If You Can't Find Neutrinos,
Then They Oscillate?
With neutrinos, you
are often exposed to something called an "upper limit". But what is an "upper limit", and what does
it do for the neutrino physicists when used in place of finite values?
Exactly. That’s its function. To take the place of finite values that they
can’t measure. In neutrino experiments,
an "upper limit" is effectively a place holder in case the experimental value
they are trying to measure just happens to show up someday. In other words, they didn’t find anything,
but when they do, it’s probably smaller than this "upper limit". So, what were you expecting? A real value?
And the beauty of the
"upper limit" is that it allows the neutrino physicists to quote numbers
greater than zero when they didn’t find what they were looking for.
Raymond Davis,
the Nobel Prize winning neutrino physicist, recounted the comments made by a
reviewer of his "upper limit" approach to reporting his neutrino data:
"Any experiment such as this, which does not have the
requisite sensitivity, really has no bearing on the question of the existence
of neutrinos. To illustrate my point, one would not
write a scientific paper describing an experiment in which an experimenter
stood on a mountain and reached for the moon, and
concluded that the moon was more than eight feet from the top of the mountain."[1]
But "upper limits"
stuck, and experimentalists reporting nothing but
"upper limits" continued to be published.
And by the middle of
1968, Davis had published three separate unsuccessful experiments that all failed to detect neutrinos. All three of these
experiments were using Bruno Pontecorvo’s recommendation of using Cl-37 as the
target atom for neutrino absorption (1954, 1964, and 1968).
Now, this should have raised the question
as to whether Cl-37 was a valid approach to detecting neutrinos. Do neutrinos really interact with Cl-37 at
all? Perhaps they don’t interact with
any form of matter? Or perhaps there are
no neutrinos?
But nope, the neutrino physicists didn’t
speak openly about this. Instead, the
lack of the discovery of even a single neutrino became the "solar neutrino
problem", which hit the presses shortly after Raymond Davis reported the
results of his first two experiments at the Homestake Mine.
And instead of publicly questioning
whether Cl-37 was a valid approach in detecting neutrinos, everything else was
thrown at the wall.
The theories explaining this "solar
neutrino problem" were numerous and diverse, including such ideas as solar
helium-3 overabundance, quark catalysis, the existence of a neutrino magnetic
moment, neutrino decay, solar instability, an overly rapid rotating solar interior,
etc.
But the one that was to become the savior of the "solar neutrino problem"
was heavily promoted by the same person that came up with using Cl-37 in
the first place. Bruno Pontecorvo. It was also a less professionally damaging
explanation to both experimentalists and theorists alike.
One should certainly be suspicious about
Pontecorvo’s motivations. After all, a
lot of time and money had been invested in his Cl-37 approach to neutrino
detection. And the experimental results
were far below prediction.
After all, there were a lot of physicists
involved in this mess that have spent a lot of money and time,
only to find nothing. It certainly
didn’t hurt Pontecorvo’s career to promote some other reason why
neutrinos hadn’t been detected using Cl-37.
And according to Pontecorvo, that reason
would be quite simple: neutrinos change into other neutrinos, and back again. They oscillate.
It was brilliant. You can’t detect neutrinos because they’ve
changed into something else that can’t be detected.
In 2003, a report on the CHOOZ experiment
authored by 40 physicists summarizes this attitude:
"Several experiments, studying
solar [5,6,7,8] or atmospheric neutrinos [9,10,11, 12,13,14], have measured
fluxes consistently lower than expectations. This
can be interpreted as due to various forms of neutrino oscillations[emphasis added]."[2]
Okay, so the physicists were having
trouble detecting solar and atmospheric neutrinos. And among the many dozens of possible
explanations, oscillation stuck to the wall.
So how did Pontecorvo’s spin on the
problem of detecting neutrinos end up with the universal belief in neutrino
oscillation?
Let’s go back to 1954, when Davis reported
his first negative result using Pontecorvo’s Cl-37 method. Pontecorvo
was certainly aware that this was a problem with either neutrino theory or the way
the Cl-37 experiments were conducted.
Pontecorvo believed that neutrinos were detectible,
and his Cl-37 approach was the best way to do it.
But so far, nothing has been detected, and an "upper limit" was
constructed in place of an actual finite experimental number.
A year later, after Davis’s first reported
negative result, Murray Gell-Mann and Abraham Pais proposed
that neutral kaon decay into pions could be explained
by a "particle mixture" approach, and that a neutral kaon has an antiparticle
that it could transition to and from via a weak interaction.[3]
In other words, the
particle can "oscillate". Now, kaons
decay very quickly, and if there are transitions between kaon states before
decay, they do not "oscillate" longer than a small fraction of a second.
