Neutrino Oscillation: Learn About the Experiment

[michealsmith]

cann anyone tell me about tghe neutrino oscillation experimtent

 

[jtbell]

"The" neutrino oscillation experiment? There are a whole bunch of them:

http://www.google.com/search?q=neutrino+oscillation+experiment

 

[michealsmith]

ok what do u know about the T2k

 

[Gluonium]

The outcome was that Neutrino's oscilate, which means that they must have mass. This shook the standard model a bit because it predicted that they did not have mass.

If i recall correctly, they experiment was just a beam of neutrinos and on a few occaisions some of the neutrinos oscillated.

 

[arivero]

Short history: Georgi told the proton was to decay at a measurable probability, Japanese did big inversion money to build the detectors but no proton was detected to disintegrate. Then they turned the detectors into neutrino detectors and oscillation of neutrinos was detected! Big success because nobody had taken upon his shoulders the work of neutrino detection. After this, laboratory experiments are done not to confirm it but to refine the measurements so we can get some hints on the value of the mass. The recent experiment if one of these.

If the USA had filled with water the SuperCollider it had been better inversion than just to bury it.

 

[SpaceTiger]

Short history: Georgi told the proton was to decay at a measurable probability, Japanese did big inversion money to build the detectors but no proton was detected to disintegrate. Then they turned the detectors into neutrino detectors and oscillation of neutrinos was detected! Big success because nobody had taken upon his shoulders the work of neutrino detection.

On the contrary, I think Ray Davis and John Bahcall had taken quite a lot on their shoulders.

 

[jtbell]

Then they turned the detectors into neutrino detectors and oscillation of neutrinos was detected! Big success because nobody had taken upon his shoulders the work of neutrino detection.

Lots of accelerator experiments involving neutrinos had tried to detect neutrino oscillations as a sideline to their main work, but none had found any. I did a search like that as my PhD dissertation project.

The experiments that finally observed neutrino oscillations explored different energy and distance ranges, where the effects are easier to detect.

 

[ZapperZ]

Lots of accelerator experiments involving neutrinos had tried to detect neutrino oscillations as a sideline to their main work, but none had found any. I did a search like that as my PhD dissertation project.

The experiments that finally observed neutrino oscillations explored different energy and distance ranges, where the effects are easier to detect.

Er.. the MINOS collaboration had just had their first results reported here just last week! In fact, if Fermilab doesn't get funding beyond 2009 for the Tevatron, it WILL become predominantly a neutrino factory for MINOS. So I don't think it is a side project any longer.

Zz.

 

[jtbell]

Right, MINOS is very much an accelerator-based experiment. I was referring to earlier generations of accelerator-based neutrino experiments, say from the 1970s up to the early to mid 1990s. A lot of them had their data analyzed in various ways to set limits on neutrino oscillation parameters, long before the first positive evidence came from Super-K etc.

There was a colloquium at the University of South Carolina last week about the recent results, but we're at the end of the semester here so things are crazy enough with tests and exams that I couldn't take the afternoon off to drive down to Columbia.

 

[Michael Mozina]

THE CLAIM
We claim the discovery of neutrino oscillations therefore mass. In short, we observe a deficit of muon neutrinos coming from greater distances and at lower energies, from their production by cosmic rays high in the atmosphere to the detector buried deep underground. The behaviour of this deficit as a function of energy and arrival angle tells us that muon neutrinos oscillate, which is to say that they alternatingly change from one type of neutrino to another as they travel at close to the speed of light.

I have a couple of layman's questions that perhaps someone could explain.

I can't quite grasp why the absense of atmospheric muon nutrinos from the far side of the Earth automatically equates into neutrino flavor changes. In other words, why couldn't the muon neutrinos simply be more apt to be absorbed or deflected by dense mass compared to the electron neutrino?

If the fact that there are three types of neutrinos means that at least some of them must have mass, aren't we assuming different masses for different kinds of neutrinos? If they are different masses to begin with, how does a neutrino "gain or lose mass" to change to a different type? Wouldn't a change of mass violate conservation of energy laws?

Pardon my naivate' on this issue, I just don't understand how evidence of a deficit of received neutrinos of one type automatically equates into evidence of a flavor change.

 

[jtbell]

In other words, why couldn't the muon neutrinos simply be more apt to be absorbed or deflected by dense mass compared to the electron neutrino?

