Chameleon-Like Behavior of Neutrino Confirmed 191
Anonymous Apcoheur writes "Scientists from CERN and INFN of the OPERA Collaboration have announced the first direct observation of a muon neutrino turning into a tau neutrino. 'The OPERA result follows seven years of preparation and over three years of beam provided by CERN. During that time, billions of billions of muon-neutrinos have been sent from CERN to Gran Sasso, taking just 2.4 milliseconds to make the trip. The rarity of neutrino oscillation, coupled with the fact that neutrinos interact very weakly with matter, makes this kind of experiment extremely subtle to conduct. ... While closing a chapter on understanding the nature of neutrinos, the observation of neutrino oscillations is strong evidence for new physics. The Standard Model of fundamental particles posits no mass for the neutrino. For them to be able to oscillate, however, they must have mass.'"
Excited! (Score:5, Insightful)
Reading TFS made me very excited about the potential fundamental developments in physics. Except I don't know a thing about physics, so I'm really not sure what I'm excited about. All these words like muon, tau, and neutrino have little place in my everyday life, but they sound so interesting!
This is what the Average American must feel like when they hear stories about Web x.0 laden with the latest buzzwords on CNN. I can finally relate!
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The significance of this discovery is that the Standard Model is wrong. The transformation of neutrinos mean they have mass, whereas the Standard Model predicts that they have no mass. Neutrinos having mass mean they interact with matter, and that they can constitute dark matter. Or something like that. This is about all I know/or think I know about the subject.
I hope I'm alive when the Next Big Nerd figures out the Next Big Thing regarding a Theory of Everything.
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How exactly does the standard model demand that neutrinos have mass?
The SM works just fine with massive neutrinos. After all, most of the fun stuff in the SM concerns the gauge couplings; whether or not a few fermions have mass doesn't affect the overall theory.
Neutrinos could constitute dark matter if they had *more* mass. But we can put an upper limit on the masses of the electron, muon, and tau neutrinos, and that's not enough to account for the amount of dark matter we know is out there. Some sort of ex
Re:Excited! (Score:5, Insightful)
Imagine your definition of sports cars (massless particles, thus no time) didn't include convertibles (time-based oscillation). For a car to be convertible, it has to be a luxury car (have mass), not a sports car. Then, you see a sports car drive by a few times, and one of the times the top is down. You have to wonder, is it not really a sports car (the way we think neutrinos work must change), or is your definition of sports cars broken (the way we think mass works must change)?
How's that sound?
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Re:Excited! (Score:5, Interesting)
Glad to oblige.
Imagine a highway. All the north-bound cars are WHITE Toyota Camrys, and all the south-bound cars are BLACK Toyota Camrys. All the cars are moving very very very fast. At a certain point in the road, workers open gates that cause the two streams of traffic to plow into each other, head on. At the crash site, common sense would tell you that pieces of Toyota Camrys would come flying out, but instead, complete vehicles of other makes and models (Honda Civics and Nissan Sentras, many others, including vehicles larger than two Camrys, like Peterbilt 18-wheelers) appear instead. After a few seconds, some of these vehicles break apart, and become other vehicles, say a Peterbilt breaks apart and becomes a Ford F-150 and two Harley Davidson motorcycles. Particle physicists make a living by crashing different streams of vehicles into each other and observing the new vehicles that come out. They've put together a list of these, like "Peterbuilt --> Ford F-150 + 2(Harley Davidson Motorcycles)". They call this list the Standard Model. This new experiment shows that sometimes, after a while, one of the Harleys suddenly changes models, say from a Fat Boy to an Electra Glide.
Hope this helps.
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Particle physicists make a living by crashing different streams of vehicles into each other and observing the new vehicles that come out.
Are you sure you're not talking about the Mythbusters?
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Re:Excited! (Score:5, Insightful)
Chameleon-Like Behavior? (Score:5, Funny)
I don't see how changing from one thing into another is "chameleon-like behavior". I have never heard of a chameleon turning into a skink, or anything else for that matter
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I don't see how changing from one thing into another is "chameleon-like behavior". I have never heard of a chameleon turning into a skink, or anything else for that matter
Try combining a chameleon with a hammer or a microwave. Then you will understand the experiments analogy.