But to Pontecorvo, this
idea was gold. He could contort it into an
explanation as to why Davis has yet to find a neutrino. Pontecorvo therefore presented the very bold neutrino
oscillation hypothesis:
"If
the theory of the two-component neutrino is not valid (which is hardly probable
at present) and if the conservation law for the neutrino charge does not apply,
then in principle neutrino → antineutrino transitions could take place in
vacuo."[4]
It’s all very
logical. If a neutrino conservation law for
charge does not apply, then a neutrino could transition into an
antineutrino. Why not? But imagine saying that same thing about electrons and
positrons.
Nonetheless, Pontecorvo was all in with his
"oscillating neutrino" hypothesis, and used it to explain why Reines and Cowan
had problems detecting them:
"The
cross section of the process [antineutrino + proton → positron + neutron]
from reactor must be smaller than expected. This is due to the fact that the
neutral lepton beam which at the source is capable of inducing the reaction
changes its composition on the way from the reactor to the detector."[5]
Pontecorvo speaks
with surety about this. The problem
wasn’t with the fact that his Cl-37 approach to neutrino detection didn’t
work. It wasn’t the experiments or the
theory.
The problem is with
the neutrinos. They are changing into
something else. After all, neutral kaons
have just been proposed to do just that by none other than a giant among contemporary
physicists, Murray Gell-Mann.
While this sounds very
much like a "dog ate my homework" theory, it had the cover of Gell-Mann’s proposal of transitioning neutral kaon
antiparticles.
Kaons are unstable
particles, and have very short lifetimes, unlike the prevailing theory about neutrinos,
which were stable.
And further,
Gell-Mann’s theory had a neutral kaon transitioning between itself and its own
antiparticle. And yet, Pontecorvo’s
oscillation not only includes an electron neutrino and its own antiparticle, but
also an oscillation between an electron neutrino and a muon neutrino.
So how did Pontecorvo
slip this one in so easily? How did he
go from the particle-antiparticle Kaon transition proposed by Gell-Mann, and
into a transition between electron and muon neutrinos?
In 1967, Pontecorvo
published a paper where his "neutrino oscillation" was first mentioned:
"There
will occur oscillations el-neutrino ↔ mu-neutrino, which can in
principle be observed not only by means of measurements of the intensity and
the 'time-variation' of the original particles far from their source,
but also by means of detection of new particles.
It
is true that one cannot observe directly the
transformation of a reactor neutrino into a mu-neutrino, since low energy
mu-neutrinos (E smaller than the muon mass) cannot be registered. On the other hand high energy mu-neutrinos can convert into normally
active el-neutrinos.
We
note that the formulation of the neutrino-oscillation problem in vacuum is
complicated by the existence of a large number of
possibilities [emphasis added]."[6]
And with Pontecorvo,
there are always a large number of possibilities. So, Pontecorvo just throws out the "el-neutrino ↔
mu-neutrino" oscillation proposal in a section of the paper titled: "REMARKS ON
METHODS OF DETECTION FOR NEUTRINO OSCILLATIONS".
While
Pontecorvo is usually assigned credit for the concept of "neutrino
oscillation", the idea was already in the air in the form of "quantum
superposition".
In 1962, Maki,
Nakagawa and Sakata introduced "neutrino mixing", which proposed that electron
and muon neutrinos were a linear combination of two "true neutrinos", and these
"true neutrinos" have different masses.
So,
quantum superposition has been pulled out of the physicist’s bag of tricks, and
muon and electron neutrinos are assumed to be linear combinations of two "true
neutrinos". Maki et al. outline their
proposal of their new "true" neutrinos:
"It should be stressed at this stage that the
definition of the particle state of neutrino is quite arbitrary; we can speak
of ‘neutrinos’ which are different of weak neutrinos but expressed by the
linear combinations of the latter. We assume that
there exists a representation which defines the true neutrinos through
some orthogonal transformation applied to the representation of weak neutrinos
[muon and electron neutrinos] ...."[7]
So,
Maki presumed that muon and electron neutrinos were linear combinations of two
new "true" neutrinos. But this approach wasn't exactly the same as Pontecorvo's.
While
Pontecorvo’s oscillation theory was ballyhooed as a great insight into the "solar
neutrino problem", he actually threw this theory out
there to address the current problems in detecting reactor and accelerator
generated neutrinos. Pontecorvo even
derived theoretical calculations of neutrino oscillation lengths.
"To such a mass value
there corresponds a length of 10 cm for megavolt-neutrinos (from reactors), and
100 m for gigavolt-neutrinos (from accelerators)"[8]
And ironically,
Pontecorvo uses it to explain the results of a recently published paper[9] by none other than Frederick Reines, where
the experimental cross section came up short from the theoretical cross section. Pontecorvo gave his thoughts on the
shortfall:
"In experiments involving el-neutrinos
from reactors, the existence of an oscillation length which is definitely smaller than the reactor diameter, as well as the
reactor-detector distance (approximately 10 m) would lead to a decrease by a
factor of two of the intensity of active particles which hit the detector,
since the number of anti-el-neutrinos from a reactor
and the number of sterile particles would be equal for large distances. This
would lead to a cross section for the reaction ne
+ p → e+ + n, as
measured in the experiments of Nezrick and Reines [22]
which is half as large as the one computed for a two-component neutrino. There is apparently no such discrepancy.