I haven't seen the detailed analysis of these experiments, but I'm sure it must include estimating what fraction of neutrinos of each type are absorbed while traveling through the earth, using neutrino interaction cross-sections predicted by the standard model (and studied experimentally) and current models of the Earth's structure.

how does a neutrino "gain or lose mass" to change to a different type? Wouldn't a change of mass violate conservation of energy laws?

Neutrino oscillations are not "mass oscillations." They are "flavor oscillations." The basic idea is that neutrinos of a particular flavor (e, mu or tau) do not have a single definite mass, but rather have certain probabilities of being three different masses. For each flavor, the possible masses are the same, but the probabilities are different.

According to a quantum-mechanical treatment of this system, if you create a neutrino of a particular flavor in a way that does not give you knowledge of which mass it has, its wavefunction is a superposition of the wavefunctions for all three masses. As the neutrino travels, the three wavefunctions in the superposition interfere with each other, giving oscillating probabilities for each of the three flavors. So when we detect it, it might be anyone of the three flavors. However, it has the same mass at production and at detection, chosen at random from one of the three possible values.

 

[Michael Mozina]

I haven't seen the detailed analysis of these experiments, but I'm sure it must include estimating what fraction of neutrinos of each type are absorbed while traveling through the earth, using neutrino interaction cross-sections predicted by the standard model (and studied experimentally) and current models of the Earth's structure.

The fact that neutrinos actually posess mass seems pretty "new" from a particle physics standpoint. I guess I'm a bit skeptical that we can already rule out some sort of scattering/absortion affect this early in the process.

Neutrino oscillations are not "mass oscillations." They are "flavor oscillations." The basic idea is that neutrinos of a particular flavor (e, mu or tau) do not have a single definite mass, but rather have certain probabilities of being three different masses. For each flavor, the possible masses are the same, but the probabilities are different.

I guess this concept is just hard for me to "wrap my head around". In the realm of photons, the mass of a photon does not vary, but it's wavelength changes, thus we have "high" and "low" energy photons. A photon however does not typically change energy states unless there is some kind of interaction with something else. If the 'mass' of a neutrino particle varies, how does one determine the energy state of the three types of neutrinos?

According to a quantum-mechanical treatment of this system, if you create a neutrino of a particular flavor in a way that does not give you knowledge of which mass it has, its wavefunction is a superposition of the wavefunctions for all three masses. As the neutrino travels, the three wavefunctions in the superposition interfere with each other, giving oscillating probabilities for each of the three flavors. So when we detect it, it might be anyone of the three flavors. However, it has the same mass at production and at detection, chosen at random from one of the three possible values.

I suppose that is as comprehensive an answer as I'm likely to get based on my own lack of understanding of the mechanical models that are being used to describe a triple wave function for a single particle.

I suppose I'd feel a lot better if we could aim neutrinos at a detector and measure (detect) the fact that some of the neutrinos actually changed into another form of neutrino. As it stands, it seems like a lack of a "detection" of a single kind of neutrino is simply being "interpreted" as a change from one state to another without actually seeing/detecting such the actual transition into another form. At the moment we only detect a miss, rather than detecting a hit of a different kind of neutrino. Detecting a missing neutrino is not identical to detecting a hit of a different kind of neutrino, but that seems to be the way the data is "interpreted" at the moment.

Thank you for your clear explanation of the triple wave function that is currently attributed to a neutrino. I admit I remain skeptical, but that explanation does seem to help. Thanks. :)

 

[Michael Mozina]

A couple more layman type questions came to me at lunch.

Why does current theory favor an "intrinsic triple wavelength" rather than some kind of transition occurring along the way due to say a interaction at the nuclear level? In other words, at first I originally assumed that neutrinos might change "wavelength" since a photon is a close neighbor from a mass standpoint. I could grasp how the neutrino wavelength might be affected along the way, based upon a physical process inside an atom, but I don't really "grok" the whole three wavelengths at once concept.

Wouldn't it make more sense to believe the neutrino's wavelength was altertered by an interaction with an atomic nucleus, rather than believing it has three separate wavelengths at once?

