Friday, January 8, 2016

Neutrinos DO Have Mass: The 2015 Nobel Prize in Physics

This article is for non-physicists. It is as non-technical as possible. I hope you will find the links helpful and easy to follow.

Arthur B. McDonald (leader of the Sudbury Neutrino Observatory (SNO)) and Takaaki Kajita (leader of the Super-Kamiokande collaboration) just proved (October, 2015) that neutrinos oscillate, and this proves that these elusive particles have mass.

What Is a Neutrino?

If you had to describe a neutrino in one word it would be "elusive." And maybe right after that, "weird." These particles are very challenging to get to know.

Until recently physicists thought that neutrinos were massless and traveled at light speed, much like photons. Unlike photons, which are boson particles of force, neutrinos are leptons (see the particle chart below). Neutrinos don't form ordinary matter but they contribute mass to the universe. Like electrons, these particles have lepton characteristics such as a half-integer spin and they don't interact with the strong fundamental force. That's the force that holds atomic nuclei together. Boson particles, in contrast, have an integer spin. Particle spin isn't important to understand here but it's helpful to know a bit about it. Particles have a built-in form of angular momentum. Spin itself is real mystery: like the orbital revolution of a spinning top, it has a direction and a magnitude but the direction can't be described in ordinary three-dimensional space and it never speeds up or slows down. Instead it's a built-in part of the particle.

Particles of matter and force are organized in the Standard Model, shown below right. This will be a handy reference for this article. The up quark, down quark, and electron form ordinary atoms of matter (shown as blue boxes). Three types of neutrinos are written by their symbol, v. These particles are stable but they do not form atomic matter. All unstable particles (particles that decay into stable particles) are shown in pink boxes.

Neutrinos are the second most abundant particle in the universe, right behind photons. Like photons, they started flooding the universe after it exploded into existence as the Big Bang. A cosmic neutrino map of these relic particles could be made in theory, analogous to the photon map of the cosmic microwave background radiation, or CMB map. Photons from the Big Bang decoupled, or slipped free, from other particles and began to stream throughout space when the universe was about 379,000 years old. Those relic photons paint a picture of what the universe was like at that very early time. They provide a great deal of information but this is as far as physicists can peek back into the universe's past. Neutrinos decoupled much earlier than photons did, by some accounts when the universe was only around one second old. These particles could potentially be very useful in offering a much earlier peak back into the very young universe.

New neutrinos are created all the time through certain kinds of radioactive decay, in fusion and in fission reactions, in supernovae (star explosions), and when cosmic rays strike atoms. Cosmic rays are very powerful beams of radiation and matter that come from giant supernovae and massive black holes. Most of the neutrinos around Earth come from the ongoing fusion reaction deep inside the Sun. About 65 billion of them pass through every square centimeter of our bodies every second. We feel nothing thank goodness because they almost never interact with other particles in our bodies and elsewhere. We, and Earth itself, are almost entirely invisible to neutrinos.

This is precisely what makes neutrinos very difficult to detect and study. Like photons, neutrinos also come in a wide range of energies, depending on how they were created. As an example, a cosmic neutrino map would be fantastic but it comes with a big hitch. Like Big Bang photons, the wavelengths of Big Bang neutrinos stretched out as the universe expanded. While once-gamma photons (very high energy) are now detectable as low energy microwaves, the Big Bang neutrinos have too little energy to be detected using current technologies. Creating a cosmic neutrino map will be a big technical challenge.

Neutrinos are abundant and they are everywhere in the universe but until 1959 no one even knew that they existed. In 1930, Wolfgang Pauli first suspected that an unknown particle carried off energy and momentum during a spontaneous process called radioactive beta decay. This is the process in which unstable atoms decay into stable atoms. For example, carbon-14, used in radioactive dating, decays at a known rate into stable carbon-12. In 1956, Clyde Cowan and Fred Reines found a particle that potentially fit the bill by studying particles that are created in nuclear (fission) power plants. It took until 1968 to physically detect a neutrino in a detector in the bottom of a mine in South Dakota. It happened to be a solar neutrino.

