The speed of light may have been broken.

[Farsight]

What you see is completely irrelevant.

See the Classical analogue section of the wiki article where there's a public-domain image by Daniel Schaal:

The standard model includes neutrino oscillation and it includes a neutrino mass (which is required for neutrino oscillation).

Since when? This CERN press release Particle Chameleon Caught in the act of Changing dated 31 May 2010 said this:

"In the theories that physicists use to explain the behaviour of fundamental particles, which is known as the Standard Model, neutrinos have no mass. For neutrinos to be able to oscillate, however, they must have mass: something must be missing from the Standard Model".

 

[Farsight]

I know I have read about this somewhere, but since there a number of knowledgable posters here...,

Leaving off the tau neutrino due to its short half life, do the electron and muon neutrinos oscillate equally into one another or is there a bias in the oscillation?

Not sure, but see Three-neutrino probabilities and these public-domain images by Strait.

I looked at the area under the black line as compared to the area under the blue line to get an idea of how much time the neutrino spends as an electron neutrino versus a muon neutrino. It looks like the electron neutrino spends more of its time as an electron neutrino, and the muon neutrino spends more of its time as a muon neutrino.

 

[prometheus]

Since when? This CERN press release Particle Chameleon Caught in the act of Changing dated 31 May 2010 said this:

"In the theories that physicists use to explain the behaviour of fundamental particles, which is known as the Standard Model, neutrinos have no mass. For neutrinos to be able to oscillate, however, they must have mass: something must be missing from the Standard Model".

en.wikipedia.org/wiki/Standard_Model_%28mathematical_formulation%29#Including_neutrino_mass. Wow. I googled "standard model neutrino mass."

 

[OnlyMe]

en.wikipedia.org/wiki/Standard_Model_%28mathematical_formulation%29#Including_neutrino_mass. Wow. I googled "standard model neutrino mass."

The reference to the neutrino mass was pretty weak and just a few sections up the same Wiki page a section titled, "The charged and neutral current couplings", discusses The weak force, from the perspective of the Fermi model. Didn't that get upgraded in the early 1970s to the elctro-weak force? (A bit after my achedemic exposure ended)

If you Google, "standard model massless neutrino" one of the hits I found was,

Neutrinos: In and Out of the Standard Model - Stephen Parke - Fermi National Laboratory circa 2006
http://lss.fnal.gov/archive/2006/conf/fermilab-conf-06-527-t.pdf
The particle physics Standard Model ... In this model Neutrinos are massless. Yet recent evidence points to the fact that neutrinos are massive particles with tiny masses compared to the other particles in the Standard Model...

In this series of Lectures, I will review the properties of Neutrinos In the Standard Model and then discuss the physics of Neutrinos Beyond the Standard Model.

I don't claim any expertise on the standard model but it does seem you can find a great deal of different opionions on the web and Wiki, even from what appear to be reputable sources.

Wiki has sometimes suprized me. The problem I suspect is that if you don't have some basic understanding of what is current, it can also be misleading. It does not seem to have a consistent standard or filter for what is posted. Kind of reader be ware at times.

 

[Reiku]

The reference to the neutrino mass was pretty weak and just a few sections up the same Wiki page a section titled, "The charged and neutral current couplings", discusses The weak force, from the perspective of the Fermi model. Didn't that get upgraded in the early 1970s to the elctro-weak force? (A bit after my achedemic exposure ended)

If you Google, "standard model massless neutrino" one of the hits I found was,



I don't claim any expertise on the standard model but it does seem you can find a great deal of different opionions on the web and Wiki, even from what appear to be reputable sources.

Wiki has sometimes suprized me. The problem I suspect is that if you don't have some basic understanding of what is current, it can also be misleading. It does not seem to have a consistent standard or filter for what is posted. Kind of reader be ware at times.

The mass does the same thing to coupling particles and antiparticles together as you would find from a majorana equation. Nuetrino's are spin 1/2 so they are fermions:

$$-i(\alpha \hat{p})c\psi + \beta M c^2 \psi = i\hbar \partial_t \psi$$

This can be re-written as:

$$i\hbar \frac{\partial \phi}{\partial t} = -ic\hbar \vec{\sigma} \cdot \nabla_{\phi} + M c^2 \phi'$$

$$i\hbar \frac{\partial \chi}{\partial t} = -ic\hbar \vec{\sigma} \cdot \nabla_{\chi} + M c^2 \chi'$$

as two component equations, when this equation is under a Weyl representation

$$i\hbar \frac{\partial \eta}{\partial t} = -ic\hbar \vec{\xi} \cdot \nabla \eta + M c^2 \xi$$

and

$$i\hbar \frac{\partial \xi}{\partial t} = -ic\hbar \vec{\eta} \cdot \nabla \xi - M c^2 \eta$$

$$\eta$$ and $$\xi$$ are in fact coupled to a limit where $$M$$ is nonzero. Under mathematcial strutiny, the fact that the Nuetrino has such a ridiculously small mass incorporates the similar contention that the nuetrino could act more or less like a particle with no mass.