 

[jtbell]

I guess this concept is just hard for me to "wrap my head around". In the realm of photons, the mass of a photon does not vary, but it's wavelength changes, thus we have "high" and "low" energy photons. A photon however does not typically change energy states unless there is some kind of interaction with something else. If the 'mass' of a neutrino particle varies, how does one determine the energy state of the three types of neutrinos?

Remember, the mass of a particular single neutrino doesn't vary with time. Some neutrinos turn out to have one mass, some have another mass, and the rest have a third mass. The mass of any particular individual neutrino is the same at production and at detection; but the flavor at detection may be different from the flavor at production.

I suppose I'd feel a lot better if we could aim neutrinos at a detector and measure (detect) the fact that some of the neutrinos actually changed into another form of neutrino.

There are experiments in progress or in the works that are going to test this. They produce neutrinos of a specific type at an accelerator, then detect them far enough away so that oscillation effects should be significant.

In the meantime, there are results from the Sudbury Neutrino Observatory in Canada that detects electron, muon and tau neutrinos from the sun. The sum of the three flavors agrees (within experimental statistical uncertainty) with predictions of the number of electron-neutrinos produced by the sun according to standard solar models.

Earlier solar-neutrino detectors detected only electron-neutrinos, and they found fewer neutrinos than the solar models predict. This was the long-standing "solar neutrino puzzle" which has now apparently been resolved.

 

[SpaceTiger]

The mass of any particular individual neutrino is the same at production and at detection;

Aren't the neutrinos generally in flavor eigenstates at production -- that is, not in a particular mass eigenstate?

 

[jtbell]

Aren't the neutrinos generally in flavor eigenstates at production -- that is, not in a particular mass eigenstate?

Yes. And when the neutrino interacts (is detected) it does so as one of the flavor eigenstates, which may or may not be the one that it was created in. But energy and momentum are conserved, so because E^2 = (pc)^2 + (mc^2)^2, the mass of a particular individual neutrino, whichever mass it turns out to be, must be conserved. We can't know which mass it is, without making extremely precise measurements of the energies and momenta of the other particles involved in the production and decay processes, which is impossible in practice. At best we can state the probablilites that the neutrino has each of those masses.

The mass eigenstates and the flavor eigenstates are related by a matrix of coefficients, something like this:

|\nu_e> = a_{11} |\nu_1> + a_{12} |\nu_2> + a_{13} |\nu_3>

|\nu_\mu> = a_{21} |\nu_1> + a_{22} |\nu_2> + a_{23} |\nu_3>

|\nu_\tau> = a_{31} |\nu_1> + a_{32} |\nu_2> + a_{33} |\nu_3>

One of the major goals of neutrino oscillation research is to narrow down the values of the coefficients.

 

[SpaceTiger]

We can't know which mass it is, without making extremely precise measurements of the energies and momenta of the other particles involved in the production and decay processes, which is impossible in practice.

But isn't that just reducing to another Schrödinger's cat question -- i.e. whether the particle had a "real" mass and we just didn't know what it was or whether it was in a superposition of states. I'm not particularly opinionated on the issue, but it seems to be a debatable point, at the least.

 

[jtbell]

You can make some interesting parallels between neutrinos and other QM situations. For example, suppose we produce a muon-neutrino from pion decay:

\pi^+ \rightarrow \mu^+ + \nu_\mu

Suppose (hypothetically) that the pion has a very precisely known energy and momentum. They get divided up among the muon and the neutrino, so at the moment of production, the neutrino's energy, momentum and mass are uncertain. But now suppose (hypothetically again) that we measure the energy and momentum of the outgoing muon very precisely. Together with our knowledge of the pion's energy and momentum, this determines the neutrino's energy and momentum. If we do this precisely enough, we can determine which mass the neutrino has. In this case there are no flavor oscillations! When the neutrino interacts, it can still do so as any of the three flavors, but the probabilities of the different flavors are constant. They don't oscillate with time or distance traveled.

Disclaimer: I haven't actually seen this written up anywhere. It's based on my understanding of the QM of neutrino oscillations. Nobody who knows the subject well has contradicted me on this yet, but I'm definitely open to corrections.

This is very much like the classic two-slit interference setup for photons or electrons or whatever. If you make measurements that allow you to determine which slit the particle went through, you destroy the two-slit interference pattern.

