This paper explores the recently confirmed hypothesis that neutrinos have mass and that they spontaneously transform from one type to another. That immensely important discovery culminates 40 years of experimental research. After briefly discussing that work, we'll study the quantum mechanical explanation of these phenomena elaborating the concepts of particle mixing, and the oscillation of flavor types. These rather esoteric ideas lead to the prediction that morphing neutrinos must have mass, but there's a much more elegant relativistic argument that brings us to this same conclusion.

1.
J. N.
Wilford
, “
Neutrinos Have Mass, Panel Says
,”
The New York Times
,
C9
(Oct. 24,
1995
). This article presages a growing popular interest in morphing neutrinos.
See for example,
G. P.
Collins
, “
SNO Nus Is Good News
,”
Sci. Am
,
18
(Sept.
2001
);
A.
Fisher
, “
Neutrinos Weigh In
,”
Popular Sci.
,
24
(Sept.
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);
A.
MacRobert
and
D.
Tytell
, “
Solar-Neutrino Problem Solved
,”
Sky & Telescope
,
18
(Sept.
2001
);
R.
Kunzig
, “
The Unbearably Unstoppable Neutrino
,”
Discover
,
33
(Aug.
2001
);
P.
Weiss
,”
Physics Bedrock Cracks, Sun Shines In
,”
Sci. News
,
388
(June 23,
2001
).
2.
The Liquid Scintillating Neutrino Detector (LSND) was the first accelerator-based experiment to generate results suggesting neutrino oscillations. The work is presently being repeated at Fermilab using the Mini-BooNE detector, which contains 250,000 gallons of ultra-pure mineral oil.
3.
In the standard model a neutrino is completely polarized; its spin vector is antiparallel to its linear momentum vector. Thus, the neutrino is left-handed, whereas the antineutrino is right-handed. But these characteristics are relativistically invariant only if the particles travel at c. Otherwise an observer moving faster than the neutrino in the same direction will see it receding, its momentum vector reversed, and its handedness inverted.
4.
The neutrino deficit appears to depend on energy (solar neutrinos have energies of only up to about 15 MeV). Davis's 600-ton (dry cleaning fluid) radiochemical detector in the Homestake mine in South Dakota found about one-third of the predicted number of events. The Kamiokande light water Cherenkov experiment (1986) in Japan recorded about one-half of the anticipated solar neutrino events. Two more recent radiochemical gallium experiments, SAGE and GALLEX, which had lower energy thresholds, reported values of roughly 70% of the theoretical predictions.
5.
B.
Pontecorvo
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Neutrino experiments and the problem of conservation of leptonic charge
,”
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(
1968
).
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M.
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and
A.
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,
Phys. Rev.
97
,
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(
1955
).
7.
See, for example, A. Das and T. Ferbel, Introduction to Nuclear and Particle Physics (Wiley, New York, 1994), pp. 214–249, or H. Frauenfelder and E.M. Henley, Subatomic Physics (Prentice Hall, New Jersey, 1991), pp. 242–251.
8.
K0 and its antiparticle K0¯, which have the same mass and lifetime, are distinguishable by their difference in strangeness. They are produced in strong-interaction processes such as K+ + n → K0 + p and K + p → K0¯ + n. The corresponding two linear orthonormal combinations of weak interaction eigenstates are |K0〉 = 12 {|K20〉 + |K10〉} and |K0¯〉 = 12{|;K20〉 − |K10〉}. The factor 1/2 is for normalization of the wave functions. The weak interaction does not conserve strangeness and the initially orthogonal states |K0 and |K0¯ will not remain orthogonal in time.
9.
D.J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, New Jersey, 1995), pp. 20–24 and 44–48.
10.
The K10- and K20-states actually decay, so there ought to be a multiplicative exponential term present in the phase that depends on the lifetime of each state. Since this will not be the case with neutrinos, we;ll neglect it here. See, for example, W.B. Rolnick, The Fundamental Particles and Their Interactions (Addison Wesley, Reading, MA, 1994), pp. 219–224.
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W. C.
Haxton
and
B. R.
Holstein
, “
Neutrino physics
,”
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,
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32
(Jan.
2000
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12.
The New Physics, edited by P. Davies (Cambridge University Press, New York, 1989), p. 380.
13.
Each lepton comes in both particle and antiparticle varieties, making a total of six electrically charged and six neutral leptons. These form three — electron, muon, and tau — particle-neutrino couplets: e and νe; μ and νμ; and τ and ντ. Lepton number (L) is conserved in all presently attainable processes involving any members of this family. Each of the three subsets of leptons (electron-type, muon-type, and tau-type) was also thought to conserve its own lepton number (Le,Lμ,Lτ). This cannot, however, be strictly true if morphing takes place.
14.
For a more mathematically detailed discussion of neutrino mixing, see D.H. Perkins, “Neutrino Oscillations,” in Critical Problems in Physics, edited by V.L. Fitch, D.R. Marlow, and M.A.E. Dementi (Princeton University Press, Princeton NJ, 1997), pp. 201–219. Also see W.B. Rolnick, The Fundamental Particles and Their Interactions (Addison Wesley, Reading MA, 1994), pp. 375–378, and Kane, Modern Elementary Particle Physics (Addison Wesley, Reading MA, 1993), pp. 303–309.
15.
E.
Lane
, “
Study: Neutrino Has Mass
,”
Newsday
, (
D3
April 30,
2002
).
16.
“New SNO Data Resolves Solar Neutrino Problem,” APS newsletter 2(6) 3 (June 2002).
17.
The converse, massive neutrinos morph, is not necessarily true.
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