Negative Neutrino Mass Squared: Accepted Paper Analysis

[PeterDonis]

I just came across this paper arguing that the electron neutrino may have negative mass squared:

http://arxiv.org/abs/1408.2804

It says it has been accepted for publication. I'm wondering if anyone has seen it and can comment on the paper's arguments.

 

[ShayanJ]

Weren't tachyons only instabilities in fields and not actual particles?

 

[Vanadium 50]

I don't see where it has been accepted. If a referee, I would probably not accept it. There's very little new here - Ehrlich has been going on about this for more than a decade.

It is absolutely true that the neutrino mass experiments that measure m-squared allow it to go negative in their fits. To do otherwise biases the result high. It is also true that these measurements come out negative - the PDG average is -0.6 +/- 1.9 and the statement "Given troubling systematics which result in improbably negative estimators of m2 in many experiments we use only Kraus 05 and Lobashev 99 (I think they mean Aseev 11) for our average." They then go on to comment on exactly how these two measurements are better than the ones they supersede and how the systematics are better controlled.

As for the cosmological measurements, I am not at all surprised that if one replaces constants in the calculation that the results shift, nor that with the right set, the mass squared can go negative. However, what I don't see is a good argument that these are the right constants to use, apart from the fact that they give interesting conclusions.

For me to believe neutrinos are tachyons, I would prefer to see one strong piece of evidence rather than a lot of weak ones.

 

[goyalvishal4]

Weren't tachyons only instabilities in fields and not actual particles?

Existence of Tachyons is not yet established. But If it establish it would be actual particles with imaginary mass energy and negative time. Further they will loss energy with increase in time.

 

[goyalvishal4]

I don't see where it has been accepted. If a referee, I would probably not accept it. There's very little new here - Ehrlich has been going on about this for more than a decade.

It is absolutely true that the neutrino mass experiments that measure m-squared allow it to go negative in their fits. To do otherwise biases the result high. It is also true that these measurements come out negative - the PDG average is -0.6 +/- 1.9 and the statement "Given troubling systematics which result in improbably negative estimators of m2 in many experiments we use only Kraus 05 and Lobashev 99 (I think they mean Aseev 11) for our average." They then go on to comment on exactly how these two measurements are better than the ones they supersede and how the systematics are better controlled.

As for the cosmological measurements, I am not at all surprised that if one replaces constants in the calculation that the results shift, nor that with the right set, the mass squared can go negative. However, what I don't see is a good argument that these are the right constants to use, apart from the fact that they give interesting conclusions.

For me to believe neutrinos are tachyons, I would prefer to see one strong piece of evidence rather than a lot of weak ones.

http://phys.org/news/2014-12-faster-than-light-particles.html

This article is mentioning it to be accepted in journal Astroparticle Physics http://www.journals.elsevier.com/astroparticle-physics/

However On Journal Webpage It is not there

 

[ChrisVer]

For me negative neutrino masses squared would be a disaster, because then what kind of cosmological contribution would one have?...So indeed systematic errors can play important role in determining the value.

 

[ShayanJ]

Existence of Tachyons is not yet established. But If it establish it would be actual particles with imaginary mass energy and negative time. Further they will loss energy with increase in time.

I read it here:

In the 1967 paper that coined the term,[1] Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light,[5] and instead represent an instability known as tachyon condensation.[3] Nevertheless, negative squared mass fields are commonly referred to as "tachyons",[6] and in fact have come to play an important role in modern physics.

(From this page.)

 

[goyalvishal4]

I read it here:

(From this page.)

check this part of your link containing details http://en.wikipedia.org/wiki/Tachyon#Fields_with_imaginary_mass
It is for field whose uncondensed states are tachyons but after tachyonic condensation they become positive squared mass.
But its only one case which is partially tachyonic as final excitations are not tachyons, only intermediate are. Even Higgs Boson has imaginary mass in uncondensed phase
Tachyons is rather general term whether possible or not, but include excitation which would actually travel faster than light

 

[mfb]

The paper talks about a decay chain p->n->p->n->... for high-energetic particles. Do they want to violate special relativity? Otherwise I don't think that makes sense.
I don't see enough evidence to introduce negative squared masses and violations of special relativity just to get better fits to current experimental data. It does not help to have 6 measurements consistent with the proposed negative value - they also have to be completely inconsistent with positive values to make the model interesting.

