[Bill S (OP)]

I’m thinking as I go, here, so I am numbering points for ease of reference, correction etc.

1. Neutrinos (excluding the anti- and sterile varieties) come in three flavours.
2. It is known that neutrinos have mass.
3. The masses of individual neutrinos are not known precisely.
4. Cosmological studies indicate that the combined mass of all three flavours is not less than 0.5 eV.
5. Also, the heaviest neutrino flavour cannot be less massive than about 0.05 eV.
6. It seems there is a considerable difference between the masses, with a very slight possibility (mathematically?) that the lightest could be massless.
7. The flavours in order of ascending mass are: electron-, muon- and tau-neutrinos.
8. It appears that as they travel through space, neutrinos mutate between flavours.

Now for the question! When the mutation sequence is tau > muon > electron, where does the mass/energy go? Similarly, where does the energy come from when the sequence is reversed?

My guess is that vacuum energy might come in here somewhere, but that would raise questions about the extent to which vacuum energy plays a part in the conservation of energy generally.

[imatfaal]

Bill - this is beyond my ken, but I will have a stab at it; hopefully to be corrected if JP swings by.

The idea of neutrinos oscillating between flavours is a little too classical - these are quantum mechanical particles and exist in a super-position of three states - electron- mu- and tau-  I think the upshot of this is that whilst travelling the neutrino is in an special quantum mechanical state that encompasses all three flavours of neutrino (whilst in a sense also oscillating between the three) and the detector projects out the flavour when the neutrino is observed

[lightarrow]

Now for the question! When the mutation sequence is tau > muon > electron, where does the mass/energy go? Similarly, where does the energy come from when the sequence is reversed?

Good question!
I imagine the number of neutrinos varies: more energetic neutrinos, a less number of them and vice-versa. But it's only an hypothesis, I don't know the subject too.

[JP]

Bill - this is beyond my ken, but I will have a stab at it; hopefully to be corrected if JP swings by.

I had to go to the Wiki for this one.  It's actually very cool.  It turns out that each neutrino flavor (the type, i.e. electron, muon, tau) does not have a fixed mass, but consists of a mixture of different masses. 

To see how this might work, imagine that there are three different mass quantum particles.  They all have the same energy, but different masses, which means these three particles have different frequencies.  Now imagine you have a single particle that is somehow a collection of all three masses.  It's the sum of three waves, and if you know anything about interference, when you add three waves of different frequencies together, you get an interference pattern.  This interference pattern over space is basically why neutrinos can change from one flavor to another.

Simply, a neutrino of a single flavor consists of three different masses, so it has three different frequency waves making it up.  Upon propagation, the interference between these waves causes the flavor to shift. 

The total energy obviously stays the same because each mass state has the same energy.

[yor_on]

If I get this right it assumes that a wave then can represent a mass? And the definition of a neutrinos mass then differ from the matter we see normally in that it is a quantum scale object? I know that there is a equivalence between waves and matter but? Maybe the question should be how we ever succeeded in defining a mass to them? I need to look that up methinks

[yor_on]

Hmm, and wow too btw Can't stop being impressed with all that work behind what physics finds out. A neutrino with mass was first defined ...

"For half a century physicists thought that neutrinos, like photons, had no mass. But recent data from the SuperKamiokande experiment in Japan overturned this view and confirmed that the Standard Model of particle physics is incomplete. To extend the Standard Model so that it incorporates massive neutrinos in a natural way will require far-reaching changes. For example, some theorists argue that extra spatial dimensions are needed to explain neutrino mass, while others argue that the hitherto sacred distinction between matter and antimatter will have to be abandoned. The mass of the neutrino may even explain our existence. ... 

The Standard Model

The Standard Model of particle physics can describe everything we know about elementary particles. It says that neutrinos do not have mass. Neutrinos do not have mass because they are all "left-handed" and do not bump on the mysterious "Higgs boson" that fills our entire Universe. " From Berkely. And the first experiment is mentioned here, university of Hawaii.

So, does it have a mass? Well, does a neutron have a mass? A proton then, does that have a mass?

