Negative Neutrino Mass Squared: Accepted Paper Analysis

[Vanadium 50]

From oscillations we know that the largest mass difference squared is about (1/20 eV)². Tritium endpoint experiments are sensitive at the eV level. So the degeneracy assumption is not unreasonable.

 

[TachyonBob]

Tritium experiments measure the "effective mass" squared of nu_e, defined as the weighted average defined by a formula given above by Orodruin, so it makes no difference as to whether or not they are degenerate. It's not like some tritium events record m_1, others m_2, etc. Based on KATRIN simulations they may be able to see my postulated mass.

 

[bcrowell]

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..

There is a good discussion of this in Chodos et al., Null Experiments for Neutrino Masses, Mod. Phys. Lett. A 7, 467 (1992), http://www.physics.indiana.edu/%7Ekostelec/lay/91chodoskosteleckypottinggates.pdf . Their discussion of whether this means there's Lorentz violation is ... nuanced.

 

[Orodruin]

Tritium experiments measure the "effective mass" squared of nu_e, defined as the weighted average defined by a formula given above by Orodruin, so it makes no difference as to whether or not they are degenerate. It's not like some tritium events record m_1, others m_2, etc. Based on KATRIN simulations they may be able to see my postulated mass.

If tritium experiments had infinite resolution, what they would see would be three cutoffs in the spectrum, with the one corresponding to $\nu_3$ being more difficult to see due to the small mixing. If they are degenerate (within the experimental resolution) it does not matter much to use one or the other.

My question is more related to what combination of the masses that is measured in each of your observations. In particular, the 0nubb observation can be off from the actual mass of the mass eigenstates by a factor of two even if they are degenerate due to Majorana phase interference.

 

[PAllen]

There is a good discussion of this in Chodos et al., Null Experiments for Neutrino Masses, Mod. Phys. Lett. A 7, 467 (1992), http://www.physics.indiana.edu/%7Ekostelec/lay/91chodoskosteleckypottinggates.pdf . Their discussion of whether this means there's Lorentz violation is ... nuanced.

They propose, in discussion of null experiments, that whether a given type of decay occurs is observer dependent. That is, a muon seen to decay by a certain channel by one observer, is seen not to decay this way by a different observer. My reactions is nonsense. Am I missing something? Does a consistent tachyonic neutrino model really incorporate such a thing? I would label it inconsistent if it did.

[edit: Ok, they cover this question a bit later in the paper. It's not totally ridiculous.]

 

[bcrowell]

They propose, in discussion of null experiments, that whether a given type of decay occurs is observer dependent. That is, a muon seen to decay by a certain channel by one observer, is seen not to decay this way by a different observer. My reactions is nonsense. Am I missing something? Does a consistent tachyonic neutrino model really incorporate such a thing? I would label it inconsistent if it did.

[edit: Ok, they cover this question a bit later in the paper. It's not totally ridiculous.]

They don't say that a decay in one frame is a non-event in another. They say that a decay in one frame is an absorption in another. The particle being absorbed is from a background that is present in one frame and not the other. This can supposedly happen because the vacuum is not Lorentz-invariant.

 

[vanhees71]

Again my question: Is there a theory of interacting tachyons with a proper S-matrix and causality intact?

 

[bcrowell]

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.? [...] Again my question: Is there a theory of interacting tachyons with a proper S-matrix and causality intact?

Doesn't the Jentschura paper basically answer this? Jentschura and Wundt, "Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay," Eur.Phys.J.C 72 (2012) 1894,http://arxiv.org/abs/1201.0359

The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. [...] [W]e conclude that rather painful choices have to be made in order to incorporate tachyonic spin-1/2 particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix [...]

This reads to me as a "no" answer to your question.

 

[Orodruin]

This reads to me as a "no" answer to your question.

Conclusion: If neutrinos are tachyons, then we have more problems to worry about than whether or not the measured mass squared values from different experiments agree. Similar to worrying about oscillation experiments having a $\sin^2(2\theta)$ best fit larger than one a few years back.

 

[bcrowell]

Conclusion: If neutrinos are tachyons, then we have more problems to worry about than whether or not the measured mass squared values from different experiments agree. Similar to worrying about oscillation experiments having a $\sin^2(2\theta)$ best fit larger than one a few years back.

I think we saw this in the OPERA superluminal neutrino debacle. Tachyons as real particles are so hard to accommodate theoretically that for six months we had a cottage industry of theorists trying and failing to do so.

