This article was submitted as a term paper for a course
in Particle Physics, Physics 521, given in the Spring semester by Professor
Doreen O. Wackeroth, whose guidance and assistance is gratefully acknowledged.
However, the paper was not accepted as I could not explain how two photons
could bind together or how angular momentum would be preserved if two
photons combined to form a neutrino. Possible explanations have since
been added to this article.
Abstract
A possible sub-structure for the electron neutrino is suggested.
The neutrino may consist of two aligned photons with their magnetic
and electric fields interlocked. That structure is consistent with the
properties of the neutrino, including its tiny mass, velocity slightly
less than the speed of light, helicity, internal frequency, failure
to decay, stability, and unreactiveness. Of particular interest is the
recently discovered phenomenon of neutrino oscillation, which requires
a single neutrino to have two slightly different wavelengths, also consistent
with the proposed structure. Calculations based on this structure yield
reasonable results. A few experimentally testable predictions are made.
Introduction
As science has progressed through the ages, matter has been shown to
be made of molecules, molecules of atoms, atoms of electrons and nucleons,
and nucleons of quarks. Including anti-particles, there are still at
least 61 “elementary” particles.1 A number of
current theories, such as string theory and M-brane theory, propose
sub-structures for so-called elementary particles.2 Models
of neutrinos that have mass have been constructed, but none are theoretically
compelling.3 The neutrino, long considered to be an elementary
particle, has a number of unique properties that are suggestive of an
underlying structure. It is proposed that these properties are consistent
with an sub-structure consisting of two aligned interlocked photons
with axes slightly twisted. The discussion will be limited to the electron
neutrino, which will hereinafter be referred to simply as “the
neutrino.”
Properties
Neutrinos have some very unusual and unique properties that have not
been explained.
Classification
Since the neutrino has a half integer spin of ½, it is a fermion,
along with other matter particles, such as the quarks, mesons, and hadrons.
It is a member of the family of leptons, which includes the electron,
the muon, the tau, the electron neutrino, the muon neutrino, and the
tau neutrino, each of which has an anti-particle.
Forces
The neutrino feels only the weak force and gravity.
Flavors
Neutrinos come in three “flavors,” the electron neutrino,
ve, the muon neutrino, vµ, and the tau neutrino,
vt Each flavor is associated with the corresponding
charged electron. That is, whenever an electron is created with a neutrino,
it is always an electron neutrino and not a muon neutrino or a tau neutrino,
and whenever an electron neutrino collides with matter, it always creates
an electron, never a muon or a tau, and similarly for the other flavors.
Mass
Because no right-handed neutrinos and no left-handed anti-neutrinos
have been found, it was concluded that neutrinos have no rest mass.
The reason is that if they have a rest mass, special relativity requires
that they must have a velocity less than c, the speed of light. In principle,
then, a observer going faster than the neutrino would see a right-handed
neutrino moving away from him, and no right-handed neutrinos are known
to exist.4 Neutrino oscillation, however, meant that neutrinos
have mass,5 as will be hereinafter explained. The electron
neutrino has a rest mass of <5.1 eV/c2; the muon and tau
neutrinos are more massive.
Velocity
While neutrinos were at first thought to travel at the speed of light,
c, it is now known that their speed is very slightly less than c. In
1987, a supernova exploded 180,000 light-years away. Almost 30 minutes
after telescopes detected light from the blast, neutrino detectors detected
a torrent of neutrinos. The time lag gives a neutrino from that explosion
a velocity of 0,9999999997 c (Footnote 6). Unlike other fermions, such
as the electron, the neutrino does not have to be accelerated with huge
amounts of energy to reach this extreme velocity - it travels at just
under c ab initio, without any acceleration required. Neutrinos are
believed to have a continuum of velocities7 that may depend
upon their energy.8 Like the photon, the neutrino is never
found at rest, or even moving at a velocity much less than c.
Neutrality
Unlike other elementary particles, which are either charged or are composite
particles made up of equal amounts of positive and negative charges
(e.g., the neutron), the neutrino is completely neutral. Not only is
it neutral, but it is the most neutral particle known, more neutral
than even the photon, as the photon has an electromagnetic field which
the neutrino lacks.
Magnetic Moment
Counterintuitively for a neutral particle, the neutrino has a tiny magnetic
moment of about 10-11. This is believed to be due to a loop effect,
where the neutrino generates a virtual W particle, which annihilates
back into the neutrino.