Therefore we may assume that reactor experiments exclude oscillation lengths
smaller than 10 cm (or they exclude the value F/G ≥
10-3, according to diagram b in Fig. 3), although there is no
complete certitude in this matter. [emphasis added]"[10]
So Pontecorvo was
using his oscillation calculations help explain another experimentally
determined shortfall in neutrino flux by Reines, and how to approach future
experiments based on the "oscillation length" of the neutrino. And as was often the case in his
publications, he finished it with a disclaimer (in bold).
But, as of 1968, the
neutrino proponents had a very serious problem, as Pontecorvo acknowledged in a
letter published in 1969:
"Davis
et al. [the Homestake Mine experiment] so far were not able to detect solar
neutrinos [emphasis added]. It was
shown by them that the neutrino flux at the earth from 8B decay in
the sun [5] is smaller than 2 x 106 cm2 sec-1. This limit is definitely
smaller than the theoretical predictions [6,7]. However, various
astrophysics and nuclear physics uncertainties do not allow to draw the
conclusion that we are faced with a catastrophic discrepancy [emphasis
added][7]. The purpose of this note is to emphasize
again that the result of sun neutrino experiments are
related not only to the above mentioned uncertainties but also, and in a marked
way, to properties which are so far unknown [8] of the neutrino as an
elementary particle [emphasis added]."[11]
And in this letter, Pontecorvo
acknowledges that there is no evidence for a single solar neutrino detected
using his Cl-37 methodology. But
Pontecorvo doesn’t even bother to state that there might be issues with his
Cl-37 approach, but rather, blames the problem on "properties which are so far
unknown of the neutrino".
Neutrino Oscillations or Bust
What the heck is a
"neutrino oscillation", and how does it work?
The most popular interpretation is that neutrinos oscillate because they
have mass. Supposedly, a massless
neutrino can’t oscillate because it travels at the speed of light, although there
are differing opinions on this.
To get an initial
sense of what’s going on with neutrino oscillation, let’s look at Wikipedia’s description:
"the three neutrino
states that interact with the charged leptons in weak interactions are each a
different superposition of the
three (propagating) neutrino states of definite mass. Neutrinos are emitted and
absorbed in weak processes
in flavor eigenstates but travel as mass eigenstates."[12]
According to the
above statement, neutrinos are emitted and absorbed in "flavor eigenstates" but
travel in "mass eigenstates".
What the heck are
they talking about? After all, this is
getting very convoluted, and again sounding something like a very esoteric "dog
ate my homework" theory. But the
neutrino physicists can cover two important bases with this theory.
One is how neutrino "flavors"
interact with matter. And the other is
to account for their "oscillation". And
this is done by proposing three mass eigenstates.
And nothing bails
out the neutrino physicists better than the superposition of eigenstates. You can pretty much explain anything by
inventing eigenstates and assuming they operate in superposition.
Previously, the
theory of oscillation included only electron and muon neutrino eigenstates, as only
electrons and muons were known at the time.
But when physicists found
the tau particle, they quickly presumed that there was a corresponding tau
neutrino. So they
just plugged in another flavor and mass eigenstate into their previous theory,
and were good to go.
And according to
this augmented theory, neutrinos have three flavors (eigenstates): electron (ne),
muon (nm),
and tau (nt). And it is these flavor eigenstates that interact
with ordinary matter.
Each flavor
eigenstate is supposedly a superposition of three mass eigenstates, which they
refer to as: n1, n2,
and n3. It is these mass eigenstates that travel in space.
And according to
this approach, these mass eigenstates are different from each other and have
different corresponding energies.
Therefore, they travel at slightly different velocities. And since these "mass eigenstates" propagate
at slightly different velocities, they get out of phase, and this results in
flavor oscillation. To once again quote Wikipedia:
"This results in a changing superposition mixture of mass
eigenstates as the neutrino travels; but a different mixture of mass
eigenstates corresponds to a different mixture of flavor states."[13]
So, this theory of
neutrinos that has been assigned flavor and mass eigenstates and seems to be
feeding on itself. But this approach
also requires that these "mass eigenstates" have different masses. Because this sets up their argument for
neutrino oscillation, and their proposal that these different mass eigenstates
travel at different velocities.
But is this "mass
eigenstate" proposal just another assumption that gets thrown out there because
the neutrino physicists will believe anything as long as
it can account for the shortfall of experimental evidence? Or is there something compelling about this
argument?
