In article <0013b48a-26fc-4b7c-ade4-a70929efa9a7@googlegroups.com>, <raymond.yohros@gmail.com> writes:

Why then can we not determine what % of the speed of light
the particles where traveling at and with some algebra as usual
determine their masses as well?

Note that neutrinos from the supernova 1987A in the Large Magellanic
Cloud emitted neutrinos which were detected on Earth. Since the
difference in emission times of light and neutrinos is only about 3
hours, this is negligible for the travel time of 157,000 years and thus provides a good lower limit on the speed of neutrinos (i.e. very close
to the speed of light). This gives an upper limit on the mass of the
electron neutrino of about 26 eV. Current limits are about 0.11 eV.
However, because of neutrino oscillations, we know that it is non-zero.

[[Mod. note -- To amplify one point Phillip made: measurements of neutrino oscillations tell us the *difference* between the *squares* of the masses
of different types of neutrinos, i.e., they tell us something like
m1**2 - m2**2 . But if my dim recollection is correct, they don't
easily tell us which of the 3 types of neutrinos m1 and m2 refer to.
-- jt]]

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On Thursday, March 26, 2020 at 1:53:33 PM UTC-5, Phillip Helbig (undress to reply) wrote:

In article <0013b48a-26fc-4b7c-ade4-a70929efa9a7@googlegroups.com>, <raymond.yohros@gmail.com> writes:

Why then can we not determine what % of the speed of light
the particles where traveling at and with some algebra as usual
determine their masses as well?

Note that neutrinos from the supernova 1987A in the Large Magellanic
Cloud emitted neutrinos which were detected on Earth. Since the
difference in emission times of light and neutrinos is only about 3
hours, this is negligible for the travel time of 157,000 years and thus provides a good lower limit on the speed of neutrinos (i.e. very close
to the speed of light). This gives an upper limit on the mass of the electron neutrino of about 26 eV. Current limits are about 0.11 eV.
However, because of neutrino oscillations, we know that it is non-zero.

Can it be possible that the mass of an electron neutrino
Is never the same?, unlike dirac particles.

that the 3 different flavors are simply 3 different ranges in which
the mass of the neutrino may be? But not a fixed value, like a photon
or electron? Or even c? (the probability mass range distribution.)

if there masses oscillates, that already means they move at variable speeds!

is a neutrinoless double beta decay observation the only way to conclude
that we are talking of mayorana particles?

r.y

[[Mod. note -- I believe that we know there are (at least) 3 mass
eigenstates which are stable (they do not oscillate); the 3 known
neutrino flavors are mixtures of these mass eigenstates.
-- jt]]

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On 3/26/20 12:44 AM, raymond.yohros@gmail.com wrote:

Why then can we not determine what % of the speed of light
the [neutrinos] where traveling at and with some algebra as usual
determine their masses as well?

The resolution in measuring their speed is too poor to distinguish it
from c, by many orders of magnitude. So their mass cannot be determined
from their speed. And as the moderator mentioned, one would also need to
know the energy of the neutrinos.

Also, KATRIN did not actually measure the mass of the electron neutrino,
they only put an upper limit of 1.1 eV on it. They may be able to reduce
that somewhat, but it is a very challenging measurement.

Note that neutrino oscillation measurements imply nonzero but much
smaller mass differences between the different neutrino mass
eigenstates; they cannot determine the mass of any of them.

Tom Roberts

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In article <r5ijjk$16a$1@gioia.aioe.org>, "Phillip Helbig (undress to
reply)" <helbig@asclothestro.multivax.de> writes:

Note that neutrinos from the supernova 1987A in the Large Magellanic
Cloud emitted neutrinos which were detected on Earth. Since the
difference in emission times of light and neutrinos is only about 3
hours, this is negligible for the travel time of 157,000 years and thus provides a good lower limit on the speed of neutrinos (i.e. very close
to the speed of light). This gives an upper limit on the mass of the electron neutrino of about 26 eV. Current limits are about 0.11 eV.
However, because of neutrino oscillations, we know that it is non-zero.