Anti-neutrino and Helicity
Unlike all other fermions, where the anti-particle differs from the
particle only in charge, the anti-neutrino does not differ in charge
(neutrinos are neutral) but in helicity. All neutrinos are left handed
and all anti-neutrinos are right handed.
Decay and Stability
Neutrinos have since their conception been considered to be elementary
particles.9 Since they have the smallest rest mass of any
known fermion, there is no other fermion that they can decay into, and
they are not known to decay.
Of all the particles, none is more stable than the neutrino. It is
capable of passing through 130 light years of solid iron before interacting
with another particle.10 And, unlike all the other particles,
including even the electron, it is so stable that it will not annihilate
even with its own antiparticle.
Energy
While the energy of a fermion depends upon its velocity, the energy
of a neutrino is not due (entirely) to its kinetic energy, but also
to an internal frequency, v, according to the equation E = hv. Neutrinos,
like photons, have a continuum of energies proportional to their frequency.11
Proposesd Sub-Structure
A photon has an electromagnetic field consisting of electric and magnetic
fields at right angles. The fluctuating fields are a fixed distance
apart, equal to the wavelength:
While the exact structure of the photon is not known, it is generally
pictured as consisting of several complete cycles with the amplitudes
of the cycles diminishing at the ends of the wave train.12
The properties of the neutrino may possibly be explained if the neutrino
consisted of two intertwined photons moving together with their electric
and magnetic fields interlocked. (A good analogy is double stranded
DNA, where the sense and antisense strands bind to each other through
base pairs.) An end view of the two photons would show the attraction
between opposing electric and magnetic fields:
As can be seen in the above drawing, in order for the
electric fields to line up positive- to-negative and the magnetic fields
to line up north-to-south, it is necessary for one of the photons to
be rotated 90° and for the relationship between the electric and
magnetic fields to be reversed.
While photons do not bind directly to other photons as
there is no carrier of a binding force, photons can fluctuate into a
hadronic state via the reaction by forming a quark-antiquark pair, and
they can bind the two photons together.13 (A fluctuation
into an electron-positron pair may also produce binding.) A fluctuation
to a quark-antiquark pair or to an electron-positron pair would also
account for the slight magnetic moment of the neutrino.
In addition to the problem of how two photons would bind
together, the reaction of two photons with a spin of 1 to form a neutrino
with a spin of ½ does not conserve angular momentum. While angular
momentum is certainly conserved, it is possible that the neutrino is
not formed by that reaction, but by a reaction involving another particle
that carries off angular momentum.
The interlocking of these fields should not only cancel any external
or net electric and magnetic fields that the two photons would otherwise
display, but should bind the two photons together through the powerful
electromagnetic force, giving the neutrino its extraordinary stability.14
If the average distance between the centers of the fields is small,
the electromagnetic force would be very large, ample to prevent the
neutrino from breaking apart in even the most energetic collisions.
It is further proposed that the axes of the two photons are not linear,
but spiral slightly around each other (as a DNA double helix does) as
shown in the following drawing of the two axes
The slight rotation of the axes may be due to the reduced amplitude
of the photons at the ends of their wave trains, which may pull the
trains together at their ends, twisting the axes of the photons. Also,
if the two photons do not have exactly the same wavelengths, the fields
may be directly opposite at the centers of the wave trains, but offset
slightly at the ends, which may twist their axes.
There will be, of course, two possible configurations for the neutrino,
a clockwise twist and an counterclockwise twist, corresponding to an
anti-neutrino and a neutrino, and this would explain why the anti-neutrino
differs from the neutrino in helicity rather than in charge. There is
no reason to expect that the conflicting helicities of the neutrino
and the antineutrino would result in the disengagement of the photon
pairs that comprise them, should the neutrino collide with its anti-neutrino,
and no such annihilation has been observed. This would be consistent
with the proposal that the neutrino is a Majorana particle and does
not have an anti-particle.
If the axes are twisted slightly, then other properties of the neutrino
may be explained. First, while each photon would continue to move at
the speed of light, each would now follow a helical path instead of
a linear path. Thus, the photon velocity c will have a forward component
and a rotational component. The forward component of the velocity of
the photon will be equal to the velocity of the neutrino, which will
be slightly less than c.
If the proposed structure is correct, the number of helical rotations
per linear distance of neutrino travel should be proportional to the
frequency of the photons because the amount of twisting should depend
upon the binding force between the two photons, which should increase
with frequency. That is, if the two photons that comprise a neutrino
have a long wavelength, they should travel a long linear distance for
each helical rotation and if they have a short wavelength (high frequency)
they should have many rotations in that same distance.
