BS813: How neutrinos have zero mass but can show flavours
David Noel
<davidn@aoi.com.au>
Ben Franklin Centre for Theoretical Research
PO Box 27, Subiaco, WA 6008, Australia.
What are Neutrinos?
The nature of Neutrinos has been a subject of scientific research since the 1930s, but even today, some 90 years later, there is considerable confusion and argument about them.
In the everyday world, the distinction between mass and energy entities is usually clear-cut. This is partly because everyday entities are usually present in large, obvious amounts.
When you dive deep down the size spectrum, to what is called the atomic level, the distinction between a mass entity and an energy entity may not be so clear. We see light from the Sun, and to us it is apparent that this is energy. But down at the atomic level, when we talk about photons of light and sub-atomic particles, their nature is not always clear-cut.
And such is the case with neutrinos. Figure F1 shows a table of common sub-atomic particles [7], and their masses.
Figure BS813-F1. Sub-atomic particles. From [7].
It can be seen that two of these particles (the neutron and the proton) have masses close to 1 amu (atomic mass unit). The third particle (the electron) is much smaller, the first two are around 1800 times as massive as the third.
It is in this lower range (together with the electron) that we find neutrinos. Neutrinos are essentially tiny scraps of mass/energy left over when nuclear reactions occur involving the big boys, the neutron and the proton.
What standard science tells us about Neutrinos
According to Wikipedia [2], "A neutrino is .. an elementary particle ... that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small that it was long thought to be zero. The rest mass of the neutrino is much smaller than that of the other known elementary particles. The weak force has a very short range, the gravitational interaction is extremely weak due to the very small mass of the neutrino, and neutrinos do not participate in the electromagnetic interaction or the strong interaction. Thus, neutrinos typically pass through normal matter unimpeded and undetected.
Although neutrinos were long believed to be massless, it is now known that there are three discrete neutrino masses with different tiny values (the smallest of which could even be zero), but the three masses do not uniquely correspond to the three flavors: A neutrino created with a specific flavor is a specific mixture of all three mass states (a quantum superposition). Similar to some other neutral particles, neutrinos oscillate between different flavors in flight as a consequence. The three mass values are not yet known as of 2024."
How fast do neutrinos travel. and do they have mass?
According to accepted physics, elementary mass/energy entities can be treated as particles (they are made up of mass), or photons (packets of electromagnetic energy). The distinction between the two is that photons travel at the speed of light (and have no mass), while particles (with mass) must be stationary or travelling at less than light speed.
So do neutrinos have mass or not? According to the source [2] quoted above, neutrinos do have mass, in fact 3 different levels of mass, but their mass values change all the time between the levels. This phenomenon has been called Neutrino Oscillation.
In my view, whatever we may from time to time accept as what mass is, it cannot be a quantity which changes by itself. Theory could allow mass to change into energy, and vice versa, but the best view of the situation is perhaps that in trying to measure the mass of very tiny entities, the aspect which they present is itself variable.
So my conclusion is that Neutrinos are Photons, and so do not have mass, and they travel at the speed of light.
If it is a particle with mass, theory says a neutrino should have to travel below the speed of light. But in 2012 a consensus was achieved that neutrinos do, in fact, travel at light speed [8].
This is now the prevailing view. In [8] it says "Today (Jun 8, 2012), at the Neutrino 2012 conference in Kyoto, Japan, the OPERA collaboration announced that according to their latest measurements, neutrinos travel at almost exactly the speed of light."
Why should anyone think differently? In [1] it says "We know that neutrinos have mass because we have observed them change from one flavor into another, a process that can happen only if the neutrinos have mass. Interestingly, that process also requires the different flavors to have different masses".
In what follows, a recent model for the nature of light will show how photons can have different "flavours" without having mass.
An earlier article in this series, BS805: The Photon Hoop Model for light [5] explained the concept of "photon hoops". In this model, light (or more widely, electromagnetic radiation of any sort) is treated as made up up tiny moving hoops, each equivalent to a half-wavelength in the usual wave treatment of light.
The concepts are best explained using some graphics from [5]. The first shows Photon Hoops impinging on a crystal lattice, an ordered assembly of atoms.
Figure BS813-F2. Photon Hoops striking a crystal lattice. From [5].
This figure is a representation of photon hoops striking the outer surface of a simple crystal surface. Only one slice through the grid of atoms in the crystal is shown, and the atoms are arranged in one of the simplest ways, at the corners of cubes. In the modern interpretation, each atom consists of a dense central nucleus surrounded by an electron cloud.