[[Mod. note -- To amplify one point Phillip made: measurements of neutrino oscillations tell us the *difference* between the *squares* of the masses
of different types of neutrinos, i.e., they tell us something like
m1**2 - m2**2 . But if my dim recollection is correct, they don't
easily tell us which of the 3 types of neutrinos m1 and m2 refer to.
-- jt]]

I now see that what I wrote is somewhat confusing. The only sentence
which refers to neutrino oscillations is the very last one, added to
emphasize the point that while upper limits have been decreasing, unlike
the mass of the photon or graviton it is ruled out that the mass of the neutrino could be exactly zero, because of neutrino oscillations, even
there is no lower limit on the mass from more-direct measurements of the
mass. As Jonathan mentioned, they tell us something about the
differences of the squares of the masses, not the masses themselves.
(I'm not absolutely sure that the case of one massless and two massive neutrinos is not allowed, but I think that the implication is that all
three types have a non-zero mass.)

With regard to the time-of-flight measurements from supernova 1987A,
note that massless neutrinos would all have the same time of flight,
even with different energies. With a mass, different energies would
lead to differences in the times of flight. The measured spread on
arrival times can put an upper limit on the mass.

While probably most expect the electron neutrino to be the lightest and
the tau neutrino the heaviest, like the corresponding charged particles, apparently an inverted mass hierarchy is possible, with some other
ordering. In other words, we don't know if the electron neutrino is necessarily the lightest one.

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Tom Roberts wrote:

raymond.yohros wrote:

Why then can we not determine what % of the speed of light
the [neutrinos] where traveling at and with some algebra as usual
determine their masses as well?

The resolution in measuring their speed is too poor to distinguish it
from c, by many orders of magnitude. So their mass cannot be determined
from their speed. And as the moderator mentioned, one would also need to
know the energy of the neutrinos.

Also, KATRIN did not actually measure the mass of the electron neutrino,
they only put an upper limit of 1.1 eV on it. They may be able to reduce
that somewhat, but it is a very challenging measurement.

Note that neutrino oscillation measurements imply nonzero

Which in turn implies irregularity of shape?

but much smaller mass differences between the different neutrino
mass eigenstates;

Three masses gives two differences; is there anything like an integral
common denominator?

they cannot determine the mass of any of them.

So how are the differences determined?

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Ned Latham <nedlatham@internode.on.net> writes:

Tom Roberts wrote:

but much smaller mass differences between the different neutrino
mass eigenstates;

Three masses gives two differences; is there anything like an integral
common denominator?

Differences between the SQUARES of the masses. And there are three pairs of squares of mass differences.

Three equations and three unknowns, in theory this should be solvable or at least reduced to a degenerate.

Is it possible for exactly one of the eigenstates, or exactly one neutrino mass to be exactly 0, or do all 3 need nonzero mass?

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Tom Roberts <tjroberts137@sbcglobal.net> writes:

On 3/26/20 12:44 AM, raymond.yohros@gmail.com wrote:

Why then can we not determine what % of the speed of light
the [neutrinos] where traveling at and with some algebra as usual
determine their masses as well?

The resolution in measuring their speed is too poor to distinguish it
from c, by many orders of magnitude. So their mass cannot be determined
from their speed. And as the moderator mentioned, one would also need to
know the energy of the neutrinos.

Re SN 1987A, what is believed to be the reaction(s) which produce the
majority of its neutrinos? What is the energy of those neutrinos?

Assuming the SN1987A progenitor is relatively stationary wrt us, and
from the time between neutrino detection and visible evidence of the
supernova, we know the neutrinos must be going at very close to c.
However, there should be an estimate of their minimum speed (still
nearly c, of course, and from that we should be able to determine the
minimum gamma of the neutrinos from our reference. From that and the
estimated energy of the neutrinos, we should be able to put an upper
limit on their masses, and it would have to be very small for such a
large gamma. I assume this has been done, correct? Or does neutrino oscillation throw everything off?

Speaking of which, I don't see how a neutrino could convert to a
different type with a different mass without violating conservation of
energy, momentum or both. What is happening with this?

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On Sunday, March 29, 2020 at 3:43:29 PM UTC-5, Michael Moroney wrote:

Speaking of which, I don't see how a neutrino could convert to a
different type with a different mass without violating conservation of energy, momentum or both. What is happening with this?

and the irony is that conservation laws are the reason they
where discovered!