 

[Vanadium 50]

Do they want to violate special relativity?

Yes.

 

[PeterDonis]

Weren't tachyons only instabilities in fields and not actual particles?

This Usenet Physics FAQ article has a good discussion of tachyons:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

 

[PeterDonis]

I would prefer to see one strong piece of evidence rather than a lot of weak ones.

This was my sense after skimming the paper, that it was giving multiple very weak pieces of evidence but no strong evidence (AFAIK no strong evidence exists of neutrinos, or any other particles, being tachyons). Thanks for the confirmation. :)

 

[mfb]

Yes.

Then they need really strong evidence. Especially in a field where 2-3 sigma effects come and go all the time and even 5 sigma effects can disappear.

 

[ShayanJ]

This Usenet Physics FAQ article has a good discussion of tachyons:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

Thanks for that. But this only treats scalar tachyons which isn't useful when we talk about neutrinos. I checked some QFT texts but non of them treat tachyons(which isn't surprising). Not much was on internet too. Can you suggest a text that treats tachyons?(Specially fermionic ones)

 

[PeterDonis]

this only treats scalar tachyons

The original paper by Bilaniuk and Sudarshan (referenced in the article) turns out to be available online:

https://www.uam.es/personal_pdi/ciencias/jcuevas/Teaching/Taquiones.pdf

It doesn't explicitly discuss solutions of equations of motion the way the Usenet article does; however, the considerations raised in the paper appear to me to apply to any tachyonic particle, regardless of spin.

Can you suggest a text that treats tachyons?(Specially fermionic ones)

Google shows a number of articles that appear to discuss tachyonic solutions of the Dirac equation. AFAIK the general solution properties of the Klein-Gordon equation that are discussed in the Usenet article should also hold for the Dirac and Maxwell equations, since both of those are known to be consistent with relativistic causality.

 

[ShayanJ]

The original paper by Bilaniuk and Sudarshan (referenced in the article) turns out to be available online:

https://www.uam.es/personal_pdi/ciencias/jcuevas/Teaching/Taquiones.pdf

It doesn't explicitly discuss solutions of equations of motion the way the Usenet article does; however, the considerations raised in the paper appear to me to apply to any tachyonic particle, regardless of spin.
Google shows a number of articles that appear to discuss tachyonic solutions of the Dirac equation. AFAIK the general solution properties of the Klein-Gordon equation that are discussed in the Usenet article should also hold for the Dirac and Maxwell equations, since both of those are known to be consistent with relativistic causality.

But I think whether or not the following sentence is true, depends to a high extent on the equation that the particle obeys. This is the main reason I ask for further references. Or its a general thing not depending much on spin?

localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal.

 

[PeterDonis]

I think whether or not the following sentence is true, depends to a high extent on the equation that the particle obeys.

I don't have a reference, as I said, but I'm curious why you think this would depend to a high extent on the equation of motion. The Dirac and Maxwell equations share a lot of properties with the Klein-Gordon equation, including, as I mentioned, consistency with relativistic causality. Indeed, multiplying the Dirac equation by its complex conjugate gives you the Klein-Gordon equation (this is one way of expressing the fact that two fermions with opposite spins can form a zero-spin bound state). So I'm not sure why you would expect a drastic difference in the behavior of tachyonic solutions to these equations.

 

[Matterwave]

If neutrinos are Tachyons, wouldn't the neutrinos from SN1987A have arrived here much earlier? Is this addressed in the paper? My internet connection is very poor, and loading it is taking some time lol.