The left-hand (pink) hoop is shown as moving easily between atoms, retaining its orientation unchanged as it goes. The middle (yellow) hoop also moves through a clear path, but is rotating on its axis as it does so, so it changes from round to flat as the edge of the hoop comes into view.
The right-hand (green) hoop is shown as hitting the electron cloud of an atom and bouncing off. This is not relevant in the current article.
In the current model, neutrinos are just very tiny light packets, small versions of what you think of as photons. Their behaviour is mostly that typical of photons. Where they start to diverge from the pattern typical of any sort of radiation is when they are very small relative to the mass entities they encounter, such as the atoms in a solid or liquid.
Everyday photons, such as those from visible-range light, are likely to be absorbed, reflected, or diverted when they encounter a solid. Neutrinos are so tiny relative to the atoms in a crystal lattice that their movement may be mostly governed by very small gravitational influences from the atoms. More on this later.
Neutrino flavours A, B, & C
Here then is the basis for saying neutrinos do not need mass to have flavours. Figure F2 can be taken to represent neutrinos passing through a solid. We can distinguish 3 states or flavours of these, which we can call A, B, and C.
We can think of these labels as Anticlockwise, Basic, and Clockwise. The yellow hoop in Figure 2 is spinning. Its motion may be clockwise or anticlockwise. The pink hoop is not rotating, its motion can be thought of as basic.
This picture on the micro-scale is equivalent to the two directions of polarization of light on the macro-scale, with the third state being non-polarized. So the classification into A, B, and C flavours in neutrinos has its parallel in everyday photons.
Behaviour of everyday photons in passing through a crystal lattice can be thought of as similar to balls passing through a pinball machine. The collisions and other events occurring are gross and noisy.
When neutrinos pass through a material, the difference in scales is such that it's more like a comet passing through a solar system. Most of the comet's movements are governed by the gravitational effects of distant bodies, subtly influencing its passing.
About anisotropic bodies
Many of the substances with which we are familiar are what's called anisotropic, that means, their properties are different in different directions. This is very obvious when a light beam falls on quartz crystals. The beam is split into parts because the refractive index of quartz is different in different direction.
Look again at Figure 2,. the passage of photon hoops through a solid. The pink (flavour B) hoop can pass through the solid because it has found a path which is unobstructed even while in a wide aspect. The yellow (flavour A or C) photon may only be able to pass because it can wriggle its way through -- it may follow a helical path though a helix-shaped space in the surrounding solid.
Figure BS813-F3. Nuts and bolts. From [9].
This is like how a point on the thread of a bolt can follow a helical path through a nut as the bolt is screwed in, as in Figure F3. A standard bolt would be flavour C, clockwise. This bolt could not pass through a nut with the same hole size but of flavour A (anticlockwise, left-hand) thread.
In the same way, a smooth shaft of diameter equal to that of the outside of the thread (flavour B) could not pass through a tube with a diameter of the inside of the thread.
The Solar Neutrino problem
What are solar neutrinos? Here is an extract from [4]. "Solar neutrinos are exactly what they sound like: neutrinos from the sun. The sun is the source of most of the neutrinos that are passing through you at any moment. About 100 billion solar neutrinos pass through your thumbnail every second.
An interesting thing happened when scientists started looking for those neutrinos in the 1960s. Only about one third to one half of the predicted number of neutrinos actually showed up in detectors. This became known as the solar neutrino problem."
To avoid problems of contamination from neutrinos produced at the Earth's surface, the detectors used to measure solar neutrinos have been built deep underground, usually in deep mine sites. One of these detectors. the Sudbury Neutrino Observatory. has been built 2000 metres underground in a Canadian nickel mine [6]. The actual detection material is one thousand tons of heavy water, placed in a central spherical cistern with transparent acrylic walls.
Figure CM602-F4. The Sudbury Neutrino Observatory (SNO). From [6]
An earlier project. the Homestake experiment [4], used 100,000 gallons of dry cleaning fluid (perchloroethylene) to search for neutrinos. It was housed a mile underground in the caverns of the Homestake Gold Mine in South Dakota, which was then an active mine, and is now used for science experiments, including further neutrino research in the Deep Underground Neutrino Experiment.
In this experiment, John Bahcall had predicted how many neutrinos should arrive from the sun and transform one of the chlorine atoms in the detector into an argon atom. But only one third of the neutrinos seemed to arrive. Researchers weren’t sure if the problem was in the experiment, the calculations, their model of the sun, or their picture of neutrinos. Some scientists thought that the neutrino model was the error, but many were sceptical.