I'm sure it has something to do with distance,temperature and the medium
they travel, and again, conservation laws will give us the clue once
again. It is all part of solving the vacuum catastrophe, our current
crisis in physics

r.y

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[[Mod. note -- I apologise for the delay in processing this article,
which the author posted on Sunday 2020-03-29.
-- jt]]

Michael Moroney wrote:

Ned Latham <nedlatham@internode.on.net> writes:

Tom Roberts wrote:

but much smaller mass differences between the different neutrino
mass eigenstates;

Three masses gives two differences; is there anything like an integral common denominator?

Differences between the SQUARES of the masses.

There have to be differences of the square roots of the squares too.

And there are three pairs of squares of mass differences.

You're right. I have no idea how I did that.

Three equations and three unknowns, in theory this should be solvable
or at least reduced to a degenerate.

Is it possible for exactly one of the eigenstates, or exactly one
neutrino mass to be exactly 0, or do all 3 need nonzero mass?

You know my opinion on that. They must all be non-zero.

There is still the question of whether there is an integral common
denominator.

[[Mod. note -- The neutrino-oscillation observations give information
(only) on the differences between the squares of the masses.

We have no reason to expect the masses to be in integer ratios.
-- jt]]

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On Friday, March 27, 2020 at 3:17:02 AM UTC-5, Tom Roberts wrote:

On 3/26/20 12:44 AM, raymond.yohros@gmail.com wrote:

Why then can we not determine what % of the speed of light
the [neutrinos] where traveling at and with some algebra as usual
determine their masses as well?

The resolution in measuring their speed is too poor to distinguish it
from c, by many orders of magnitude. So their mass cannot be determined
from their speed. And as the moderator mentioned, one would also need to
know the energy of the neutrinos.

Ice cube detected neutrinos in the order of 1 Pev's(bert and ernie)
and big bird was 2 Pev's!
That may be around 2 magnitude orders higher than protons
spinning on the LHC!

of course the sources and flight times of these cosmic
neutrinos where undetermined but there are clues about where
In the sky they may have come to point telescopes.
one of those may have been a blazar, PKS B1424-418

The point i tried to make in my second post was that we
may be tempted to think that their masses may not be
fixed values beside their 3 stable eigenstates.

And this is not the first time we observe something like this in nature
You may say that a z bosons may be 91.19 Gev/c2
But you can find them at other values with less probabilities!

Flying at variable speeds, variable mass distributions,
Fermions but with some bosonic characteristics, this
Particles truly hold the answers to the best
question we can ask.

cheers
r.y

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In article <693dc170-665b-478d-b351-3c543da09c36@googlegroups.com>, raymond.yohros@gmail.com writes:

On Sunday, March 29, 2020 at 3:43:29 PM UTC-5, Michael Moroney wrote:

Speaking of which, I don't see how a neutrino could convert to a
different type with a different mass without violating conservation of
energy, momentum or both. What is happening with this?

It's a difficult concept, but not unknown in particle physics. Observed particles can be mixtures of other particles, and the state of the
mixture can changed during propagation, so it's not like one type of
neutrino can change into another (which would indeed be forbidden by conservation laws).

and the irony is that conservation laws are the reason they
where discovered!

Isaac Asimov wrote a book on the neutrino. The neutrino makes its
introduction about halfway through the book. The first half is about conservation laws.

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On 31/03/2020 11:14, Phillip Helbig (undress to reply) wrote:

In article <693dc170-665b-478d-b351-3c543da09c36@googlegroups.com>, raymond.yohros@gmail.com writes:

On Sunday, March 29, 2020 at 3:43:29 PM UTC-5, Michael Moroney wrote:

Speaking of which, I don't see how a neutrino could convert to a
different type with a different mass without violating conservation of
energy, momentum or both. What is happening with this?

It's a difficult concept, but not unknown in particle physics. Observed particles can be mixtures of other particles, and the state of the
mixture can changed during propagation, so it's not like one type of
neutrino can change into another (which would indeed be forbidden by conservation laws).

and the irony is that conservation laws are the reason they
where discovered!

Isaac Asimov wrote a book on the neutrino. The neutrino makes its introduction about halfway through the book. The first half is about conservation laws.

It's indeed a not so easy concept, and it's not so easy to find an
entirely correct treatment in the literature. First of all of course
mixing means that the "type of neutrino" changes. To understand in which
sense one needs a bit of QFT background.