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No, it may not. The neutrino's energy (which is the exact analog to a photon's "colour") is conserved. The rest energy changes, but this means the original neutrino and the resulting one are on different rest referentials (and the change in mass is very small, inside the uncertainty principle). There is nothing "yet to be discovered", except possibly what is the mass generation mechanism (Dirac, like all other particles, or Marjorana).
"Chameleon-like behaviour" is just the "scientific" journalist's way of s
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Neutrinos do not see the strong force, which is where the color charge comes from. Neutrinos interact with the weak force, and gravity. They have no color charge, and no electric charge, so they are basically dumb to the idea of the strong and electromagnetic forces.
Neutrinos acting like Microwaves (Score:2)
Just find the people from the Movie 2012 to help you figure out how to make the Neutrinos act like Microwaves, then you could totally make this experiment easy! ... seriously... did anyone else need a friend to "dumb up" the science dialog for them?
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Just find the people from the Movie 2012 to help you figure out how to make the Neutrinos act like Microwaves, then you could totally make this experiment easy! ... seriously... did anyone else need a friend to "dumb up" the science dialog for them?
I had the pleasure of (involuntarily) watching that piece of shit this weekend. Sadly, the liberties taken with science were the least of that movie's problems. I'd start with the terrible script, lack of editing (solid hour too long), screwed up pacing, repe
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Compared to that, they could have said that neutrinos turn into faerie dust and I'd have been fine.
This I at least could have understood.
None of their scientific babbling made any sense to me until my friend's boyfriend explained what the heck they were trying to say.
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Was their science advisor a magic 8-ball?
My sources say no.
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oscillation (Score:3, Interesting)
The Standard Model of fundamental particles posits no mass for the neutrino. For them to be able to oscillate, however, they must have mass.
Unless oscillation is the fundamental thing and mass is just a sometimes effect of oscillation... but then IANAP.
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They explained this on NOVA a while ago (Score:2)
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Alas my humor remains too subtle...
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No matter. Give it some time and things might change.
How in the universe? (Score:4, Interesting)
How could something have mass and so weakly interact with normal matter? My understanding is that most neutrinos pass through the earth unmolested.
(insert obligatory Catholic priest joke here).
I's thought that neutrinos being massless made this possible.
Re:How in the universe? (Score:5, Funny)
Re:How in the universe? (Score:5, Informative)
How could something have mass and so weakly interact with normal matter?
Neutrinos are thought to have a very small mass. So exceedingly small that they barely interact with anything (they also have no charge, so they are even less likely to interact). But zero mass and really, really, really small but not zero mass, are two different things.
Re:How in the universe? (Score:5, Informative)
How could something have mass and so weakly interact with normal matter?
Neutrinos are thought to have a very small mass. So exceedingly small that they barely interact with anything (they also have no charge, so they are even less likely to interact).
The fact that they barely interact with anything has nothing to do with the fact that they are nearly massless. Photons are massless and they interact with anything that carries an electric charge. Electrons are much lighter than muons, but they are just as likely to interact with something. The only force that gets weaker as the mass goes down is gravity, which is by far the weakest of the fundamental forces.
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Photons also interact with gravity - stellar masses and above can cause gravitational lensing.
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>>I thought that phenomenon was caused by the curvature in space-time, so IMHO it wasn't "interaction" per-se.
Gravity is just curvature of time-space.
Maybe.
The really interesting thing about photons, to me, is that time doesn't pass for them (because they're massless). So if you were a photon, would you experience all points in spacetime simultaneously?
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> So if you were a photon, would you experience all points in spacetime
> simultaneously?
You wouldn't "experience" at all.
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The fact that they barely interact with anything has nothing to do with the fact that they are nearly massless. Photons are massless and they interact with anything that carries an electric charge. Electrons are much lighter than muons, but they are just as likely to interact with something. The only force that gets weaker as the mass goes down is gravity, which is by far the weakest of the fundamental forces.