Moreover, the rotational component of the velocities of the photons
in the intertwined pair will be observed as rest mass.15
This can be most easily seen by imagining for a moment that the entire
velocity of the photons is rotational. In that case, the neutrino would
be at rest, relative to the laboratory frame of reference, and its entire
energy could be measured by weighing it. In other words, its entire
energy would be in the form of its rest mass.16 If that is
true, then when the rotational component of the velocity of the photons
in the neutrino is tiny, the rest mass would be correspondingly tiny.
In order to match the electromagnetic fields of the two photons, the
two photons will have to have approximately the same wavelengths. Since
the light spectrum is continuous, this means that neutrinos can also
have a continuous spectrum of wavelengths, which explains the internal
frequency of the neutrino that gives neutrinos different energies.
The phenomenon of neutrino oscillation strongly supports the proposed
sub- structure. Neutrino oscillation requires the neutrino to consist
of two waves that do not have exactly the same wavelength.17
Two photons of slightly different wavelengths would meet that requirement.
The following side view shows the axes of two photons that differ slightly
in wavelength:
The two slightly-differing wavelengths of the photons
in the neutrino interfere slightly, which creates an oscillation between
two different frequencies,18 which would correspond to the
different flavors of neutrino. While the electromagnetic coupling between
the two photons that comprise a neutrino would be maximized if the two
photons had exactly the same wavelength, a small difference in wavelength
would not reduce the binding force much, especially if the wave train
is not very long.
Predictions
This explanation for the sub-structure of the neutrino leads
to several predictions that it may be possible to test experimentally.
Both the velocity and the rest mass of the neutrino should be directly
proportional to the number of rotations (helical turns) per unit of
linear distance traveled. That is, if there is no rotation, the linear
velocity of the neutrino should be c and its rest mass should be zero
and, if the entire velocity component of the two photons is rotational,
the linear velocity should be zero and the rest mass should equal the
entire energy of the neutrino. Therefore, if the number of rotations
per unit of linear distance traveled is proportional to the frequency
of the neutrino, the linear velocity and the rest mass should also be
proportional to the frequency.18 This would make the neutrino
unique in yet another way, being the only particle having a continuum
of rest masses and a continuum of velocities19 proportional
to that rest mass.
Also, since both of the photons in a neutrino must have wavelengths
that are nearly the same in order to bind together, this suggests that
if a laser beam is split, one portion is rotated 90° and the two
portions are recombined colinearly with reversed electric-magnetic field
positions (e.g., possibly by moving in opposite directions), it may
be possible to create neutrinos from photons.20 This would
not violate conservation of angular momentum if (1) the photons move
in opposite directions, (2) a photon moving in the opposite direction
had an angular momentum of -1, and (3) a neutrino- antineutrino pair
was created.
Since neutrino oscillations require that the two photons have slightly
different wavelengths, it may be possible to produce neutrinos that
do not oscillate by using photons that have exactly the same wavelengths.
And, unless there is a quantum effect,21 unique neutrinos
other than the electron, muon, and tau neutrinos might be created by
controlling the difference between the wavelengths.
Calculations
In accordance with the proposed neutrino sub-structure, the ratio of
the rest mass of the neutrino to its energy should be the same as the
ratio (c - v)/c, where “v” is the linear velocity of the
neutrino. As a particular example to test the reasonableness of the
proposed sub-structure, let us use a neutrino linear velocity of 0.9999999997
c22 and an energy of 1 MeV23. This gives a rest
mass of about 3x10-4 eV/c2 (3x10-10/
1x106), which is within the known neutrino rest mass range
of <5.1 eV/c2. Using c = 3x108 m/s, that same
linear velocity suggests that each photon in a neutrino will travel
a linear distance of 2.9999999991x108 meters in a second
(0.9999999997 x (3x108)) and a rotational distance of 0.09
meters in that same second (3x108 - 2.9999999991x108).
A rest mass of 3x10-4 eV/c2 suggests a frequency
of 7.2x1010 cycles/s (E/h = (3x10-4 eV/c2)
/ (4.14x10-15eV•s)), which gives a wavelength (c/v)
of 4.1x10-3 meters. Dividing by 2pi gives a radius of 6.6x10-4
meters, suggesting the distance between each photon and the neutrino
axis. The wavelength is the circumference of the circle, so there would
be 137 rotations per second (0.09/6.6x10-4). In this example,
that would mean that the two photons rotated once for every 2,200,000
meters (3x108/137) or 1400 miles that the neutrino traveled.