First of all one has to remember that the identification of certain
states of a quantum field, the socalled one-particle Fock states, as
particles apply only to (asymptotic) free fields. These are spanned by
the one-particle states of definite momentum, mass and spin (or for
massless particles helicity). Thus only mass eigenstates are
interpretible as particles which are sufficiently far away from other
particles they interact with ("asymptotic free states").

Interacting QFT lets you calculate transition rates from one initial
asymptotic free state (usually two particles) to another final
asymptotic free state (where you can have, of course, any number of
newly created particles as far as the corresponding reaction is allowed
by the conservation laws).

Now neutrinos are the uncharged leptons and thus take part in the
electroweak but not the strong interaction. The electroweak interaction
within the Standard Model is described by a chiral gauge theory, and in
the Standard Model the neutrinos are treated as massless Dirac
particles, of which only the left-handed part interacts via the weak interaction.

Now with the discovery of neutrino oscillations this is not entirely
correct anymore, and one has to extend the Standard Model. The
implication of neutrino mixing is that first of all at least two of the
three neutrino states must get massive and second that the neutrino
flavor eigenstates are not the neurtino-mass eigenstates.

In consequence strictly speaking you cannot directly observe neutrinos
but only via the reaction of neutrinos with other directly observable particles. This is because, the neutrinos are created in flavor
eigenstates, e.g., by the decay of muons to muon neutrinos + something
else (nearly 100% decay channel is mu->e+\bar{\nu}_e + \nu_{\mu}). These
are not the mass eigenstates and thus on their propagation they
oscillate between the different flavor eigenstates, and you can only
observe them by some reaction in the detector material via other
particles. The reaction is again in a flavor eigenstate through the weak interaction. Due to the oscillation you have some probability to detect
each of the three flavors, and this probability is determined by the
distance between the source and the detector ("long baseline
experiments") and the mixing matrix (a unitary matrix, called the Pontecorvo---Maki---Nakagawa---Sakata matrix which describes the
transformation between mass- and flavor-eigenstates.

This is in close analogy with the quark-mixing matrix (the Cabibbo-Kobayashi-Maskawa), where also the d-, s-, b- flavor eigenstates
are not the same as the mass eigenstates. As there you also have
CP-violating phases for the neutrinos. The difference is that in contradistinction to the charged quarks, which are clearly Dirac
fermions, the neutral neutrinos could well be also Majorana particles,
i.e., they could be "strictly neutral" and thus their own antiparticles.
In this case there are two more CP-violating phases. Whether or not this
is the case or whether or not the neutrino-mixing matrix violates CP is
not yet known. Also the neutrino masses are not well known.

For an effective description of neutrino oscillations, see the Wikipedia article:

https://en.wikipedia.org/wiki/Neutrino_oscillation

but be aware that this is an effective description, which doesn't take
into account the above mentioned quantum-field theoretical
creation-detection mechanism which makes everything consistent with both
energy and (!!!) momentum conservation as in any other scattering
process. For the full QFT treatment see

https://arxiv.org/abs/1008.2077

--
Hendrik van Hees
Goethe University (Institute for Theoretical Physics)
D-60438 Frankfurt am Main
http://fias.uni-frankfurt.de/~hees/

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On 3/29/20 3:43 PM, Michael Moroney wrote:

Re SN 1987A, what is believed to be the reaction(s) which produce the majority of its neutrinos? What is the energy of those neutrinos?

The usual suspects: nuclear interactions giving neutrinos of a few MeV,
and particle decays that can be either lower or higher energy.

Assuming the SN1987A progenitor is relatively stationary wrt us, and
from the time between neutrino detection and visible evidence of the supernova, we know the neutrinos must be going at very close to c.
However, there should be an estimate of their minimum speed (still
nearly c, of course, and from that we should be able to determine the
minimum gamma of the neutrinos from our reference. From that and the estimated energy of the neutrinos, we should be able to put an upper
limit on their masses, and it would have to be very small for such a
large gamma. I assume this has been done, correct? Or does neutrino oscillation throw everything off?

The difficulty is understanding the astrophysical processes that emit
the neutrinos,and those that emit the light. The neutrinos were detected
BEFORE the light from SN1987A, so the astrophysical processes dominate
the time difference, not slower propagation due to nonzero neutrino mass.