Good point, I should have been more expansive. There are definitely many more reasons that neutrinos are non-interactive.
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I
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Photons have no rest mass and no charge. They aren't hard to detect.
Re:How in the universe? (Score:5, Interesting)
Neutrinos only interact through the weak forces, which require them to be extremely close to other particles with which they interact. Such interactions also require the neutrino to have a lot of energy, since the force-carrying particles are quite massive. This is why all these experiments use neutrinos generated by very energetic reactions (accelerators, the sun, cosmic rays, etc.).
When I worked with BooNE, an experiment researching neutrino osculations, our detector was a 40 ft tank lined filled with clear, food-grade mineral oil and lined with photo tubes capable of detecting a few photons. The neutrinos were generated by bursts of protons crashing into a special block (I don't remember the material), and the byproducts at the given energy levels would be one type of neutrino. The interactions from different types of neutrinos would have different decays, which produced different signature rings of photons on the walls of the detector. In generating 10^9 + neutrinos, we only expected a handful of interactions.
Gravity is also on the table, but it's impossible to measure neutrinos based on that.
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neutrino osculations
You learn something new every day [wiktionary.org]
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Photons are also massless and also interact with matter. Photons/electrons are also waves/particles which make them rather interesting. There might be different types of neutrinos. Some with mass, other with none. Since neutrinos are the results of a proton collision, the opposite - recreating a proton with a neutrino/strange quark collision might also explain this "mass-like" behaviour. Interesting nonetheless.
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How could something have mass and so weakly interact with normal matter? My understanding is that most neutrinos pass through the earth unmolested.
(insert obligatory Catholic priest joke here).
I's thought that neutrinos being massless made this possible.
I'm not sure why this was modded flamebait (is a reference to our propensity to joke about the Catholic church flamebait?), but to answer the question, being massless has nothing to do with a particle's ability to interact weakly. Quarks can interact weakly (as well as strongly and electromagnetically) and they certainly have mass. The top quark, in fact, is quite heavy.
Re:How in the universe? (Score:5, Interesting)
It isn't their mass that makes them so unlikely to interact with ordinary matter. It is because they don't interact via the Electromagnetic or Strong Nuclear forces (at least not at the energies we are discussing here). Because we can't use gravity to directly detect them (or any other elementary particle) because of its incredible weakness, that leaves only the Weak Nuclear force, which is *extremely* short range. That short range means that a neutrino must pass *very* close to an electron or a quark to have any chance what-so-ever of interacting: Something like 10 to the minus 16th power meters. For comparison, a hydrogen atom has a diameter of around 10 to the minus 10th meters - or a million times larger.
A single *proton* has a diameter of around 10 to the minus 15th meters - or still 10 times larger than the distance in question.
So hundreds of neutrinos could pass directly through the very nucleus of an atom and *still* not interact with anything. And that is matter with a density more than a trillion times as dense as anything in your ordinary experience.
To neutrinos, other matter barely exists at all.
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You have mass. Now, tackle an elephant.
In a similar way, neutrinos have so little mass compared to even hydrogen that they don't really interact.
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Supposedly if you took a hydrogen atom and scaled it up so that the single proton nucleus was the size of a basketball, the electron would end up as a tiny spec "orbiting" miles away. The proton is the center, and the electron forms the outer edge of the atom. But all of that space in between is empty. Even take a heavier atom, like lead and scale it up. You get more basketballs hanging out at the center, then a whole bunch of empty space, then a bunch of tiny electrons flying around. The heaviest, most d
Douglas Adams was right (Score:2)
Robust result? (Score:3, Insightful)
Offhand, this doesn't seem like a very robust result - we're only talking about a single observation, after all. Does the equipment allow them to determine the source of the observed tau neutrino? How can they be sure that it came from the muon neutrino stream from CERN rather than being random background?
There's also no mention of a control, e.g., another tau neutrino detector close to the same muon neutrino source. Even if there was, is a single detection versus no detections statistically significant?