 

[SpaceTiger]

But now suppose (hypothetically again) that we measure the energy and momentum of the outgoing muon very precisely. Together with our knowledge of the pion's energy and momentum, this determines the neutrino's energy and momentum. If we do this precisely enough, we can determine which mass the neutrino has.

Isn't that why the existence of neutrino oscillations suggests flavor violation in the charged sector? If the flavor eigenstates of the charged leptons weren't exactly equal to their mass eigenstates, then the energy-momentum states of the muon would be tangled with those of the neutrino. Then the experiment you're describing would be analogous to EPR -- precise measurements of the energy and momentum of the muon would cause the neutrino mass wave function to "collapse".

 

[jtbell]

Isn't that why the existence of neutrino oscillations suggests flavor violation in the charged sector?

I don't remember reading about that. Do you have a reference?

As I recall (it's been a long time since I read about this), mixing of the charged leptons isn't independent of neutrino mixing. If you start out assuming that the charged leptons also mix, you can redefine the "flavor basis states" for the charged leptons or for the neutrinos (or both? I forgot which) so as to put all the mixing with one set of particles or the other. That is, you basically combine the two mixing matrices.

Hey, I'm on sabbatical as of Monday! I've got an excuse to start doing some serious reading about all this stuff again. I might as well start with this:

http://pdg.lbl.gov/2005/reviews/numixrpp.pdf

 

[Michael Mozina]

Remember, the mass of a particular single neutrino doesn't vary with time. Some neutrinos turn out to have one mass, some have another mass, and the rest have a third mass. The mass of any particular individual neutrino is the same at production and at detection; but the flavor at detection may be different from the flavor at production.

I guess my resistance is to the notion that it changes flavors in flight as something intrinsic to the neutrino itself. I can more easily relate to a "change" that occurred in the solar atmosphere to change it from one energy state to another (like a wavelength change) but I less easily relate to assigning different neutrinos different masses and believing that the neutrino just waffles inbetween energy states for purely internal reasons.

There are experiments in progress or in the works that are going to test this. They produce neutrinos of a specific type at an accelerator, then detect them far enough away so that oscillation effects should be significant.

If we can detect a changed neutrinos from a specific and known and controlled transmitter, or I see a physical model to explain this affect, then I'll have to rethink my objections. Until that time, I suppose I'm likely to remain a bit skeptical to the idea they change flavors as an intrinsic part of being a neutrino. Even when neutrons decay into hydrogen atoms, it's a one way trip.

In the meantime, there are results from the Sudbury Neutrino Observatory in Canada that detects electron, muon and tau neutrinos from the sun. The sum of the three flavors agrees (within experimental statistical uncertainty) with predictions of the number of electron-neutrinos produced by the sun according to standard solar models.

Of course I don't personally subscribe to the "standard" solar model so that particular argument is somewhat less convincing to me than to most. :)

Earlier solar-neutrino detectors detected only electron-neutrinos, and they found fewer neutrinos than the solar models predict. This was the long-standing "solar neutrino puzzle" which has now apparently been resolved.

I suppose I'll have to "wait and see". When they detect more than a "missing" neutrino of one type, and detect a neutrino change from a known source, then I'll feel a lot more comfortable with the idea. Even then I might may not be able to rule out a single "change" of state due to an external influence.

If I'm understand you correctly, "distance" of some sort does seem to matter, but not necessarily the medium it traverses? In other words, it is not a density of material issue, it would change "flavors" even in a pure vacuum (assuming such a thing existed)?

 

[SpaceTiger]

I don't remember reading about that. Do you have a reference?

Nothing that discusses our thought experiment explicitly. There is some discussion of charged LFV here:

http://lanl.arxiv.org/abs/hep-ph?papernum=0202054"

 

[Michael Mozina]

I have another rather basic question about the current neutrino experiments.

No matter how I try to rationalize the method, I cannot logically understand how a "missing" neutrino can be considered evidence of a "changed" neutrino.

In other words, the very methods we use to detect and observe neutrinos are based upon the QM principles of scattering and absortion of neutrinos. It therefore seems very probable that a "missing" neutrino may simply have been absorbed or scattered somewhere between the transmitter and the detector. Since we can't rule out scattering/absortion proceess, I fail to understand how a "missing" neutrino can logically be equated to evidence of "flavor changing" neutrinos. Can someone explain the logic of how and why missing neturinos are interpreted to have changed flavor rather than simply being absorbed or scattered along the way? Try as I might, I just cannot understand how absorption and scattering were ruled out as a cause of these missing neutrinos, or why a "flavor change" is considered to be a superior explanation for these missing neutrinos.