By applying a common astrophysical model, Arnett and Rosner calculate an
upper bound on neutrino mass of 12 eV [Arnett and Rosner, PRL _58_
(1987), p1906]. That is significantly higher than other experiments'
upper limits. And the uncertainty in the astrophysics involved is large.

Speaking of which, I don't see how a neutrino could convert to a
different type with a different mass without violating conservation of energy, momentum or both. What is happening with this?

Neutrino oscillation is not a "conversion". Rather it is the usual
quantum mechanical process of projecting a wavefunction onto different
basis eigenstates. When the weak interaction creates a neutrino, it is
created in a "flavor eigenstate" -- either nu_e, nu_mu, or nu_tau
(electron, muon, and tau neutrino). But those are not the same as the
"mass eigenstates" (which are better called "eigenstates of the
propagation Hamiltonian"). These latter eigenstates describe how the wavefunction (amplitude) propagates. Each mass eigenstate has nonzero
overlap with each flavor eigenstate, but with different factors, so each
flavor eigenstate has different fractions of the mass eigenstates. Since
the mass eigenstates have different masses, their amplitudes vary in
space along the propagation direction with different wavelengths (this
is the usual rotation of their complex phase). This would be
unobservable by itself, but when the neutrino interacts in the detector,
it does so as a flavor eigenstate, and the different mass eigenstates in
the wavefunction interfere, giving a different amplitude for the flavor eigenstates than when it was created. That difference is a function of
which flavors are involved, the distance between creation and detection,
and the energy of the neutrino -- measurements on earth over several
hundred kilometers can provide considerable detail of the process
because the neutrino beam has a range of energies.

As for conservation of 4-momentum, remember that in QM no wavefunction
is perfectly sharp. The creation interaction expressed as a flavor
eigenstate has sufficient indeterminacy in 4-momentum to have nonzero
overlaps with each of the mass eigenstates. Each mass eigenstate
propagates independently, conserving 4-momentum. Since their amplitudes
vary differently in space, and the flavor eigenstates have different
fractions to the mass eigenstates, at the detector the overlap with
flavor eigenstates is different from what it was at creation. So at
creation the neutrino had a definite flavor, but at the detector it has
nonzero amplitude to be each of the three flavors; for a given neutrino
the detector will see only one of them, but for the beam there will be a distributions of all three flavors, even if the beam was all created as
a single flavor.

Tom Roberts

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On 20/03/31 6:17 PM, Hendrik van Hees wrote:
...> Now neutrinos are the uncharged leptons and thus take part in the

electroweak but not the strong interaction. The electroweak interaction within the Standard Model is described by a chiral gauge theory, and in
the Standard Model the neutrinos are treated as massless Dirac
particles, of which only the left-handed part interacts via the weak interaction.

Now with the discovery of neutrino oscillations this is not entirely
correct anymore, and one has to extend the Standard Model. The
implication of neutrino mixing is that first of all at least two of the
three neutrino states must get massive and second that the neutrino
flavor eigenstates are not the neutrino-mass eigenstates.

And do you think the right-handed part will still not be interacting?

What does that mean for neutrinos standing still? Or more precisely,
neutrino fields at energies much lower than their mass? Is there a kind
of 'electroweak-static' theory, like we have classical electrostatics
for QED with the electrons at much lower energy than their mass?

--
Jos

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Tom Roberts <tjroberts137@sbcglobal.net> writes:

On 3/29/20 3:43 PM, Michael Moroney wrote:

Re SN 1987A, what is believed to be the reaction(s) which produce the
majority of its neutrinos? What is the energy of those neutrinos?

The usual suspects: nuclear interactions giving neutrinos of a few MeV,
and particle decays that can be either lower or higher energy.

I was wondering if a oarticular reaction of a certain energy dominated.
I know the general idea behind the formation of a neutron star was that
p + e = n + nu, but was there a particular energy or energy range most
of the neutrinos would have, particularly if most of the protons may be
protons in iron nuclei or something.

Assuming the SN1987A progenitor is relatively stationary wrt us, and
from the time between neutrino detection and visible evidence of the
supernova, we know the neutrinos must be going at very close to c.
However, there should be an estimate of their minimum speed (still
nearly c, of course, and from that we should be able to determine the
minimum gamma of the neutrinos from our reference. From that and the
estimated energy of the neutrinos, we should be able to put an upper
limit on their masses, and it would have to be very small for such a
large gamma. I assume this has been done, correct? Or does neutrino
oscillation throw everything off?