Oscillation and the conservation of energy? (Score:5, Insightful)
1. If an electron neutrino can spontaneously transform to a tau neutrino with higher mass, where exactly does the required energy come from? Alternatively, when a tau neutrino transforms to an electron neutrino, where does the extra energy disappear?
2. If neutrinos have mass, then they are restricted to speeds below c. If they are accelerated to near c, then according to the relativistic energy-momentum equations they should have colossal mass, not miniscule (just like electrons, for example). Is there any evidence of observing neutrinos with huge energies?
The Wiki article about neutrino oscillation paints the picture that the oscillation is a pseudo-illusionary quantum mechanical effect, and therefore questions like the two above are meaningless. Smells more like handwavium to me.
Could a real physicist push back the veil of shadows one bit? Pretty please? =)
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(ob-IANAP)
"Mass" means "proper mass" (or "rest mass"). The concept of "relativistic mass" (i.e. calling it such) has been out of vogue for more than 40 years.
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the mass is a scalar, so it cannot change in Lorentz transformations. Scalars are not subject to change in Lorentz transformations. Therefore it's mot mass that increases, but momentum, you know p=m*v. Velocity is a vector, and in fact that vector is the value that makes momentum going to infinity. It seems as if mass was increasing, but in fact it is momentum increasing. But also it is not velocity strictly increasing to inf, because velocity isn't going to infinity either. I'd need to show you the derivat
Re:Oscillation and the conservation of energy? (Score:4, Informative)
I'm not a "real" physicist - but I did study this at undergrad level, so here goes:
Heisenberg's Uncertainty Principle ( http://en.wikipedia.org/wiki/Uncertainty_principle [wikipedia.org] ) states that there must always be a minimum uncertainty in certain pairs of related variables - e.g. position and momentum, i.e. the more accurately you know the position of something, the less accurately you know how it's moving. Another related pair is energy and time - the more accurately you know the energy of something, the less accurately you know when the measurement was taken.
(disclaimer - this makes perfect sense when expressed mathematically, it onlysounds like handwavery when you translate it into English, as words are ambiguous and mean different things to different people)
Anyway, this uncertainty means that there is a small but non-zero probability of a higher-energy event occuring in the history of a lower-energy particle (often mis-stated as "particles can borrow energy for a short time, but check the wiki page for a more accurate statement). It sounds nuts, I know, but it has many real-world implications that have no explanation in non-quantum physics. Particles can "tunnel" through barriers that they shouldn't be able to cross, for instance - this is how semi-conductors work.
By implication, there is a small probability of the neutrino acting as if it had a higher energy, and *this* is how neutrino-flipping occurs without violating conservation of energy.
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> 1. If an electron neutrino can spontaneously transform to a tau neutrino
> with higher mass, where exactly does the required energy come from?
> Alternatively, when a tau neutrino transforms to an electron neutrino, where
> does the extra energy disappear?
Think of it as oscillating between a higher rest-mass state moving slower and a lower rest-mass state moving faster (yes, I know that isn't "really" what happens). The momentum doesn't change.
> 2. If neutrinos have mass, then they are restri
How science is viewed by the Normals (Score:3, Insightful)
This reminds me of the /. post a few days ago about those who are ignorant of science and proud to be so. This is how I think some of them might perceive this situation:
Last week, a Normal would have been told by Those Who Do Science that a neutrino has no mass, and that is the end of the matter. A non-physicist has nothing to contribute to the discussion. Persistent disagreement amounts to sheer ignorance, so keep quiet.
But now, it would appear that either neutrinos have mass or the Standard Model is wrong. Science has revealed its own ignorance. Everyone who was wrong last week is right this week. But the message to the Normals remains the same: it doesn't matter that we were wrong last week; eventually, We Who Do Science get it right. You still have nothing to say. Keep quiet.
The Normals perceive the above and conclude that it's hypocrisy. Hence, they can ignore science and be proud that they are smart enough to avoid hypocritical know-it-all's.