 

[PeterDonis]

If neutrinos are Tachyons, wouldn't the neutrinos from SN1987A have arrived here much earlier?

Not if their energy was large enough for their velocity to be sufficiently close to the speed of light. (Of course, that "sufficiently close" might be a problem--I haven't run the numbers to see if the required energy would be compatible with what was detected.)

Is this addressed in the paper?

Not as far as I can see.

 

[Matterwave]

From what I know of neutrinos from SN1987A, the fact that they arrived ~3 hours ahead of the light means their speed is bound very close to the speed of light. It originated from the LMC I believe, so it has been traveling to us for ~150,000 years... that they arrived only 3 hours early limits their speed to c to one part in a billion.

 

[Vanadium 50]

If neutrinos are Tachyons, wouldn't the neutrinos from SN1987A have arrived here much earlier?

No. The limit is determined by the dispersion in arrival times - we don't have an absolute measurement of when SN1987A happened. That limit can be expressed as the |m²| < few eV².

 

[TachyonBob]

Regarding my tachyon paper which HAS BEEN accepted by Astroparticle Physics, there are too many misconceptions, false statements and ad hominem arguments made about it here to reply to them. I certainly have not claimed that I have definitively proven the electron neutrino is a tachyon, only that each observation is consistent with that possibility. While each of the 6 observations may be "weak" i.e., have more mundane explanations, the interesting thing is that they all reinforce each other, not by each being consistent with nu_e being a tachyon, but by each yielding the very same tachyonic mass value within their uncertainty. The paper should be seen as a stimulus to others (especially cosmic ray researchers) to check their archived data for the 4.5 PeV signal proposed. However, unless we have another galactic supernova soon, the definitive answer as to whether I am right may need to wait until the KATRIN experiment (starting data taking this year) has 3-5 years of data. .

 

[Vanadium 50]

Not if their energy was large enough for their velocity to be sufficiently close to the speed of light.

Isn't it if their energy were small enough for their velocity to be sufficiently close to the speed of light? As a tachyon gains energy, it slows down.

However, as I mentioned earlier, we don't have a stopwatch that tells us when SN1987A went off, so we can't use absolute time measures (except the very crudest - we know the neutrinos arrived the same day as the light, and probably only about 3 hours before). One needs to look at the difference in arrival times, and that suggests that (assuming non-tachyonic neutrinos) that the mass is less than about 15-20 eV, and probably less than 10.

 

[TachyonBob]

With respect to the next supernova you do not need to know when it "went off." As I discuss in my paper there is research done by supernova modellers which indicates strongly that there should be millisecond time scale oscillations in the neutrino output. (Imagine a rapid in/out oscillation in density.) If the neutrino mass is large enough, these ms-scale oscillations will be "smeared out" due to different travel times to reach Earth. Given the observed neutrino arrival times one can then "unsmear" the data by finding the neutrino mass that best unsmears it. Check the reference on this given in my paper if you are really interested.

 

[PeterDonis]

Isn't it if their energy were small enough for their velocity to be sufficiently close to the speed of light? As a tachyon gains energy, it slows down.

As a tachyon gains energy, it slows down closer and closer to the speed of light. So the more energy it has, the closer its speed is to the speed of light. A tachyon with small energy would have a speed much, much larger than the speed of light.

 

[TachyonBob]

What you say is true, but the problem is that for the smallest energy neutrino that can be detected (around 0.3 MeV) the speed is so close to c that no Earthly experiment could hope to detect the difference. That is why I say measuring their mass is a much more sensitive test

 

[vanhees71]

From a more theoretical perspective: Are all the fundamental problems with interacting tachyons solved yet? Is the S-matrix of a model containing tachyons unitary and Poincare invariant etc.?

 

[TachyonBob]

I am not a theorist, so I cannot say with any authority that they have or have not been. As I noted in the paper Lorentz invariance is a long-standing problem, and various theorists have found ways to modify it so as to describe effective Lagrangians for tachyons. You should look at a recent paper by Jentschura & Wundt that I cited which considers the kinds of "hard choices" that need to be made in order to have a successful theory of tachyonic neutrinos. Chodos and Kostelecky have also written about this, as has Ngee-Pong Chang.