 

[Orodruin]

Sadly, it also shows how willingly (some parts of) the community jumps at an experimental anomaly without proper verification of the results ... Had it been true it would of course have been sensational and worthy of the effort, but extaordinary claims should have extraordinarily strong verification.

 

[Vanadium 50]

They say that a decay in one frame is an absorption in another.

Neither "decay" or "absorption" is really the right word here. A tachyonic neutrino is spacelike, not timelike, so terms that describe when it appears and when it disappears are ill-suited to the situation. Using language suitable for timelike intervals to describe spacelike ones will be, at best, confusing.

 

[vanhees71]

I think we saw this in the OPERA superluminal neutrino debacle. Tachyons as real particles are so hard to accommodate theoretically that for six months we had a cottage industry of theorists trying and failing to do so.

Well, but as a theorist I must admit that this is the most shameful issue about this. The only mistake of the OPERA collaboration was the somewhat careless treatment of the issue in the popular-science press. I think it was NY times that took their arXiv paper, which was a cry for help rather than the claim to have found superluminal neutrinos. Then a plethora of "theory papers" appeared at the arXiv, most of which were either trivial, and nobody should have thought that the OPERA collaboration wouldn't have checked such trivial possibilities and many obviously wrong to begin with. There were of course also serious papers showing that the OPERA result provoked huge trouble for theory. At the end it turned out to be a loose connection in a fiber and some bug in an time-measuring oscillator, partially compensating each other. That can happen at such a delicate experiment, but that (pseudo-)theorist put so many non-sense papers on the arXiv is really a waste of time for all the referees who had to review the papers at the journals :-(. Last but not least it made a very bad impression on the public opinion concerning science. In Germany, it's anyway a bit difficult to argue with some people about the necessity and usefulness of expensive big-science experiments and then you have a hard time to explain that such issues take time to be clarified. I had some reactions by lay people in the direction that this is proof that Einstein was wrong with the relativity and all the maths-loaden theoretical physics anyway (math is hated by most laymen in Germany, which has some sad tradition; even Goethe was against math and mathematicians). I usually tell them they shouldn't use their cell phones, androids, computers, and GPS anymore if they think math and physics is so bad :-(. Sorry for this OT rambling.

In any case, one has to check carefully these experimental results on the neutrino mass squares being negative. It may be even a problem with the correct analysis of the meaning of the what was measured and evaluated, given the fact that neutrinos are oscillating. I've no clue about this issue. Even neutrino oscillations are a big mess in the theoretical literature with claims as far reaching as saying that QFT is not applicable (even Lipkin wrote papers with this idea). In my opinion it's the opposite:

It can only be clearly understood using QFT, evaluating processes with proper asymptotic free states (which are necessarily always mass eigenstates and thus cannot be the neutrinos), which means one has to describe the production process and the detection process with wave functions peaking at the space-time points of detection, clearly defining the locations of the "near- and far-side detectors". I think, it's pretty easy, and I should do this calculation once myself to understand the mixing formula right. Then all debates about energy/momentum conservation and all this should be gone. I'm also pretty sure that this calculation must have been already done in the literature, and indeed there are a lot of papers with wave-packet ansatzes in QFT around, but all I've seen so far have strange arguments which seem to overcomplicate the subject, or do you have a good source about this? Perhaps such an analysis could also help to clarify what's really measured as "the electron-neutrino mass squared" in the various experiments described in Ehrlich's interesting paper.

 

[Orodruin]

I think, it's pretty easy, and I should do this calculation once myself to understand the mixing formula right. Then all debates about energy/momentum conservation and all this should be gone. I'm also pretty sure that this calculation must have been already done in the literature, and indeed there are a lot of papers with wave-packet ansatzes in QFT around, but all I've seen so far have strange arguments which seem to overcomplicate the subject, or do you have a good source about this?

Evgeny Akhmedov and Joachim Kopp discussed the QM wave-packet vs QFT approach in 2010: 10.1007/JHEP04(2010)008

 

[vanhees71]

Great! I've to read the paper carefully, but I think there all the issues are thoroughly discussed.

 

[Matterwave]

Well, but as a theorist I must admit that this is the most shameful issue about this. The only mistake of the OPERA collaboration was the somewhat careless treatment of the issue in the popular-science press. I think it was NY times that took their arXiv paper, which was a cry for help rather than the claim to have found superluminal neutrinos.

I think you are forgetting that OPERA themselves issued a press conference on the matter. Sure they again stated during the press conference that they were asking for verification or non-verification of their results, but they knew the kind of sensationalism that the media would attribute to their results and yet they still issued a press conference. =/

 

[Vanadium 50]

I think you are forgetting that OPERA themselves issued a press conference on the matter

Where and when?