BTW: Yes, this is post if Offtopic, but it's not Flamebait or Troll. I'm not agreeing with this POV; I'm passing on my perception of it. And how else can one discuss the interrelationship between topics without being regarded as Offtopic in regards to one post or the another?
I wish I had an answer of how to fix the above problem. Eliminating arrogant PhD's would be helpful, but that would leave all of the arrogant Normals -- and the rest of us aren't free from shocking amounts of arrogance at times, either. We could use another Sagan to highlight that math+science is a process that anyone can join in on once the ground-rules are mastered. However, it would me imperative that the next spokesperson not be hostile to religion -- the Normals are hypersensitive to this issue, and getting in their face about the matter only increases the alienation. [Not saying that Sagan was hostile to religion -- just saying then next spokesperson cannot be.]
Re:Who would have guessed (Score:5, Funny)
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Where's the Eddy Bauer version fit in; between Sports and Luxury?
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This particularly applies to women. If you are offered a model ask for a real one instead. Real women are far more user friendly.
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Still not right (Score:2)
Something PROVEN TO BE missing from the Standard Model? Was shocking when it was first shown by SNO and SuperK 10 years ago.
All Opera will hopefully eventually show is that the ALREADY DISCOVERED neutrino oscillations convert muon neutrinos into predominantly tau neutrinos....and yes I use the future tense. One axiom of particle physics is that you never, ever believe single events because the statistics are simply too low to be certain that there is not a background fluctuation (no matter how low you think your backgrounds are - suppose you missed something?).
Re:What if... (Score:5, Informative)
You'd need a pretty complex theory to get non-mass oscillations to match all the data we got over the past 12 years, which is very compatible with a three-state, mass-driven oscillation scenario. Besides, you'd have to explain more than what the current "new standard model" (the SM with added neutrino masses) does if you want your theory to be accepted. If two theories explain the same data equally well, the simplest is more likely.
Re: What if... (Score:3, Informative)
If two theories explain the same data equally well, the simplest is more likely./quote?
Make that "more preferred". In general we don't know anything about likelihood.
The thing about Occam's Razor is that it filters out "special pleading" type arguments. If you want your pet in the show, you've got to provide motivation for including it.
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Thanks, good catch.
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This is not a theory. It was demonstrated experimentally.
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God did it.
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If two theories explain the same data equally well, the simplest is more likely.
Is that really the case? That seems like it's a very hominid-centric assumption. I can't think of any counter examples but it seems very naïve to assume that the nature of the Universe would be simple...? Though, perhaps my understanding is limited.
Example: Relativity vs Newton (Score:3, Insightful)
If two theories explain the same data equally well, the simplest is more likely.
Is that really the case? That seems like it's a very hominid-centric assumption. I can't think of any counter examples but it seems very naïve to assume that the nature of the Universe would be simple...? Though, perhaps my understanding is limited.
Well it's VERY difficult to detect relativistic effects at human walking speed but they are still there. So you could create a whole stack of data that supports Newtonian physics over Relativity on that basis, but Relativity, though more complex is a more accurate description of the Universe.
When something doesn't fit your model, more experimentation and experience is needed, and most importantly you may need to do DIFFERENT experiments to determine whether a simpler or more complex theory is more accurate.
Re:What if... (Score:5, Insightful)
The point is that, if two different theories have the exact same predictions, they are for all intents and purposes the same theory, and describe the same universe. If that is the case, why would you spend more time teaching and learning the more complex one, when a simple explanation is enough and (by definition, since they have the same predictions) you can't tell which one is correct?
Of course, if the new theory offers a good explanation to current data, but has a different prediction than the standard model in other, still-non-tested scenarios, the theory is more interesting. You can test it at the new scenario, and you'll be able to tell them apart. This is why* we study, for example, supersymmetry and extra dimensions theories: they behave just like the standard model where we have tested it, but can be different in other cases such as the LHC.
* = of course there are other motivations to develop the theories, but they are taken seriously because they are compatible with the SM and are testable. A theory whose predictions were exactly the same as the SM for every case wouldn't be worth studying, simply because you'd never be able to see if it is right.