 

[selfAdjoint]

I have another rather basic question about the current neutrino experiments.

No matter how I try to rationalize the method, I cannot logically understand how a "missing" neutrino can be considered evidence of a "changed" neutrino.

In other words, the very methods we use to detect and observe neutrinos are based upon the QM principles of scattering and absortion of neutrinos. It therefore seems very probable that a "missing" neutrino may simply have been absorbed or scattered somewhere between the transmitter and the detector. Since we can't rule out scattering/absortion proceess, I fail to understand how a "missing" neutrino can logically be equated to evidence of "flavor changing" neutrinos. Can someone explain the logic of how and why missing neturinos are interpreted to have changed flavor rather than simply being absorbed or scattered along the way? Try as I might, I just cannot understand how absorption and scattering were ruled out as a cause of these missing neutrinos, or why a "flavor change" is considered to be a superior explanation for these missing neutrinos.

The original Homestake detector could only respond to neutrinos of the electron type. The Solar models predicted a certain flux of electron neutrinos. Homestake only detected a third as many neutrinos as predicted. This is the "missing neurinos". The modern explanations is that the predicted flux of electron neutrinos leaves the Sun but along the way to Earth they oscillate between electron, mu, and tau types and by the time they reach the detector they are in a steady state of equal numbers in each type, so only a third of the original number in the electron type that the detector saw.

 

[SpaceTiger]

In other words, the very methods we use to detect and observe neutrinos are based upon the QM principles of scattering and absortion of neutrinos. It therefore seems very probable that a "missing" neutrino may simply have been absorbed or scattered somewhere between the transmitter and the detector. Since we can't rule out scattering/absortion proceess, I fail to understand how a "missing" neutrino can logically be equated to evidence of "flavor changing" neutrinos.

I think you're misunderstanding the measurements. It used to be about "missing" neutrinos because we only made detectors that looked for electron neutrinos. Doing so, we found fluxes that were lower than predicted by the solar model. Since then, we have observed muon and tau neutrinos that, when added with the incoming electron neutrinos, give a total flux consistent with that predicted by the standard solar model. If you wanted to explain this result in some way other than oscillations, I would think the real challenge would be finding a natural source of muon and tau neutrinos that gives a flux on the same order of magnitude as the nuclear reactions in the sun.

As for your question about neutrinos "scattering" away, we have both measurements and a well-established theory that give neutrino cross sections that are extremely low, much too low to produce significant scattering between us and the sun.

 

[CarlB]

I guess my resistance is to the notion that it changes flavors in flight as something intrinsic to the neutrino itself. I can more easily relate to a "change" that occurred in the solar atmosphere to change it from one energy state to another (like a wavelength change) but I less easily relate to assigning different neutrinos different masses and believing that the neutrino just waffles inbetween energy states for purely internal reasons.

In QM, one always has the option of analyzing the problem in whatever set of orthogonal wave functions one prefers. For the case of the neutrinos, one can analyze them in the electron, muon and tau neutrino basis, or one can analyze them in the m1, m2 and m3 basis.

Whichever way you choose, the calculation will get the same result and that will (according to current theory) match experimental results. But analyzing neutrinos in the flavor basis is a little strange. The result is just the same as what you would get if you tried to make an analysis of a particle that was partly an electron and partly a muon. The neutrinos are much more obvious and simple if you analyze them in their mass basis like you do all the other leptons and quarks.

If we analyze the problem from the point of view of the electron, muon and tau basis, then we find that the wave function starts out as a pure electron (anti) neutrino. However, to propagate a wave function through space requires that we write the wave function in the mass basis and then figure out how the three mass waves propagate, and then put it back into the flavor basis. So the result is just like what you'd get if you did the problem in the mass basis.

If you want to think of the neutrinos as physical particles (and physical particles always have masses or zero mass), then you have to work the problem in the mass basis. In that basis, the original neutrino was a mixture of three mass eigenstates when it was emitted, and then its three portions propagated differently. So, as it moves, the different masses cause the three different parts to acquire different phases and this causes them to interfere with each other.