It will be apparent that the photon hoop model of neutrinos, with its 3 flavours (A, B and C), offers a solution to the solar neutrino problem -- whatever detection material was used, its structure was such as to only detect one flavour of neutrino.
Back to the general light model
In [5] photon hoops were first considered as single entities, as particles, albeit two-dimensional particles. In most common situations, the hoops making up a light beam will normally be strung in a continuous line, as in Figure F5. All the hoops will have the same polarization, that is, will lie in the same plane.
Figure F2 shows individual hoops. Figure F5 following depicts a string of hoops, each following another, with no space between them.
Figure BS813-F5. A string of Photon Hoops approximating a sinusoidal light waveform. From [5].
It will be immediately obvious that the string of hoops much resembles the conventional depiction of light as a sinusoidal wave. However, this wave is mirrored in its axis. In conventional wave optics, one wavelength, one complete cycle, is the distance over which the wave rises from its zero mid-value, peaks, falls back through the mid-point to a trough, and rises again to the midpoint.
The frequency of the light is the number of times this cycle is completed in one second. The Photon Hoop Model uses the same general picture, but the length of each hoop is half a wavelength, and the number of hoops passing per second is twice the frequency.
The photon hoop model thus combines the two older approaches to understanding light, the wave model and the particle model. These older models have served us well in the past, even though apparently contradicting. But the new model does offer more analytical scope, with the possibility of calculating optical parameters from gravitational effects of structural layouts on hoops.
Effects of gravity on light
The influence of gravity on electromagnetic wave movements is sometimes not realized, because it is a second- or third-order effect. Perhaps its best-known manifestation is in gravitational lensing, where the light from very distant objects is focussed towards the observer by a massive intervening structure such as a galactic cluster.
A more poorly known effect is the Gravitational Red Shift which occurs when light is emitted from a massive star, the light from which is shifted to longer (red) wavelengths by the star's own gravity.
The third effect, that of reddening the light from very distant galaxies (Gravitational Drag), is well known, but wrongly attributed to expansion of the Universe. The true position is explained in Refining the Zwicky Constant [10].
In theory, it should be possible to track the gravitational passage of visible-light photon hoops through a crystal like that represented in Figure F2 to calculate the crystal's refractive index. In practice such calculations fall into the many-body problem area, not easy to use.
Effects of gravity on neutrino flavours
When considering the effects of gravity on passage of the tiny neutrino hoops, the pattern is more like that of a lonely comet swinging into the Solar System -- most comets will venture in and out without noticeable effects.
But in a few cases, the gravitational influence of other Solar System bodies may give a surprise. This was when the case when comet Shoemaker–Levy 9 broke apart in July 1992. and collided with Jupiter in July 1994 [11]. This has a parallel with the rare capture of a neutrino.
As for the way neutrinos appear to change their flavour during passage, this could be due to gravitational effects from the ordered matter they pass through, reversing or stopping the spin direction of the neutrinos.
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References and Links
[1]. Vern Bender. Neutrinos are among the most abundant particles in the Universe. https://vernbender.com/20317-2// .
[2]. Neutrino. https://en.wikipedia.org/wiki/Neutrino .
[3]. Neutron Decay. https://www.sciencedirect.com/topics/physics-and-astronomy/neutron-decay .
[4]. Solar neutrinos.https://neutrinos.fnal.gov/sources/solar-neutrinos/.
[5]. David Noel. BS805: The Photon Hoop Model for light: A new model to aid analysis and computation of light reflection and refraction phenomena. www.aoi.com.au/BaseScience/BS805/ .
[6]. David Noel. BS811: Can Neutrinos be treated as tiny single Photon Hoops?. www.aoi.com.au/BS/BS811/ .
[7]. The Atom and Electromagnetic Radiation. https://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/atom_emrframe.html .
[8]. Neutrinos don't outpace light, but they do shape-shift. https://www.newscientist.com/article/dn21899-neutrinos-dont-outpace-light-but-they-do-shape-shift/ .
[9]. Should I choose fine or coarse threaded bolts?. https://www.nord-lock.com/learnings/bolting-tips/2010/choose-fine-or-coarse-thread-bolts/ .
[10]. David Noel. Refining the Zwicky Constant: A new more soundly-based constant for inter-galactic distances, replacing the Hubble Constant. www.aoi.com.au/Zwicky/ .
[11. Comet Shoemaker–Levy 9. https://en.wikipedia.org/wiki/Comet_Shoemaker%E2%80%93Levy_9 .
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