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It's that all the bits of the nature of the Universe that we /do/ understand are simple, so we figure that the bits we're still trying to understand are probably also simple.
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The basic idea isn't that the 'simpler' theory wins (relativity >> newton in complexity) but rather the simplest model that explains all the data. A model that adequately explains everything we've observed without resorting to special cases (i.e. "the universe does X unless these extremely specific conditions are met, in which case it does Y') is far more likely to be true than a model that resorts to special cases, since the universe doesn't exactly check to see if the planets happen to be aligned wh
Re:What if... (Score:5, Insightful)
No it is not more likely. That’s a common misconception. It is only the one you should pursuit first. Actual facts make things more likely. Not simplicity. Simplification is a artifact injected by humans, because they prefer it for efficiency. (What is commonly calley “laziness”)
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In our experience nature also prefers simplicity. Note that simplicity has a special meaning in this case. It is more likely, based on all our experiience, that a theory that manages to explain more with fewer rules is correct.
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You should first learn to make logically sound arguments.
Experience is not likeliness. It is only a hint that this could be more likely.
Example: Go to Africa. Your experience of nearly all people around you being white will suddenly not have anything to do with the likeliness anymore. And it does not need to be Africa. Some parts of the US suffice. Or South America for example.
As you see, there are more factors to likeliness than just “pure experience”. Because experience is a function with a ne
Re:What if... (Score:5, Insightful)
Re:What if... (Score:4, Funny)
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It actually is true! (Score:2)
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I actually don't mean to be ironic here. Perhaps they're mathematically the same. IANAPP (I am not a particle physicist). Still, just because something appears to change doesn't mean that it wasn't the observer that changed, right?
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Why couldn't the particle stay the same, but the whole universe oscillates around it?
Did Spock come from the future to tell you that you discovered this?
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No, they're not the same. Mass-induced oscillation is a known fact in particle physics (search for "neutron kaon oscillation" for background), and neutrinos behave in exactly the predicted way; only with big mixing angles, unlike the almost-zero angles in the quark sector's CKM matrix.
Careful (Score:2)
...only with big mixing angles, unlike the almost-zero angles in the quark sector's CKM matrix.
Careful - you are confusing quark mixing with CP violation. The complex phase which gives CP violation in quark mixing is almost zero, the actual quark mixing angle is quite significant. For example the Cabibbo mixing angle for udsc mixing is ~13 degrees. [wikipedia.org]
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~13 degrees is small, compared to the two main angles in the PMNS matrix (ok, \theta_13 is smaller, but the atmospheric and solar angles are really big). In fact, CKM angles are so big that you can treat the matrix as an identity matrix with a perturbation; in the neutrino sector, the mass and flavour eigenstates are so different that this type of treatment is meaningless.
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Proofreading is a good idea, people should do that... Of course I meant CKM angles are so SMALL that you can treat it as an identity matrix plus a perturbation.
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That's the way I've always understood the mass/oscillation connection too. But then I thought... wait... don't photons oscillate too? They're just coherent oscillations of the EM field; oscillating back and forth between electric and transverse magnetic in free space. If there's something different about neutrino oscillation which makes it necessary for the neutrino to travel at sublight, what is it specifically?
Re:What if... (Score:5, Informative)
That's the way I've always understood the mass/oscillation connection too. But then I thought... wait... don't photons oscillate too? They're just coherent oscillations of the EM field; oscillating back and forth between electric and transverse magnetic in free space. If there's something different about neutrino oscillation which makes it necessary for the neutrino to travel at sublight, what is it specifically?
The situation you describe with the EM field is an example of wave-particle duality. Light can behave like both a wave and a particle, but it doesn't make sense to analyze it both ways at the same time. As a wave, it does manifest itself as oscillating electric and magnetic fields and as a particle, it manifests itself as a photon, which doesn't change into a different type of particle. (There's no such thing as an "electric photon" and a "magnetic photon".)