With the limit where $$M=0$$ reduces to the Weyl equation

$$\frac{\partial \xi v'}{\partial} = -c\vec{\sigma} \cdot \nabla \xi v'$$

This only suits right solutions for antiparticles for nuetrinos $$v'$$. So it may not be troublesome or cumbersome to think of a mass under the Weyl limit. In fact since the particles mass is so small, it more or less behaves like a particle without a mass. Plus as we see it is easy to invoke an equation which can satisfy only left moving nuetrino's since no right handed one's have been observed in nature.

 

[James R]

Well, that clears that up, I guess. :shrug:

 

[OnlyMe]

Well, that clears that up, I guess. :shrug:

Could you explain it to me then, please?

Actually, I must admit once more, it has been too long since I dealt with mathematics on that level, without a better narrative I have to work though it very slowly and often look up the math and symbols elsewhere before I can begin to follow it. That is my own issue.

Sometimes I go to the trouble and sometimes I just take a pass.

 

[Farsight]

It's above my pay grade. So is Weyl Spinors and Dirac's Electron Equation by William Straub, but I thought I'd mention it. It was written in 2005, and includes this:

"By following the spins and directions of the outgoing muons, Lederman was able to deduce the following rule:
1: ALL NEUTRINOS ARE LEFT-HANDED (described by φL)
2: ALL ANTINEUTRINOS ARE RIGHT-HANDED (described by φR)
(Lederman received the Nobel Prize for his experimental verification of parity violation in 1988.) Neutrinos must be massless and travel at the speed of light if these laws are to hold. Otherwise, a Lorentz transformation could be used to effectively make a neutrino travel in a direction opposite to its line of motion, and the above rules would not hold; in that case, neutrinos and their antimatter partners would both exhibit left- and right-handedness. In recent years, there has been speculation that neutrinos have a small but non-zero mass, and that they can convert into different types (there are three kinds of neutrino). This belies the fact that to date no right-handed neutrinos have ever been observed, but the jury is still out on this".

On the off chance that it's relevant, does anybody know anything about travelling breathers?

 

[Reiku]

Could you explain it to me then, please?

Actually, I must admit once more, it has been too long since I dealt with mathematics on that level, without a better narrative I have to work though it very slowly and often look up the math and symbols elsewhere before I can begin to follow it. That is my own issue.

Sometimes I go to the trouble and sometimes I just take a pass.

Right, so what is this again?

$$\frac{\partial \xi v'}{\partial} = -c\vec{\sigma} \cdot \nabla \xi v'$$

I think we established that it described antineutrinos.... don't know how accurate that is at the moment, I often forget the signs. The second equation in your coupled set up vanish because $$\phi = \chi$$ when $$M=0$$. Now this is actually related to parity (you may understand parity under CPT-symmetry.) The Weyl equation is only permitted for right handed antineutrino's since a nuetrino is only ever left handed.

For that purpose you may introduce a transformation $$\alpha \rightarrow -\alpha$$. Anticommutator relations are preserved in the Dirac Equation which would describe the neutrino. The transformation also effects $$\sigma \rightarrow -\sigma$$ so the Weyl equation becomes

$$\frac{\partial \xi v}{\partial} = c\vec{\sigma} \cdot \nabla \xi v$$

For a nuetrino. Simply a neutrino must have a mass at a specific limit which allows us to make these valid transformations.

 

[OnlyMe]

Right, so what is this again?

$$\frac{\partial \xi v'}{\partial} = -c\vec{\sigma} \cdot \nabla \xi v'$$

I think we established that it described antineutrinos.... don't know how accurate that is at the moment, I often forget the signs. The second equation in your coupled set up vanish because $$\phi = \chi$$ when $$M=0$$. Now this is actually related to parity (you may understand parity under CPT-symmetry.) The Weyl equation is only permitted for right handed antineutrino's since a nuetrino is only ever left handed.

For that purpose you may introduce a transformation $$\alpha \rightarrow -\alpha$$. Anticommutator relations are preserved in the Dirac Equation which would describe the neutrino. The transformation also effects $$\sigma \rightarrow -\sigma$$ so the Weyl equation becomes

$$\frac{\partial \xi v}{\partial} = c\vec{\sigma} \cdot \nabla \xi v$$

For a nuetrino. Simply a neutrino must have a mass at a specific limit which allows us to make these valid transformations.