1. Veltman, Martinus, Facts and Mysteries in Elementary Particle Physics,
World Scientific Publishing Co Pte. Ltd. (2003), page 69.
2. Eichten, E. et al., “New Tests for Quark and Lepton Substructure,”
Fermilab- Pub-83-015-T; Peskin, Michael E., “The Compositeness
of Quarks and Leptons,” Proceedings of the 1981 International
Symposium on Lepton and Photon Interactions at High Energy (1981).
3. Kane, Gordon, Modern Elementary? Particle Physics, Westview Press
(1993).
4. Muirayama, Hitoshi, “The Origin of Neutrino Mass,” Physics
World, May, 2002.
5. Kane, Gordon, ibid, pages 303-311. Seiden, Abraham, Particle Physics,
Addison Wesley (2005), pages 333-345. “Neutrino Oscillations,”
http://ww.ps.uci.edu/-superk/oscillation.html; Murayama, Hitoshi, “Neutrino
Physics: Evidence for Neutrino Mass,” http://hitoshi.berkeley.edu/neutrino/neutrino3.html
(2002).
6. The Five Common Particles, Summary of Elementary Particle Physics,
Northwestern University, http://www.physics, northwestern.edu/classes/2004Spring/Phyx103/fiveparticles.doc
7. Okun et al., "Comment on Equal Velocity Assumption for Neutrino
Oscillations," Modern Physics Letters A, argue that “equal
velocity is forbidden by simple kinematic considerations.”
8. G.R. Kalbfleisch, The Velocity of the Neutrino, Brookhaven National
Laboratory (May, 1975) speculates that there may be “a dependence
of the velocity upon the energy of the neutrino.”
9. Veltman, Martinus, ibid, page 69. 10. ?Concepts of Modern Physics,
Arthur Beiser (1967). 11. ?Reynolds, David J., “A Solution for
the Solar Neutrino Problem,” http://www.btinternet.com/~david.reynolds1/
“Wave particle duality dictates that a neutrino will, in its own
frame of reference, have a frequency related to its rest mass via Plancks
constant.”
12. In addition to the conventional structure shown in the drawing,
where the electric cycles alternate positive and negative and the magnetic
cycles alternate north and south, it is possible that the positive and
negative electric cycles (and the north and south magnetic cycles) may
be in opposition, and that structure may even be more likely.
13. Particle Physics Booklet, Particle Data Group, Lawrence Berkeley
National Laboratory, July, 2004.
14. The fields of ordinary photons do not interlock because the fields
are waves that superimpose. However, because the neutrino velocity is
less than c, the fields have fermion properties and can act on other
fields, just as the fields of electrons.
15. Sternglass, Ernest J., Before the Big Bang, Four Walls Eight Windows
(1997), pages 135, 158.
16. This reasoning suggests the source of mass for all particles.
17. Casper, Dave, "Neutrino Oscillations," http://www.ps.uci.edu/~superk/oscillation.html
18. Reynolds, David J., “A Solution for the Solar Neutrino Problem,”
http://www.btinternet.com/~david.reynolds1/ “Wave particle duality
dictates that a neutrino will, in its own frame of reference, have a
frequency related to its rest mass via Plancks constant.”
19. Okun et al., "Comment on Equal Velocity Assumption for Neutrino
Oscillations," Modern Physics Letters A, argue that “equal
velocity is forbidden by simple kinematic considerations.”
G.R. Kalbfleisch, The Velocity of the Neutrino, Brookhaven National
Laboratory (May, 1975) speculates that there may be “a dependence
of the velocity upon the energy of the neutrino.”
20. Light by light scattering has been observed as a quantum mechanical
effect. Veltman, Martinus, ibid., page 252.
21. Quantum effects may permit only certain frequencies. In addition,
the twist in the axes of the photons will introduce a stress and at
high frequencies the stress may be too great for the neutrino to form.
22. "The Five Common Particles, Summary of Elementary Particle
Physics," Northwestern University, http://www.physics, northwestern.edu/classes/2004Spring/Phyx103/fiveparticles.doc
23. Since the mass of an electron is 0.511 MeV, one might suspect that
the energy of each photon in the neutrino would also be about 0.511
MeV, especially since an electron and a positron annihilate to form
two photons, each with an energy of 0.511
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