Neutrinos, too, are described quantum mechanically by wavefunctions, and these wavefunctions have frequencies associated with them, related to the energy of the particle. But these have nothing to do with the oscillation frequencies described here, in which a neutrino of one flavor (eg. mu) can change into a different flavor (eg. tau). Quantum mechanically speaking, we say the mass eigenstates of the neutrino (states of definite mass) don't coincide with the weak eigenstates (states of definite flavor: i.e. e, mu, or tau). Without mass, there would be no distinct mass eigenstates at all, and so mixing of the weak eigenstates would not occur as the neutrino propagates through free space.
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Thanks. I just found some [uci.edu] equations [ucl.ac.be] that appear to reinforce what you said.
Since the oscillation frequency is proportional to the difference of the squared masses of the mass eigenstates, perhaps it's more accurate to say that neutrino flavor oscillation implies the existence of several mass eigenstates which aren't identical to flavor eigenstates. Since two mass eigenstates would need different eigenvalues in order to be distinguishable, this means at least one mass eigenvalue has to be nonzero. There's pr
Re:What if... (Score:4, Interesting)
I don't know of any superselection-rule -- it's possible, in theory, for the electron neutrino to have zero mass but the muon neutrino to have nonzero mass.
But then you'd have to explain why one flavor was massive while the other was massless, which has never happened before. Since there's lots of precedent for three flavors with different nonzero masses, people just figure that the neutrinos are the same way.
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That's fascinating. Do you have a good reference in mind that discusses this topic? I find the idea of a superposition which sometimes travels at lightspeed and sometimes travels slower than light to be... very bizarre.
Re:What if... (Score:4, Interesting)
I don't know of any superselection-rule -- it's possible, in theory, for the electron neutrino to have zero mass but the muon neutrino to have nonzero mass.
You can't have oscillations between massless and massive states. Remember, SR says that time stands still for massless particles. If you look at the equations for neutrino oscillations, for example here [wikipedia.org], you'll see there are expressions involving both the mass squared (for the time evolution of the wavefunction), and mass difference squared, for the mixing amplitudes. So, for quantum mechanical mixing between states, you need both non-zero masses and non-zero mass differences. There may be other, weird mixing theories which don't require mass differences, but they would be quite exotic. On the other hand, mixing of particles with zero masses would violate SR, which would be highly surprising!
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The time-dependent Schrödinger's equation doesn't apply for massless particles. It was never intended to. It isn't relativistic. Try to apply a simple boost and you'll see it's not Poincaré invariant. The main point is that you get the same probabilities if you use a relativistic theory, but you need A LOT of work to get there.
Oscillations work and happen in QFT, which is Poincaré-invariant and assumes special relativity. I can't find any references in a quick search, but I've done all the (q
Re:What if... (Score:4, Informative)
No. All flavour eigenstates MUST be massive: they are superpositions of the three mass eigenstates, one of which can have zero mass. Calling the three mass eigenstates n1, n2 and n3; and the three flavour eigenstates ne, nm and nt, we'd have:
ne=Ue1*n1+Ue2*n2+Ue3*n3
nm=Um1*n1+Um2*n2+Um3*n3
nt=Ut1*n1+Ut2*n2+Ut3*n3
So, if any of n1, n2 or n3 has a non-zero mass (and at least two of them MUST have non-zero masses, since we know two different and non-zero mass differences), all three flavour eigenstates have non-zero masses.
Also, remember that the limit for the neutrino mass is at about 1eV, while it's hard to have neutrinos travelling with energies under 10^6 eV. In other words, the gamma factor is huge, and they're always ultrarelativistic, travelling practically at "c".
Another point is that the mass differences are really, really small; of the order of 0.01 eV. This is ridiculously small; so small that the uncertainty principle makes it possible for one state to "tunnel" to the other.
I really can't go any deeper than that without resorting to quantuim field theory. I can only say that standard QM is not compatible with relativity: Schrödinger's equation comes from the classical Hamiltonian, for example. To take special relativity into account, you need a different set of equations (Dirac's), which use the relativistic Hamiltonian. In this particular case, the result is the same using Dirac, Schrödinger or the full QFT, but the three-line Schrödinger solution becomes a full-page Dirac calculation, or ten pages of QFT. In this particular case, unfortunately, the best I can do is say "trust me, it works; you'll see it when you get more background".