I guess here I have to agree with James, that clears it all up???

As far as I was aware antineutrinos are hypothetical. Some even suggest the neutrino may be its own anti particle. In any case anti neutrinos appear only in the mathematical models as far as I am aware. i.e. Never been detected.

As far as the math goes, still in the same place as earlier. Define your terms and use full derivations or I have to get out the books and look too much up.

So you understand this better, while physics was my major, my achedemic exposure was late 1960's. The weak nuclear force was still just the weak nuclear force. The elctro-weak force had not yet been worked out. Calculators were not allowed in classes or for tests (we were expected to use pencils and paper, maybe a slide rule), and computers were pretty much limited to mainframes a few minis perhaps.., no internet! Then I spent forty years working in an unrelated field.

So, you see why when the commentary in a post does not fully explain the math, I wind up deciding, is it worth the effort to go look the background information up? or maybe not! I can do it if it seems important or interesting, that is not always the case...

BTW I never posted any associated math, so I am fairly certain that portion in bold above designates your clarification should have been directed at someone else, who maybe did not need it anyway.

 

[Reiku]

I guess here I have to agree with James, that clears it all up???

As far as I was aware antineutrinos are hypothetical. Some even suggest the neutrino may be its own anti particle. In any case anti neutrinos appear only in the mathematical models as far as I am aware. i.e. Never been detected.

As far as the math goes, still in the same place as earlier. Define your terms and use full derivations or I have to get out the books and look too much up.

So you understand this better, while physics was my major, my achedemic exposure was late 1960's. The weak nuclear force was still just the weak nuclear force. The elctro-weak force had not yet been worked out. Calculators were not allowed in classes or for tests (we were expected to use pencils and paper, maybe a slide rule), and computers were pretty much limited to mainframes a few minis perhaps.., no internet! Then I spent forty years working in an unrelated field.

So, you see why when the commentary in a post does not fully explain the math, I wind up deciding, is it worth the effort to go look the background information up? or maybe not! I can do it if it seems important or interesting, that is not always the case...

BTW I never posted any associated math, so I am fairly certain that portion in bold above designates your clarification should have been directed at someone else, who maybe did not need it anyway.

Where do you want me to start...? The Dirac equation?

In all honesty, I thought the operations where pretty much standard. You don't need to look far and deep to understand the mathematical operations here.

 

[Reiku]

And what do you mean we haven't observed antineutrinos?

We have observed them.

''The antineutrinos observed so far all have right-handed helicity (i.e. only one of the two possible spin states has ever been seen), while the neutrinos are left-handed.''

http://en.wikipedia.org/wiki/Antineutrino#Antineutrinos

So I won't be taking this further until you actually read up on them first.

 

[OnlyMe]

And what do you mean we haven't observed antineutrinos?

We have observed them.

''The antineutrinos observed so far all have right-handed helicity (i.e. only one of the two possible spin states has ever been seen), while the neutrinos are left-handed.''

http://en.wikipedia.org/wiki/Antineutrino#Antineutrinos

So I won't be taking this further until you actually read up on them first.

Wiki seems to present some confusing information on this subject. In one place only left handed neutrinos have been detected in another right handed....

I could not locate a non-Wiki source for the actual detection of the antineutrino. The theory predicts such and decays in which they are predicted do occur, but trying to dig out any experimental observation that supports the antineutrino as a separate particle is more work than I want to do at this time.

As I said some, even suggest that the neutrino is its own antiparticle.

As far as explaining the math don't bother. If I wanted to go back to school on it I would, but I have no horse in the race.., I am retired.

My intent had been to remind folks that some lay people read these forums and are interested. Some common sense explanation of what you are talking about would go a long way, for many readers.

 

[Reiku]

Wiki seems to present some confusing information on this subject. In one place only left handed neutrinos have been detected in another right handed....

I could not locate a non-Wiki source for the actual detection of the antineutrino. The theory predicts such and decays in which they are predicted do occur, but trying to dig out any experimental observation that supports the antineutrino as a separate particle is more work than I want to do at this time.

As I said some, even suggest that the neutrino is its own antiparticle.

As far as explaining the math don't bother. If I wanted to go back to school on it I would, but I have no horse in the race.., I am retired.

My intent had been to remind folks that some lay people read these forums and are interested. Some common sense explanation of what you are talking about would go a long way, for many readers.