I recently saw a great lecture on the subject, one that will take you from the beginning to a pretty complete understanding of the solar and atmospheric neutrino oscillations here:

Recent Developments in Neutrino Physics
Alexei Smirnov
http://physics.ipm.ac.ir/conferences/lhp06/notes/smirnov1.pdf
http://physics.ipm.ac.ir/conferences/lhp06/notes/smirnov2.pdf
http://physics.ipm.ac.ir/conferences/lhp06/notes/smirnov3.pdf

There is an audio that goes along with the above that can eventually be accessed by clicking on "program" here:

IPM School and Conference on Lepton and Hadron Physics
http://physics.ipm.ac.ir/conferences/lhp06/

These files are coming to you from Tehran, Iran, and you should download them and access them from your own computer instead of trying to open them directly from the webpage, at least that is what I did. The above really does explain this at a very basic and easy to understand level, but also at a very complete and good academic introduction. It goes into parametric oscillation and all that, even effects such as the different density of the core of the earth. I should mention that my work on the neutrino masses is mentioned in the above, in the cells about "empirical relations". My paper is here:
http://brannenworks.com/MASSES2.pdf

Here, let me translate the problem into the charged leptons so you can see why it is that the neutrinos are "weird".

Suppose we have a particle emitted from the sun but we don't know whether it is a muon or an electron. Instead, the particle is emitted in a combined state, call it the "chtulu" state. For example, suppose that the chtulu state is a mixture of electron and muon like this:

|chtulu> = 0.8 |electron> + 0.6 x e^{2i\pi/5} |muon>

I've normalized the above as 0.8^2 + 0.6^2 = 1. And I've put in a phase difference of 2 pi/5. But you can suppose the chtulu state is whatever mixture of electron with muon you like. (Or more generally, electron, muon and tau.)

How do we account for this in QM? What we have to do is to write the particle as a combined wave function with two sets of wave functions, one for the electron, the other for the muon. Then we let these two wave functions propagate in the usual manner, separately. At the place where the particle is received, we want to know whether it arrives as a chtulu.

To make the calculation, we recombine the electron and muon wave functions. Since the electron and muon have different masses, their wave functions will not have had the same phase change in the propagation. That could cause them to beat against each other, so even though the particles were emitted in a "chtulu", they may not be received as a chtulu. Basically, the reason is that the chtulu is not a real particle in the sense that it has a mass. The real particles are the electron and muon. For the neutrinos, the real particles are the m1, m2 and m3.

Historically, the neutrinos were once thought to be massless, so for historical reasons they are called the electron, muon and tau neutrinos. In fact, this is a deviation from the way that particles are labelled in the rest of particle physics. The real particles are the m1, m2, and m3 neutrinos. which, unfortunately, don't have consistent names.

Carl

 

[Michael Mozina]

Thank you Carl. I will have to take some time to go through the references and papers you provided, and think a bit about these concepts before I can really ask "the right" questions. I really appreciate the time you took to carefully explain the theory. I "think" I at least understand where you are coming from from a theoretical perspective. My resistance I suppose comes from conservation of energy laws in the final analysis, based on the idea that each neutrino has it's own mass/energy state. I think I'm starting to understand the intrinsic flavor changing theory a bit better and how these conservation laws are being addressed.

I suppose I am still a bit "uncomfortable" with the assumption that the flavor change is primarly a function of "time" and "distance" (assuming that I'm following your logic properly), rather than being in some way related to the medium in which the neutrino travels. Even still, I think I at least have a better understanding of the theory that flavor change is internal to the neutrino. I very much appreciate your time and effort to educate me a bit.

Would it be fair then to suggest that we should expect X amount of every type of neutrino based solely on "distance" and "time", or are you suggesting there is also an external influence involved in the transition process? In other words, if the neutrinos passed through a pure vacuum (assuming such a thing existed), would they be received as three different flavors after traveling a specific distance and length of time with no external interactions until reaching the detector?

 

[Michael Mozina]

The original Homestake detector could only respond to neutrinos of the electron type. The Solar models predicted a certain flux of electron neutrinos. Homestake only detected a third as many neutrinos as predicted. This is the "missing neurinos". The modern explanations is that the predicted flux of electron neutrinos leaves the Sun but along the way to Earth they oscillate between electron, mu, and tau types and by the time they reach the detector they are in a steady state of equal numbers in each type, so only a third of the original number in the electron type that the detector saw.