Wait a second! Re:What if... (Score:3, Interesting)
Does that fact that light is polarizable, has known frequencies of oscillation, and no mass (but has momentum), throw a wrench into all this claim that you need mass to oscillate? Probably not on these forums, but it still makes me pause to think about it.
Re:Wait a second! Re:What if... (Score:5, Informative)
Light doesn't oscillate in this way. A photon is a photon, and remains a photon. Electric and magnetic fields oscillate, but the particle "photon" doesn't. Neutrinos start as one particle (say, as muon-neutrinos) and are detected as a completely different particle (say, as a tau-neutrino).
The explanation for that is that what we call "electron-neutrino", "muon-neutrino" and "tau-neutrino" aren't states with a definite mass; they're a mixture of three neutrino states with definite, different mass (one of those masses can be zero, but at most one). Then, from pure quantum mechanics (and nothing more esoteric than that: pure Schrödinger equation) you see that, if those three defined-mass states have slightly different mass, you will have a probability of creating an electron neutrino and detecting it as a tau neutrino, and every other combination. Those probabilities follow a simple expansion, based on only five parameters (two mass differences and three angles), and depend on the energy of the neutrino and the distance in a very specific way. We can test that dependency, and use very different experiments to measure the five parameters; and everything fits very well. Right now (specially after MINOS saw the energy dependency of the oscillation probability), nobody questions neutrino oscillations. This OPERA result only confirms what we already knew.
Re: (Score:2)
Right above I speculated that it's not possible for a particle to oscillate between massive and massless eigenstates. Do you have a reference showing that one mass eigenvalue can be zero? I'm curious to see how a massive particle which travels at v a
Re: (Score:2)
Well that got butchered. Change "I'm curious to see how a massive particle which travels at v at c is mandatory." to:
I'm curious to see how a massive particle which must travel slower than light can oscillate into a massive particle that must travel at exactly the speed of light. I'd always figured a superselection rule would prevent this sort of thing...
Re: (Score:2)
Mass eigenstates don't oscillate. n1 is always n1, unless you try to measure it, in which case its eigenfunction collapses into the interaction base (ne+nm+nt). That's quantum weirdness for you.
The interactions (production and detection) happen in the flavour base. The propagation happens in the mass base. This means you never oscillate "from massless to massive": you are created with a mixture of massive and massless states, which travel differently, changing the probability of each flavour.
Re: (Score:3, Interesting)
First, it's one thing to claim that electron-positron collisions produce gamma rays. This is a (generally) non-repeated event with a clear discontinuity in time. Before the discontinuity, particles travel slower than light. Afterwards, the products of the collision travel at lightspeed. But an oscillating particle varies smoothly and repeatedly between the two sta
Re: (Score:2)
"A photon can only produce a real electron-positron pair when it has at least twice the rest-energy of an electron and it hits a nucleus."
Or another photon.
Re: (Score:2)
The problem is, according to Special Relativity, massless particles move at the speed of light, and time does not advance for them.
But can't photons be generated and absorbed? Wouldn't that be a change in state over time? How about Doppler shifting.. doesn't that indicate the frequency and energy level of a photon can change over time?
Maybe massless particles can change over time if they are being changed by some (unknown) property of spacetime.
Re: (Score:2)
Firstly, neutrinos have non-zero mass. Go ahead at read some of the links on Wikipedia [wikipedia.org].
Secondly, that only holds if you assume a 3D + time-arrow universe. At these scales I'm not sure you can make that assumption.
Re: (Score:2, Insightful)
We've been observing only a third of neutrinos from the sun, and the speculation was that the rest were oscilliating into others not being detected, and that would be possible if neutrinos had mass, and that means one or the other symmetries in the standard model needs to be tweaked, and so on.
Get it? No, I don't get it either, but I'm no physicists.