 

[OmCheeto]

Where and when?

That might be in reference to the following:

9/22/2011
Here is the msnbc story:
msnbc
It seems that the measurement team is asking for confirmation, so don't be too hasty.

9/22/2011
The researchers are now looking to the United States and Japan to confirm the results.

I'm currently watching the 9/23/2011 webcast, to see if I can confirm this.

ps. Have you ever seen their neutrino detector?
Check out slide #8.
Holy Cow!

 

[Vanadium 50]

I'm currently watching the 9/23/2011 webcast, to see if I can confirm this.

That's a CERN seminar, not a press conference. Matterwave said there was a press conference. I want to know where and when this was.

 

[Nugatory]

It may be just me, but I think that the handling of the OPERA debacle is fundamentally off-topic in this thread.

 

[Matterwave]

That's a CERN seminar, not a press conference. Matterwave said there was a press conference. I want to know where and when this was.

I was only told about the press conference. Because my advisor was quite annoyed about it at the time, and he was quite annoyed that CERN gave a press conference on the matter (he works in Neutrinos and so everyone was bothering him asking him if tachyonic neutrinos were possible). I basically just echoed his words on the matter lol.
Of course it's possible I misheard or misinterpreted what he said.

 

[Vanadium 50]

It may be just me, but I think that the handling of the OPERA debacle is fundamentally off-topic in this thread.

Feel free to split it off. If you really want to be adventurous, maybe you could find the original OPERA thread and graft it on to that.

I was only told about the press conference

I am unaware of one. There was a CERN seminar. CERN, not OPERA, did issue a press release after that.

 

[Matterwave]

I am unaware of one. There was a CERN seminar. CERN, not OPERA, did issue a press release after that.

I do recall now that it was CERN that my advisor was angry at. It's been a few years...cut me some slack. -.-

 

[Vanadium 50]

...cut me some slack. -.-

Hey, it was you who accused OPERA of doing this when they didn't. I'm just setting the record straight - they didn't do what you accused them of. (Which makes this even more off-topic)

 

[Larry Pendarvis]

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.

If there are tachyonic neutrinos, would there be some with a small enough absolute mass that their velocity is great enough to escape from inside an event horizon? And if we can detect them (which is the claim), then a tachyonic telescope could someday give us information back to the Big Bang and even earlier.

 

[Vanadium 50]

Tachyons are spacelike, not timelike, so you can't talk about "escaping" (or decay, or creation). It's like saying "This happened before Fresno". It just doesn't make any sense.

 

[Larry Pendarvis]

Tachyons are spacelike, not timelike, so you can't talk about "escaping" (or decay, or creation). It's like saying "This happened before Fresno". It just doesn't make any sense.

Yes but then why can anyone say they have been detected or deduced? Sounds like a magickal Catch-22, nothing can be said about them, we can't even say they travel faster than light, so why do we read about neutrinos arriving before photons? The "photons are delayed" explanation makes sense, so why does anyone go into this Tachyon stuff at all?
If we can detect neutrinos in any way (which we can), and if you are correct that a Tachyon would be Magickal (spacelike), then obviously we can discount all Tachyon theories.

 

[PeterDonis]

If there are tachyonic neutrinos, would there be some with a small enough absolute mass that their velocity is great enough to escape from inside an event horizon?

I'm not sure how the mass would affect a tachyon's ability to escape from inside an event horizon.

if we can detect them (which is the claim), then a tachyonic telescope could someday give us information back to the Big Bang and even earlier.

We don't need a tachyonic telescope for that; the Big Bang is not a black hole. The problem is not that there are no timelike (or lightlike) paths from the early universe to us now; there are. The problem is that the early universe was very hot and opaque; most of the information about conditions then was quickly erased by thermal fluctuations. If we can figure out a way to detect neutrinos from that era (which won't have interacted as much with the hot, dense matter back then), they won't need to be tachyons to give us information.

 

[PeterDonis]

why does anyone go into this Tachyon stuff at all?

My guess is that it's more fun than just accepting the humdrum explanations for things.

 

[Larry Pendarvis]

I'm not sure how the mass would affect a tachyon's ability to escape from inside an event horizon.

We don't need a tachyonic telescope for that; the Big Bang is not a black hole. The problem is not that there are no timelike (or lightlike) paths from the early universe to us now; there are. The problem is that the early universe was very hot and opaque; most of the information about conditions then was quickly erased by thermal fluctuations. If we can figure out a way to detect neutrinos from that era (which won't have interacted as much with the hot, dense matter back then), they won't need to be tachyons to give us information.