 

[vanhees71]

Ok, I'll have a look, but I'm pretty doubtful, whether you have all these constraints fulfilled one expects from a physically sensible S-matrix (unitarity, causality, Poincare covariance, linke-cluster principle).

 

[Matterwave]

No. The limit is determined by the dispersion in arrival times - we don't have an absolute measurement of when SN1987A happened. That limit can be expressed as the |m²| < few eV².

I admit I am not very knowledgeable about theoretical tachyons, and I can't even access this paper since my internet connection is so poor. So I can't really comment much further lol.

 

[Orodruin]

My question is the following: Are these observations actually computing the same thing? Neutrinos are mixed and a priori there is no such thing as an electron neutrino mass. If you look at 0nubb experiments, they are measuring an effective electron neutrino mass involving all of the mass eigenstates, mixings with the electrons and the Majorana phases of the PMNS matrix. The combination that should appear in tritium beta decay is different and does not provide the possibility of phase cancellation.
I do not know enough CR physics to know what combination would appear as the effective electron neutrino mass in those. However, with the quoted mass square it seems to me that all neutrino mass eigenstates would be degenerate and thus tachyons.

If part of this is explained in the paper I had a difficulty finding it as I am currently half absent and only access the internet on my iPhone, which makes reading a paper difficult.

 

[OmCheeto]

Would it be possible to avoid the negative mass, by applying a small mass to photons?
Someone once told me that it was theoretically possible.

of Ask Dr. Neutrino Date: 97/03/13
If photons have a small rest mass, they can no longer move at the speed we call "c". I know its confusing that in this situation "c" can no longer be described as the "velocity of light", but the situation is completely consistent and satisfactory, and is open to various experimental tests, which yield the limit of about 10^-20 eV for the photon mass.

The value doesn't seem to have changed much over the last 17 years:

Is there any experimental evidence that the photon has zero rest mass?
...It is almost certainly impossible to do any experiment that would establish the photon rest mass to be exactly zero. The best we can hope to do is place limits on it. ...
The new limit is 7 × 10−17 eV ...

{edit} ps. Where are my manners? Welcome to PF TachyonBob! :)

 

[ChrisVer]

Neutrinos are mixed and a priori there is no such thing as an electron neutrino mass

Are you sure about this? Because in certain interaction channels they give the boundaries of flavor neutrino masses (such as Tritium for the electron neutrino).
In general the flavor neutrinos are a mixture of fixed mass-eigenstates, so they can have a mass...
eg. for 3 flavors there exists $<\nu_e | m | \nu_e > = a_1 m_1 + a_2 m_2 + a_3 m_3 \ne 0$
where $a_i$ are given by the PMNS matrix.

 

[Orodruin]

Are you sure about this? Because in certain interaction channels they give the boundaries of flavor neutrino masses (such as Tritium for the electron neutrino).

Yes. This type of experiments essentially assume that the mass eigenstates are degenerate. There are also studies of the beta decay spectrum for the case when the experiment is accurate enough to resolve the mass differences between the mass eigenstates, in which case the spectrum looks quite different.

eg. there exists <νe|m|νe>=a1m1+a2m2+a3m3≠0 = a_1 m_1 + a_2 m_2 + a_3 m_3 \ne 0

This is essentially the combination that appears in 0nubb experiments (or rather the square of this). For tritium decay, you usually see $m_{\nu_e, \rm eff} = \sum_i |U_{ei}|^2 m_i$.

 

[mfb]

Yes. This type of experiments essentially assume that the mass eigenstates are degenerate.

For previous tritium experiments this was probably a very good approximation, given the large upper limits compared to the small m^2 differences. I saw a KATRIN talk discussing those differences, but it is questionable if they can see it if I remember correctly.