"Prior to SNO, all solar neutrino experiments had been able to detect only electron neutrinos. The genius of SNO is that the detector was based on a novel material: heavy water, in which each molecule contains one or two atoms of deuterium. Deuterium is a heavy version of hydrogen whose nucleus, a "deuteron," consists of both a proton and a neutron. All kinds of neutrinos can react with deuterium by simply splitting apart the deuteron, giving a free proton and free neutron. This is an example of a neutral-current (NC) reaction. But only electron neutrinos can convert the neutron into a proton, incidentally also producing a spare electron (a charged-current, CC, reaction). For further redundancy, as a consistency check SNO also made use of a third reaction (neutrino-electron elastic scattering). Since the elastic scattering may occur via both NC and CC mechanisms, it can occur with all three types of neutrino, but with a known, increased probability for electron neutrinos. The three different reactions can be distinguished by the characteristic patterns of light that they produce in the detector.

What SNO found is that when all three types of neutrinos can be detected, the neutrino rates match the predictions for solar neutrinos. On the other hand, if only CC reactions are considered, the rates of only electron neutrinos match the results obtained by most previous experiments (read on to see why I emphasize "most"). But electron neutrinos can only turn into the other two types if neutrinos have mass! Q.E.D."

From Neutrino Mass, Princeton.

[yor_on]

And yeah, "For example, some theorists argue that extra spatial dimensions are needed to explain neutrino mass, while others argue that the hitherto sacred distinction between matter and antimatter will have to be abandoned." which makes me smile happily. It's all about what one mean by 'degrees of freedom' to me for the moment. We define it from what we observe, as well as what we 'not observe' naturally, except as our classical vacuum. Then joining it up into a 'common for all' SpaceTime, assuming that this is what degrees of freedom mean. But it's trickier than that to me, those degrees of freedom that exist for us are the ones we get mediated by radiation as I think. And that's not the whole story.

[Bill S (OP)]

Thanks folks for the input.

JP, as usual your explanation is great.  I read it once, and thought "I understand that".  Trouble was, I read it again, and now I'm not so sure.  The more I think about it the less sure I am about where the mass is and what's going on.  Is it me, or is that a feature of QM?

[evan_au]

A neutrino oscillates between the three different kinds (and back again), so:

• No energy is permanently lost or gained (but it may be temporarily "borrowed", which is permitted by Heisenberg's uncertainty principle).
• The neutrino travels close to the speed of light, but this does not mean that all kinds travel at the same speed.
• Less massive neutrinos would travel closer to the speed of light, giving the three kinds the same energy.
• It does not mean that all three states will be observed with equal likelihood.

[yor_on]

Evan, what do you mean by the last point? "It does not mean that all three states will be observed with equal likelihood." ? You can't be thinking of different masses there, because if you do a neutrino should constantly vary its 'speed', right? But then we have this.

"the muon neutrinos are disappearing somewhere along the way, presumably oscillating into another flavor -- not electron neutrinos (that would be too easy) but either tau neutrinos or one of the hypothetical sterile neutrinos. If the theoretical infrastructure of physics is sound, then neutrino oscillation implies, ipso facto, that the particles have mass. There has to be a difference of mass between the two neutrino types for oscillation to occur, according to the rules of quantum mechanics. And that means at least one type of neutrino has to have a mass greater than zero."

But how can they do that? To state that they change mass seems also no less than implying that we 'know' how mass, as in matter, comes to be? I must have missed that one? And if they have a mass at one moment, and none at another, then those instants when there is a apparent mass also must change the room time topology as well as the relativistic 'energy' assumed to exist in the room time geometry. Not sure I understand neutrinos at all but the only way I can assume it not to behave so weirdly would be to assume it to be indeterministic, existing in a probability cloud of sorts, until 'measured'.

[lightarrow]

• No energy is permanently lost or gained (but it may be temporarily "borrowed", which is permitted by Heisenberg's uncertainty principle).

This is not correct. It's a myth I also believed, because of popular books, but it's false. Energy is *always* conserved.

[evan_au]

The probability of detecting a given neutrino as being of a given type is estimated in the graphs of http://en.wikipedia.org/wiki/Neutrino_oscillation#Three_neutrino_probabilities
This ignores the possibility of additional (as yet undetected) flavours of neutrinos.

The probability of detecting a particular flavour depends on the energy of the neutrino, and how far it has traveled. The three probabilities are not equal.