My thought was that as energy is lost, the velocity must increase, since it takes added energy to decrease speed toward light-speed.
My thought was that a spacelike path would get us farther back than either a timelike or a lightlike path. Since our observable universe is just the right size and mass to be a black hole inside of which we are now, the only path out (or in, for us to observe) would be spacelike.

 

[mfb]

If we can figure out a way to detect neutrinos from that era (which won't have interacted as much with the hot, dense matter back then), they won't need to be tachyons to give us information.

PTOLEMY - maybe.

My thought was that a spacelike path would get us farther back than either a timelike or a lightlike path.

No, just potentially to larger distances.

Since our observable universe is just the right size and mass to be a black hole inside of which we are now

The equations for "small" black holes do not work for the universe as a whole.

 

[PeterDonis]

My thought was that as energy is lost, the velocity must increase, since it takes added energy to decrease speed toward light-speed.

This is true, tachyons do behave this way. However, "energy" here is not the same as "mass" in the sense of invariant mass, which is how the term was being used in this thread.

our observable universe is just the right size and mass to be a black hole inside of which we are now

No, it isn't. Check your numbers. Anyway, as has already been pointed out, the spacetime that describes our universe is very different from the spacetime that describes a black hole.

the only path out (or in, for us to observe)

Even if our observable universe were the interior of a black hole (which it isn't, see above and other comments in this thread), this would not follow. We are already inside our observable universe, so we don't have to see out or in.

 

[Larry Pendarvis]

This is true, tachyons do behave this way. However, "energy" here is not the same as "mass" in the sense of invariant mass, which is how the term was being used in this thread.
No, it isn't. Check your numbers. Anyway, as has already been pointed out, the spacetime that describes our universe is very different from the spacetime that describes a black hole.
Even if our observable universe were the interior of a black hole (which it isn't, see above and other comments in this thread), this would not follow. We are already inside our observable universe, so we don't have to see out or in.

If you were inside a black hole whose event horizon is the size of out photon-observable universe, what do you suppose you WOULD see, if there was infalling matter? Outside the event horizon, of course, you would never see that matter reach the event horizon, since it would take infinite time. But inside, as you say the equations don't work so good. Likewise, as the black hole evaporates, what would the disappearing mass look like to those inside? Something leaving? Some negative-mass-squared virtual particles entering and becoming "real" on the inside? Do negative-mass-squared virtual particles carry negative virtual information?

 

[PeterDonis]

If you were inside a black hole whose event horizon is the size of out photon-observable universe, what do you suppose you WOULD see, if there was infalling matter?

You would not see what we see in our actual universe. Once again, the spacetime that describes our actual universe is very different from a black hole spacetime. I suggest familiarizing yourself with both models; look up FRW spacetime (that describes the universe) and Schwarzschild spacetime (that describes a black hole) and see how they're different.

inside, as you say the equations don't work so good.

That's not what I said. The equations of GR work perfectly fine inside a black hole. The solution of those equations that describes a black hole (inside and outside) is very different from the solution that describes the universe as a whole.

as the black hole evaporates, what would the disappearing mass look like to those inside?

An evaporating black hole is yet another different solution to the equations; a classical Schwarzschild black hole does not evaporate. In an evaporating black hole, anyone who falls in will never see the hole evaporate or lose any mass; they will hit the singularity and be destroyed before they can observe any evaporation or mass loss.

(Note that all evaporating black hole solutions are speculative since BH evaporation is a quantum effect and we don't have a complete theory of quantum gravity. What I described just now is one type of speculative solution. Another is that you can't fall into a quantum black hole at all, because quantum effects at the horizon create a "firewall" that destroys anything passing through. Yet another is that quantum effects prevent an actual event horizon from ever forming; all that actually forms is an "apparent horizon" that emits Hawking radiation, but anything that falls inside the apparent horizon will, in principle, eventually come back out again. If you want to go into this in more detail, you should start a separate thread--or search PF for the numerous threads that already exist on this topic.)

 

[Larry Pendarvis]

If you want to go into this in more detail, you should start a separate thread--or search PF for the numerous threads that already exist on this topic.)

Are you aware of an open thread that addresses tachyonic behavior with respect to black holes? If not, I will try to start one.
I am gratified that I have found a forum where an "educated layman" can have his misconceptions corrected. The forums where I am qualified to post are no help, and those where I am not qualified don't want to talk to me.