Let’s look at one of
the mathematical approaches to account for neutrino oscillations. To simplify the argument, let’s only consider
neutrino oscillation in the two-flavor case (electron and muon), as tau
neutrinos are relatively rare:
In this equation, in
the term |eiE2t - eiE1t |2, E1 and E2 are the associated energies of the two neutrino mass eigenstates,
m1 and m2. Since
only upper limits have been established for neutrino masses and not discrete
values, we can’t positively identify m1 as the mass component for
the electron neutrino, and m2 for the muon neutrino. But in the parlance of neutrino mass states, it
is presumed that m1 < m2.
If m1 and
m2 have different values, and their associated energies E1 and E2 are
also different, then we can plug them into conventional complex plane wave
equations, such as eiE2t and eiE1t.
Because E1 ≠
E2, these two plane wave equations will therefore have different phases, so we
have constructive and destructive interference, which is the foundation of
neutrino oscillation. Since the term |eiE2t - eiE1t |2 will get a
non-zero result, this is multiplied by cos2q
sin2q to get the probability of
oscillation, where q
is the neutrino "mixing angle".
But what is this
magical neutrino mixing angle?
It’s sort of like a
relationship between the neutrino mass eigenstates and flavor eigenstates, in
the form of an "angle", which is just a proxy for the factors used to predict
the probability of an oscillation event given an initial flavor of the neutrino.
The mixing angle is inherited
from generalized quantum eigenvectors defined to address phenomena where the initial
angle of the motion of a quantum particle is important in the outcome of an
experiment.
So don’t think of a mixing
angle as an angle, but rather, something associated with the probability of
observing a neutrino created in one state and evolving into another state.
But getting back to
the last expression in the above equation,
where we see the heart and soul of the
argument for neutrino oscillation. And
what a strange argument it is. Note the squared mass difference
between the (m2)2 and (m1)2. In algebraic notation:
Δm2 = (m2)2 - (m1)2
Now, keep in mind
that we still don’t have experimentally determined masses for neutrinos. Instead, we have "upper limits". But we do have experimentally determined
squared mass differences, or Δm2.
How
does that work? How are they able to
compute the squared mass difference without knowing the original masses?
That
comes from experimental estimates of the mixing angle. And since we know the time
it takes the neutrinos to travel from the source to the detector, we can solve the
above equation for Δm2.
So,
the neutrino physicists don’t have to know the actual masses of neutrinos. They don’t even have to know which neutrinos
have more mass. They just have to presume that neutrinos have mass eigenstates, and
those eigenstates have different masses.
Now
that we have roughly described one of the most common approaches underlying neutrino
oscillations, in the next section, let’s take a closer look as to why neutrino physicists believe
they have proved them.
Please send comments to Charles Brack at brack@wtfphysics.com
[1] Bahcall, John and Davis, Raymond. Essays
In Nuclear Astrophysics (Cambridge University Press, 1982), pp. 243-285.
[2] Apollonio et al. "Search
for neutrino oscillations on a long base-line at the CHOOZ nuclear power
station." Eur.Phys.J. C27:331-374, 2003. https://arxiv.org/abs/hep-ex/0301017
[3] Gell-Mann, M. and Pais, A. "Behavior of neutral particles under charge
conjugation," Phys. Rev. vol. 97, no. 5, pp. 1387– 1389, 1955.
[4] Pontecorvo,
B. "Mesonium and antimesonium,"
Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, vol. 33, p. 549, 1957, Soviet Physics-JETP, vol. 6,
p. 429, 1958.
[5]
Ibid.
[6]
Pontecorvo, B. Neutrino Experiments and
the Problem of Conservation of Leptonic Charge.
Soviet Physics JETP Vol. 26, No. 5. MAY, 1968.
[7] Maki,
Z., Nakagawa, M., Sakata, S. Remarks on
the Unified Model of Elementary Particles, Prog. Theor. Phys. 28, 870 (1962).
[8]
Pontecorvo, B. May,
1968.
[9] Nezrick, F. and Reines, F. Fission-Antineutrino Interaction
with Protons, Phys.
Rev. 142, 852 – Published 25 February 1966
[10]
Pontecorvo, B. May,
1968.
[11] Gribov, V. and Pontecorvo, B. Neutrino Astronomy and Lepton Charge. Physics Letters, Volume 28B, number 7, 20
January 1969
[12] https://en.wikipedia.org/wiki/Neutrino_oscillation#cite_note-FukudaHayakawa1998-8
[13]
Ibid.
[14]
Lipari, P. Introduction to Neutrino
Physics, Dipartimento di Fisica,
Universita` di Roma "la Sapienza", and I.N.F.N., Sezione di Roma, P.A. Moro 2, I-00185 Roma, Italy. https://cds.cern.ch/record/677618/files/p115.pdf
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