The difficulty is understanding the astrophysical processes that emit
the neutrinos,and those that emit the light. The neutrinos were detected >BEFORE the light from SN1987A, so the astrophysical processes dominate
the time difference, not slower propagation due to nonzero neutrino mass.

By applying a common astrophysical model, Arnett and Rosner calculate an >upper bound on neutrino mass of 12 eV [Arnett and Rosner, PRL _58_
(1987), p1906]. That is significantly higher than other experiments'
upper limits. And the uncertainty in the astrophysics involved is large.

OK. So this was done but answers from other methods are better.

Speaking of which, I don't see how a neutrino could convert to a
different type with a different mass without violating conservation of
energy, momentum or both. What is happening with this?

Neutrino oscillation is not a "conversion". Rather it is the usual
quantum mechanical process of projecting a wavefunction onto different
basis eigenstates. When the weak interaction creates a neutrino, it is >created in a "flavor eigenstate" -- either nu_e, nu_mu, or nu_tau
(electron, muon, and tau neutrino). But those are not the same as the
"mass eigenstates" (which are better called "eigenstates of the
propagation Hamiltonian"). These latter eigenstates describe how the >wavefunction (amplitude) propagates. Each mass eigenstate has nonzero
overlap with each flavor eigenstate, but with different factors, so each >flavor eigenstate has different fractions of the mass eigenstates. Since
the mass eigenstates have different masses, their amplitudes vary in
space along the propagation direction with different wavelengths (this
is the usual rotation of their complex phase). This would be
unobservable by itself, but when the neutrino interacts in the detector,
it does so as a flavor eigenstate, and the different mass eigenstates in
the wavefunction interfere, giving a different amplitude for the flavor >eigenstates than when it was created. That difference is a function of
which flavors are involved, the distance between creation and detection,
and the energy of the neutrino -- measurements on earth over several
hundred kilometers can provide considerable detail of the process
because the neutrino beam has a range of energies.

OK, so this is better thought of like Schrodinger's cat. You don't know
if the cat is dead or alive until you open the box. And you can't claim
the neutrino starts off as an electron neutrino, becomes a muon neutrino
then an electron neutrino then interacts as a tau neutrino, but you can
only say it has odds of X, Y and Z of interacting as each type and
actually does interact as one type. This is the same idea as if you
sent a single photon to a double slit, it has odds of showing up at
certain places on the far side, but can actually show up at only one
spot.

Correct?

As for conservation of 4-momentum, remember that in QM no wavefunction
is perfectly sharp. The creation interaction expressed as a flavor
eigenstate has sufficient indeterminacy in 4-momentum to have nonzero >overlaps with each of the mass eigenstates. Each mass eigenstate
propagates independently, conserving 4-momentum. Since their amplitudes
vary differently in space, and the flavor eigenstates have different >fractions to the mass eigenstates, at the detector the overlap with
flavor eigenstates is different from what it was at creation. So at
creation the neutrino had a definite flavor, but at the detector it has >nonzero amplitude to be each of the three flavors; for a given neutrino
the detector will see only one of them, but for the beam there will be a >distributions of all three flavors, even if the beam was all created as
a single flavor.

OK. But still if a bunch of electron neutrinos gets created and some
interact as tau neutrinos of a different mass, doesn't that still mean
that one or the other of energy and momentum must be different in the interaction? Or that's "OK" because of the uncertainty involved?

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I have an addition question about neutrino oscillation.

If you look at the article
https://en.wikipedia.org/wiki/Neutrino_oscillation and the last three
images under "Three neutrino probabilities" it shows the odds of
detection as a particular type, as a function of distance/energy when
they are created as a particular type. Of course very close to the
origin it is very likely the original type. However for the three charts
they cycle through the probabilities the odds are generally higher they
will be detected as their original type. Meaning they "remember" what
they were created as?

Also the (black) electron type curve is "different" from the muon/tau
types (red/blue). Can we 'conclude' anything from this, perhaps the
muon/tau neutrinos have a similar mass to each other and the electron
type is rather different from them?

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