Since the core of the sun is so large (producing neutrinos over a volume wider than the oscillation wavelength), other experiments are needed to pin down the oscillation, such as monitoring neutrinos from a nuclear reactor, or neutrinos produced by cosmic rays hitting the atmosphere.

There are some additional constraints on the possible neutrino masses (http://en.wikipedia.org/wiki/Neutrino#Mass). One constraint even opens the possibility that the different neutrinos may have very similar masses, which may facilitate the oscillation.

[JP]

Thanks folks for the input.

JP, as usual your explanation is great.  I read it once, and thought "I understand that".  Trouble was, I read it again, and now I'm not so sure.  The more I think about it the less sure I am about where the mass is and what's going on.  Is it me, or is that a feature of QM?

Thanks, Bill.  It is one of those weird features of QM that doesn't play nicely with intuition from everyday life.

I'll happily stand corrected if someone knows this better.  I know a good amount about QM, but I'm getting the details here from the equations on Wikipedia.  Dropping all math, it comes down to the idea that a single "flavor" of neutrino (electron, muon, tau) is actually a combination of three different particles of different masses.  The problem is that it's hard to measure these single masses, because it's the flavor, or particular combinations of the three, that interacts with other matter, including our detectors. 

What happens is that as the three mass particles propagate, their waves move at different speeds--they all have the same energy, but different masses, so their waves essentially move at different speeds.  Because of this, the thee mass waves interfere differently at different regions of space, making their sum look different at different points in space.  Since the flavor of neutrino we detect depends on what this total wave looks like, we measure different flavors at different points in space. 

The weird quantum part is to understand how a particle can be in a specific state of one variable (flavor), but at the same time is in multiple states of another variable (mass).  A famous example of this is the uncertainty principle in position and momentum--a particle can be in a state that's spread only over a small region of space, but that requires that this particle is also at the same time in a wide spread of states in momenta.  It's also related to Fourier synthesis if you've ever studied the topic--a single wave (your state in one variable) can be written as a sum over many sinusoids (states in another variable).

[yor_on]

For those masses to be able to be together over astronomic distances should set limits on the masses, right?  Or I can still assume a state of probability to it, can't I?

[JP]

I don't know, Yor_on.  I know enough QM to understand the basics of how this effect happens, but I don't know the details of a precise case where a single neutrino is emitted at from a single event.  Like all of quantum field theory, it probably involves coming up with sophisticated approximations to path integrals, which is a bit over my head.  :p

[yor_on]

If I would consider it rest masses, and then assume three different ones spontaneously expressing themselves over a astronomic distance, all keeping together, I get a headache. If I assume that this mass(es) comes to be in the measurement it becomes slightly less for me. If I on the other hand assumes that we found a particle that actually can change its mass spontaneously, still being the same 'particle' in all transformations? Then my headache gets real huge:) Because then mass at a microscopic plane is something spontaneously expressed, at least by neutrinos and what should a invariant 'rest mass' then be?

[yor_on]

Maybe all mass have to do with probability? Isn't it so that Quantum physics assume that what differs, a macroscopically defined state of matter, as a example, from a pure 'particles' indeterminism is the result of a lot of indeterministic quantum states getting 'smeared out' into a coherence? Well, as I interpret it. And if so all rest mass is indeterministic 'individually', although finding its invariant definition from its relations to its neighbors? That is a plausible mechanism, maybe(? especially if considering  a static universe, dynamically defined through a arrow, radiation, and those degrees of freedom we observe directly creating the 'limits' in where we exist. And yeah, absolute philosophy, as well as wild speculation I admit

[Bill S (OP)]

Yor_on, what you have described in your last two posts sounds remarkably like the off-beat idea for which I have taken a lot of stick elsewhere.  The idea is that the cosmos is infinite.  This is not a mathematical infinity which can be manipulated; it is physical infinity in which there is no time, no change and no differentiation of “parts” – everything just “is”.  The Universe which we observe is a 3+1 dimensional interpretation of this infinite reality.  Think of a spider walking through Flatland! 

“Philosophy…..wild speculation”, of course, but we humans have always needed to try to make sense of our world and I think speculation is good, as long as we don’t confuse it with knowledge and turn it into dogma. 

[Bill S (OP)]

The bit I left out was that QM is beginning to provide us with a window into the infinite reality which is why we find it weird.