# Thread: Are neutrinos with mass incompatible with SR?

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## Are neutrinos with mass incompatible with SR?

Another \$100 question.

If neutrinos have a mass, does that make them incompatible with SR? Because if the relativistic mass applies then a neutrinos will emit a strong gravitational field and thus will create "distortions" in the spacetime continuum.

Regards,
philippeb8

2. I don't know what you're trying to say, but Special Relativity isn't important physically, it just provides a way to estimate speeds, energy, momentum, and relative views of time.
Neutrinos probably have mass, most likely electron neutrinos are a few milli-eV. If they have more than a few eV of kinetic energy, they will travel near the speed of light. What exactly are you thinking will disrupt the space time continuum here?

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Originally Posted by antoniseb
I don't know what you're trying to say, but Special Relativity isn't important physically, it just provides a way to estimate speeds, energy, momentum, and relative views of time.
Neutrinos probably have mass, most likely electron neutrinos are a few milli-eV. If they have more than a few eV of kinetic energy, they will travel near the speed of light. What exactly are you thinking will disrupt the space time continuum here?
Well given their high speed, their relativistic mass will increase as well and this will create a "gravitational well" around them. I cannot get an estimate because the speed of the neutrinos in the Wiki pages isn't clear.

4. Originally Posted by philippeb8
Well given their high speed, their relativistic mass will increase as well and this will create a "gravitational well" around them. I cannot get an estimate because the speed of the neutrinos in the Wiki pages isn't clear.
"Relativistic mass" does not contribute in a simple way to the gravitation of an object. You need to use GR to calculate what the effect would be and the only answer I have seen is "it's complicated" (but I gather it is probably a very small effect).

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Originally Posted by Strange
"Relativistic mass" does not contribute in a simple way to the gravitation of an object. You need to use GR to calculate what the effect would be and the only answer I have seen is "it's complicated" (but I gather it is probably a very small effect).
Yes but if you create a "beam" of neutrinos then the effect will be multiplied. But if the answer is: "it's complicated" then I understand.

Thanks!
philippeb8

6. Originally Posted by philippeb8
But if the answer is: "it's complicated" then I understand.
That one would go soooo well with publius' remark in my sig

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No object with mass moving at speeds less than c is incompatible with special relativity which include neutrinos.
Does relativistic mass have gravity? explains some of the complexity in GR. Even the concept of mass in GR is complicated.

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Originally Posted by Reality Check
No object with mass moving at speeds less than c is incompatible with special relativity which include neutrinos.
Does relativistic mass have gravity? explains some of the complexity in GR. Even the concept of mass in GR is complicated.
Wow... that is fascinating!

9. Originally Posted by philippeb8
Yes but if you create a "beam" of neutrinos then the effect will be multiplied. But if the answer is: "it's complicated" then I understand.
It's not complicated. Even if gravitation worked that way, their mass is far too small to have noticable gravitational effects. I'm not sure why you expect massive neutrinos to have strong gravitational fields when no other relativistic particles do.

In electron capture, a proton and electron combine to produce a neutron and an electron neutrino. The total mass-energy of the neutrino is no more than the difference in mass-energy between the neutron and original proton/electron. Its total gravity is no more than a fraction of a percent of that of the particles involved in the reaction that produced it. Sure, we can make neutrino beams with particle accelerators...and the total gravitation of those neutrino beams is a tiny fraction of that of the charged particle beams used to produce the neutrinos, which themselves are dwarfed by the mass of equipment used to generate and accelerate those particles.

The LHC beam dumps are built to absorb a total energy of 350 MJ. Doing so increases their mass by about 3.9 micrograms. A neutrino with mass-energy equivalent to the entirety of the beams in the LHC would have the gravitation of a speck of dust.

10. Originally Posted by slang
That one would go soooo well with publius' remark in my sig
I seem to remember that publius was one of the people who gave some thought to this when it came up before. (What happened to him, by the way?)
Last edited by Strange; 2017-Mar-14 at 07:42 AM. Reason: spelling

11. Originally Posted by philippeb8
I cannot get an estimate because the speed of the neutrinos in the Wiki pages isn't clear.
It's not a Wiki problem. The reason is that their mass and velocity is not known. It is known that their velocity is very, very close to c, so their mass must be very close to zero, but we don't know how close.

12. Originally Posted by Strange
I seem to remember that publics was one of the people who gave some thought to this when it came up before. (What happened to him, by the way?)
Infracted for some (in our view) inappropriate for Cosmoquest post in OTB, and, regrettably, decided to stay away.

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Originally Posted by Jens
It's not a Wiki problem. The reason is that their mass and velocity is not known. It is known that their velocity is very, very close to c, so their mass must be very close to zero, but we don't know how close.
Conceptually it is not too hard - it is the details that are a pain. The basic issue is that for neutrinos the mass eigenstates and flavour eigenstates are not identical. When they are produced they are in a set flavour eigenstate which corresponds to a mixed mass eigenstate. The difference in masses between each state results in a phase difference, which results in a spatially varying probability for the presence of each mass state. This in turn results in a spatially varying probability of observation of each flavour state. The upshot for mass measurements is that if you could simply measure the mass of an electron neutrino it would actually be a mixture of the three mass eigenstates.