Ultimately my question and concern revolves around an internal, vs. external debate from a "causality" point of view. Let us assume for the time being that the solar neutrinos do "change" somehow between the sun and the earth. My concern is the "cause" of this change, and the "change" of energy state/mass state. Is this "change" a one time interaction, or a true "oscillation" that happens again and again? In other words, I can more easily accept that the "cause" of a one time change is somehow associated with a specific interaction with some particle between the source and the reciever. I have been less inclined to believe that neutrinos "oscillate" and change mass/energy states simply as an "internal" function.

The three wave function that Carl and others have been helping me to understand is very interesting, but I still don't see any direct evidence that would suggest that an internal "oscillation" explanation is better than an external "single change" explanation as it relates to "flavor changing".

Do you understand my concern about the difference between a one time change vs. an internal "oscillation" that happens repeatedly?

 

[selfAdjoint]

BTW, I don't know if anybody has posted on this but I just saw in the paper that Raymond Davis, who won the 2002 (I think) Nobel Prize for the original Homestake experiment that first showed the neutrino shortfall, has died. Ave atque vale frater.

 

[CarlB]

I suppose I am still a bit "uncomfortable" with the assumption that the flavor change is primarly a function of "time" and "distance" (assuming that I'm following your logic properly), rather than being in some way related to the medium in which the neutrino travels. Even still, I think I at least have a better understanding of the theory that flavor change is internal to the neutrino. I very much appreciate your time and effort to educate me a bit.

Would it be fair then to suggest that we should expect X amount of every type of neutrino based solely on "distance" and "time", or are you suggesting there is also an external influence involved in the transition process? In other words, if the neutrinos passed through a pure vacuum (assuming such a thing existed), would they be received as three different flavors after traveling a specific distance and length of time with no external interactions until reaching the detector?

Even a pure vacuum would cause neutrinos to oscillate. The presence of other matter changes things. Those links will give a damned good education in this and it will be more clear. By the way, it may have to do with interplanetary space, but technically, it's not rocket science. So keep reading and you will understand.

What's going on with conservation of energy is kind of subtle. In QM, energy is only conserved when it is present in the initial conditions. That is, it is very natural to have initial conditions for which energy is conserved, that is, the system is in an eigenstate of energy. But it is also natural for a system to be initially in a state which is not an eigenstate of energy, and for these systems, energy is not conserved.

For example, suppose the initial state is a neutron sitting out in space somewhere. Such a neutron will eventually decay (20 minute half life, if I recall) and release a neutrino. Now suppose we want this neutron to be in an eigenstate of energy. Is this possible?

No it cannot be done. Energy has to do with a system being equivalent under translations in time. This is a property that is contrary to decaying. For example, a hydrogen atom in its lowest state cannot decay and therefore can be in an energy eigenstate.

This is confusing because people often talk about the excited states of a hydrogen atom as if they were "energy eigenstates". The truth is that they are only energy eigenstates if you turn off the interaction that allows them to decay (i.e. turn off the interaction with photons).

When you analyze particles that decay along with the interaction that decays them, you will find that the energy eigenvalues are complex. The imaginary part gives the decay rate.

So you see that the problem of defining a neutron for which you know its energy precisely is a problem. Its energy is complex.

To get a neutron with a perfectly known real energy, you would have to turn the decay interaction off first and that's not a thing that is physically possible. So I'm not sure how to answer your question. In addition, when you put a particle into a perfect eigenstate of momentum, its position becomes entirely undetermined. The universe is a big place, so this is not very physical. Similarly, to get into an exact energy eigenstate, the neutron would have to live forever.

Hey, it's been 30 years since I started studying QM. It's not unlikely that I've screwed up something here. You're asking questions that are very basic, and this is stuff that one doesn't pay attention to when one gets involved in understanding the details. So please pay attention if the locals correct my interpretation.

Well at least this guy agrees with me:

"Thus the energy of a decaying state is not an eigenvalue of the system nor a constant: in particular, the energy of the state is distributed over a region with a width determined by the decay constant."
http://www.phy.uct.ac.za/courses/phy300w/np/ch1/node31.html

Carl