I don't have the time to teach lays here. If they want to understand what is going on, I advise them to do a little research into the topics they obviously are desiring to read. As for antineutrino's, some places have set up antineutrino detectors...

http://neutrinos.llnl.gov/

 

[Reiku]

And if antineutrinos haven't been observed, I ask, 'how can it be part of the understanding of the electron family?'

http://www.universetoday.com/51645/antineutrino/

 

[OnlyMe]

I don't have the time to teach lays here. If they want to understand what is going on, I advise them to do a little research into the topics they obviously are desiring to read. As for antineutrino's, some places have set up antineutrino detectors...

http://neutrinos.llnl.gov/

This link just returns a blank turquoise page for me.

And if antineutrinos haven't been observed, I ask, 'how can it be part of the understanding of the electron family?'

http://www.universetoday.com/51645/antineutrino/

There are many things that are accepted within theoretical models and included in tables etc. that have yet to be experimentally detected.

Hey, I am not saying people are not looking. Only that I had not seen the results confirming detection.

 

[Reiku]

If you read the lastt link, you would see I gave evidence for its discovery

''Beta Decay which produces electrons also produces (electron) antineutrinos. Wolfgang Pauli proposed the existence of these particles, in 1930, to ensure that beta decay conserved energy (the electrons in beta decay have a continuum of energies) and momentum (the momentum of the electron and recoil nucleus – in beta decay – do not add up to zero); Enrico Fermi – who developed the first theory of beta decay – coined the word ‘neutrino’, in 1934 (it’s actually a pun, in Italian!). It would be a quarter of a century before the (electron) antineutrino was confirmed, via direct detection (Cowan and Reines did the experiment, in 1956, and later got a Nobel Prize for it).''

 

[OnlyMe]

If you read the lastt link, you would see I gave evidence for its discovery

''Beta Decay which produces electrons also produces (electron) antineutrinos. Wolfgang Pauli proposed the existence of these particles, in 1930, to ensure that beta decay conserved energy (the electrons in beta decay have a continuum of energies) and momentum (the momentum of the electron and recoil nucleus – in beta decay – do not add up to zero); Enrico Fermi – who developed the first theory of beta decay – coined the word ‘neutrino’, in 1934 (it’s actually a pun, in Italian!). It would be a quarter of a century before the (electron) antineutrino was confirmed, via direct detection (Cowan and Reines did the experiment, in 1956, and later got a Nobel Prize for it).''

Don't spend too much time on this. I get all of that. The point I was making is that as far as I can tell, from several papers apart from Wiki the only way neutrinos and antineutrinos can be told apart depends on how they are generated, not differences in detection.., with the one exception that antineutrinos seem to change flavor a bit more often.

Again I was looking for an experimental observation that confirmed, the theoretical difference.

Like I said don't waste too much time on this.

 

[Reiku]

Don't spend too much time on this. I get all of that. The point I was making is that as far as I can tell, from several papers apart from Wiki the only way neutrinos and antineutrinos can be told apart depends on how they are generated, not differences in detection.., with the one exception that antineutrinos seem to change flavor a bit more often.

Again I was looking for an experimental observation that confirmed, the theoretical difference.

Like I said don't waste too much time on this.

Why? About ten minutes ago you were wanting me to spend time explaining this stuff to the laymen, but on the second breath you don't want me to spend much time on it at all?

We have observed antineutrino's. Just because you hadn't came across this information, you were ready to pass it off as ''wiki being unclear.'' There is ample evidence provided by wiki the antineutrino has been observed

http://en.wikipedia.org/wiki/Cowan–Reines_neutrino_experiment

 

[OnlyMe]

Why? About ten minutes ago you were wanting me to spend time explaining this stuff to the laymen, but on the second breath you don't want me to spend much time on it at all?

We have observed antineutrino's. Just because you hadn't came across this information, you were ready to pass it off as ''wiki being unclear.'' There is ample evidence provided by wiki the antineutrino has been observed

http://en.wikipedia.org/wiki/Cowan–Reines_neutrino_experiment

Really there is no reason to get worked up.

The point I was making is that the experiments detect antineutrinos not by any signature observed in the detector, but by where they came from. This is defining the particle detected by the theoretical model.

Reines and Cowan Detected the first neutrinos, circa like.., the early 1950's. The only thing that distinguishes antineutrinos from neutrinos as far as I have seen in the experimental data, is determined by the source not the detector. The difference remains theoretical, thus some (theorists) still consider the possibility that the neutrino is its own antiparticle.

The theory does accurately predicts many things. That does not make it proof in and of itself. It is predictive more than descriptive. To say anything else is about the same as saying, we know it all, we may as well go home.

You really want to spend more time on this?