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Limits on the neutrino mass are currently running ~ < 2 ev....Particle Data Group. There are some issues still unresolved. It's possible the neutrino is yet massless and travels @ c, but the experiments do not say that yet, so the 2 ev limit, is at present the concensus above which it probably does not lay. That said, there has never been an experiment in neutrino oscillations (which have been seen) without a matter path being part of the experimental track. What would be definitive is to see oscillations without a matter path....perhaps on lunar terrain, from very thin films of polarized beta emitters....electron-type antineutrinos being conjugately produced.
One of the issues is conservation of Electron Family Number. Beta decay of a neutron in a neutron rich nuclide like Co-60, should always produce an electron-type antineutrino. If it produces a neutrino instead, EFN is not conserved, and another Conservation Law drops in the wastebasket.
Another issue is the helicity of the particle. We define helicity in terms related to wood screws, and screwdrivers. Most people are right handed, and use a wood screw and screw driver similary. If you look down on the butt end of the screwdriver, and twist clockwise, the screw will go down into the wood piece. That's a right-handed screw, and it's moving away from you. If you reverse your twist, the butt end turns counterclockwise and the screw backs up, out of the wood. Similarly, in particle physics, helicity or handedness is assigned to different particles. Neutrinos left handed, antineutrinos right handed.....wrap your right hand fingers around the particle in the direction of it's spin, and if your thumb points up it's right handed, down it's left handed.
So if we switch to a left handed screw, when we turn our original screwdriver butt end clockwise, it come out and up from the wood, and when we turn counterclockwise, it goes down and in. Now go back to our massless neutrino. If it travels at "c", nothing will overtake it, and it spins away from us. But, if it has mass, then it must travel subluminally. We could at least in principle build a spaceship that travels closer to c than our emitted neutrino. Then , instead of watching it recede from us with it's spin orientation, it will maintain it's spin but be observed approaching us in our reference frame. That is a change of handedness or helicity, and we have seen our particle turn into it's antiparticle in our new reference frame. That has never been seen in a neutrino physics experiment.
So where does that leave us? Yes many experiments are showing oscillations, and the flavors of the neutrinos are mixing as they travel, but the original authors of neutrino mixing, Mikheyev, Smirnoff, Wolfenstein ...MSW flavor oscillations, suggested that the neutrino fluxes could superimpose on the mass eigenstates of matter,( John N. Bahcall, lecture, MIT, supernova 1987a) analagous to the dressed-state of an atom with photons, that results in the refractive index in optics, with the photon propagating at lower velocities in transparent media, and the MSW matter oscillation is a transitory state and a phenomenon of a matter path with neutrinos. So they publish the upper limits in the Particle Data Group. But as yet, they do not rule out massless neutrinos traveling at c and leaving the Conservation of Family Number intact.
The moon experiment would upstart that, and drop a conservation law. If we return to the moon, that should be checked out. pete

SEE:https://en.wikipedia.org/wiki/Mikhey...enstein_effect
Last edited by trinitree88; 2017-Mar-15 at 06:50 PM. Reason: typos,link

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Originally Posted by trinitree88
Limits on the neutrino mass are currently running ~ < 2 ev....Particle Data Group. There are some issues still unresolved. It's possible the neutrino is yet massless and travels @ c, but the experiments do not say that yet, so the 2 ev limit, is at present the concensus above which it probably does not lay...
If all neutrinos were massless then the oscillations would not happen. The state mixing is driven by the mass difference term. At least in current theory, which seems to agree pretty well with the evidence.

Then , instead of watching it recede from us with it's spin orientation, it will maintain it's spin but be observed approaching us in our reference frame. That is a change of handedness or helicity, and we have seen our particle turn into it's antiparticle in our new reference frame. That has never been seen in a neutrino physics experiment.
You are mixing chirality and helicity here. Helicity can change, but that doesn't change a particle into an antiparticle. Chirality is frame independent and has opposite sign for particles and antiparticles that we observe.

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Originally Posted by Shaula
If all neutrinos were massless then the oscillations would not happen. The state mixing is driven by the mass difference term. At least in current theory, which seems to agree pretty well with the evidence.

You are mixing chirality and helicity here. Helicity can change, but that doesn't change a particle into an antiparticle. Chirality is frame independent and has opposite sign for particles and antiparticles that we observe.

Shaula. then there's this: SEE:https://www.quora.com/What-is-the-di...rticle-physics

something is amiss....He has helicity Lorentz invariant, chirality not....No? You have the opposite.... pete
Last edited by trinitree88; 2017-Mar-19 at 03:42 PM. Reason: wouldn't be the first mistake I've ever made....pete

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Originally Posted by trinitree88
Shaula. then there's this: SEE:https://www.quora.com/What-is-the-di...rticle-physics

something is amiss....He has helicity Lorentz invariant, chirality not....No? You have the opposite.... pete
He has helicity invariant for massless particles. Because chirality and helicity are equivalent for massless particles (since they move at the speed of light)

Also - I think you have misread the article:
So when the particle becomes massive, you lose the boost invariance of helicity. But you can still define another property, which is Lorentz invariant, and becomes equal to the helicity if you take the limit of massless particle. This new quantity is called the chirality.
I guess you are basing your comment on the section that says:
In a sense, the massive particle has a Lorentz invariant and conserved property called helicity/chirality. When the particle becomes massive, a similar property that is both Lorentz invariant and conserved can not be defined, hence we define two different properties: helicity (which is conserved but not Lorentz invariant) and chirality ( which is not conserved but Lorentz invariant)
In this quote the first sentence should read "In a sense, the massless particle has a Lorentz invariant and conserved property called helicity/chirality" - otherwise it doesn't make sense as the second sentence refers to the particle becoming massive.

So chirality is always Lorentz invariant while helicity need not be. Helicity is only invariant for massless particles because they are moving at the speed of light so there simply isn't a frame moving faster than them.

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