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?
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.
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?
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]]
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
but much smaller mass differences between the different neutrino
mass eigenstates;
they cannot determine the mass of any of them.
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?
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.
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?
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?
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.
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!
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.
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?
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.
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.
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