect on its oscillation and (average) speed. – Árpád Szendrei Feb 18 '20 at 17:50
  • Since you asked.... In principle, the lowest mass could, quite possibly, be 0, even though the best cosmological fits favor something larger. – Cosmas Zachos Feb 18 '20 at 19:35
  • Maybe I exaggerated... Gerbino & Lattanzi '18. – Cosmas Zachos Feb 18 '20 at 19:46

2 Answers2

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The oscillation of neutrinos is closely related to the concept of superposition of quantum states.

There are three distinct 'flavors' of neutrinos: electron, muon and tau. When a neutrino is produced in a particle reaction, it's almost always produced with a specific flavour.

Neutrinos however may also have three different masses (one of them possibly being $0$). What is important to understand, that the properties of mass and flavour are not independent - you don't have, for example three electron neutrinos with diferent masses. Rather, each flavor of neutrinos is a different mixture (superpositino) of neutrinos with different masses. Any mixture of flavors can be interpreted as some mixture of masses, and vice versa.

When you have a nautrino from, for example, the Sun, it's usually produced as an electron neutrino, which is a specific superposition of mass states. Each component travels with a different speed (one possibly with the speed of light), but differences aren't big enough to separate them on the distance Sun-Earth. Ratheer, and as they travel they experience relative change in phase, from the equation $$ |\psi_i\rangle \rightarrow e^{-i(E_it-\vec p_i\vec x)/\hbar}|\psi_i\rangle$$ When they are all ultrarelativistic and traveling vith the speed very close to the speed of light, we have $$ t \approx |\vec x|/c$$ $$ E_i = \sqrt{|\vec p_i|^2c^2+ (m_ic^2)^2} \approx |\vec p_i|c + \frac{m_i^2c^3}{2|\vec p_i|}$$ $$ E_i t - |\vec p_i||\vec x| \approx \frac{m_i^2c^2|\vec x|}{2|\vec p_i|} \approx \frac{m_i^2c^3|\vec x|}{2 E_i} $$ The differences in masses cause differences in phases. As the different components of the neutrino gain different phases, they become a different mixture, a different flavor. That's why a neutrino that was produced as an electron neutrino after some time may be detected as a muon neutrino or a tau neutrino.

If you do wait long enough the neutrinos with different masses will get separated. At that point they no longer interfere with each other, and they won't oscillate - instead, a neutrino of a fixed mass has fixed chances of being detected as having one of the three flavors, and these chances do not change.

Adam Latosiński
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  • Thank you so much. So you agree that one of the possible neutrinos might be massless? Can you please elaborate on when and how the neutrinos get separated in flight (after which point they do not oscillate)? – Árpád Szendrei Feb 18 '20 at 17:41
  • @ÁrpádSzendrei Yes, one of the neutrinos may be massless. As for how seperation works, it is it is similar to how light-splitting plate splits a photon - the neutrino is simultaneously in various places with some probabilities. The neutrino splits because of the differences in velocities, with lightest part being the fastest (and being most forward), and heaviest being the slowest (and lagging behind). The neutrino can be detected in any one of these three places, but only in one - after it's detected, the wave function collapses. – Adam Latosiński Feb 18 '20 at 22:50
  • "they become a different mixture, a different flavor" - Are you saying that mass defines flavor (generation)? This seems the opposite of the usual view that generation defines mass while it is unknown what defines generation. – safesphere Feb 29 '20 at 01:44
  • @safesphere It does not. there are known three generations of neutrinos, but the mass matrix mixed them, i.e. the eigenstates of mass are mixtures of neutrinos with different mass. And vice versa - an electron neutrino is a specific mixture of mass eigenstates, and muon neutrino is a different one. A neutrino that starts as an electron neutrinos may after some time be detected as muon neutrinos because of the aqcquired phase shifts between its components of different masses. – Adam Latosiński Feb 29 '20 at 10:20
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Neutrinos are relatively hard to slow down due to their size, every time they come in contact with anything they slow down, however due to their size it is relatively rare, this is when they can be detected, finding them after they hit something however is a different story.

noam
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