Solar neutrinos and high-energy neutrinos streaming from cosmic rays have enough energy to be detected, but there are additional factors that make them challenging to study. Really the only way to study a particle's behaviour is to see how it interacts with other particles and with forces. Neutrinos are invisible to the electromagnetic fundamental force. Like photons, neutrinos are electrically neutral, which means they don't have a charge so they don't interact with the charge of other particles, such as electrons or protons. Photons and neutrinos don't interact with the strong force locked up inside atomic nuclei either. As a detection method, the strong force is much too short range to be useful anyway. There are only four fundamental forces, so this leaves two that could be used as potential detectors – the force of gravity and the weak force.

Particle-particle interaction is where "social" photons make a sharp departure in behaviour from "loner" neutrinos. The biggest problem with studying neutrinos is that they hardly ever interact with other particles. Photons, in contrast, are easy. Even though photons are massless and have no charge, they are easily detectable because they DO interact with matter, specifically with the electrons in atoms. They don’t interact with the electrical charge, but they are absorbed and emitted by electrons. The photoelectric effect, Compton scattering, Rayleigh scattering and pair production are four specific ways in which photons interact with electrons, and therefore, with matter. The photon and the electron, in fact, share a close unique relationship as particles. At very high energy, they even become interchangeable. No such relationship like this exists for the neutrino.

The aloofness of the neutrino isn't all bad news. In some ways it is one of the particle's most attractive qualities. It makes them potentially great candidates for peering into and through dense cosmic objects. For example, we can't see into the middle of the Milky Way or deep into the Sun using photons of light because the photons are diffused and obscured by dust, gas and radiation. They interact with matter and attenuate in other words. Photons created in the center of the Sun are so mired down by other particles they take approximately 170,000 years (perhaps even longer because estimates very) just to get to the Sun's surface. The sunlight that strikes Earth is very old. Neutrinos, also created in the center of the Sun, waste no time and fly straight out instead. The light from the Sun tells us what was happening inside it 170,000 years ago. The neutrinos tell us what is happening inside it today. Looking with neutrinos is analogous to looking with X-rays, such as taking an X-ray image of a joint, but far, far better. Physicists can potentially see deep into the dense cores of galaxies and neutron stars using neutrino telescopes. The IceCube Neutrino Observatory in Antarctica is a great example (the link is an interesting read). It not only studies far way objects and cataclysmic events like gamma ray bursts but the atmospheric neutrino background and the neutrino itself as well.

Neutrinos have just been proven to have mass, so they must interact with gravity (and we might assume with the also recently discovered Higgs boson too (the link explains how this boson "gives" mass to particles, though "gives" is not really the right word for it). Particles with mass are attracted to each other and this makes them detectable, in theory. The practical problem here is that neutrinos must have so little mass (I'll go into this in more detail in a bit) that they pass right through all ordinary matter. Any attractive force is too small to deflect them and therefore it is too small to detect them. Adding to the challenge of detecting miniscule mass, gravity itself is such a weak fundamental force that it is undetectable at the particle level anyway.

This being said, neutrinos are very abundant and the universe is very large. Knowing that the particles now have even a tiny mass places them as possible contenders for the mysterious dark matter of the universe. Atomic matter, the kind of everyday matter we are familiar with, contributes just 5% to the total mass/energy of the universe, while dark matter contributes much more, about 27%. No one knows what dark matter is made of, but the too-fast rotational rates of massive galaxies, for example, offer very strong evidence that it exists (they act as though they are far more massive than they are).

In addition to gravity, neutrinos interact with the weak fundamental force, and this is how physicists detect and study neutrino behaviour. The weak nuclear force is involved in radioactive decay. The weak force is the only practical detection option. It is the only detectable way in which the neutrino (very occasionally) interacts with particles of matter. The weak force interaction is the basis behind the indirect observations of neutrinos at the underground SNO in Canada and the Kamiokande Observatory in Japan. These are the observations that lead to the 2015 Nobel Prize in physics.

Before we go into these experiments, there is one other characteristic of neutrinos to mention, and it is the reason I call them weird. As mentioned earlier, neutrinos are leptons like electrons are. The electron is one flavour of a trio of charged lepton particles (see the particle chart shown earlier). It has two heavier cousins – the muon and the tau particles. Aside from mass and stability, the muon and tau particles are identical to electrons. Both massive cousins are highly unstable. They quickly decay into  electrons and other particles through particle decay.

One thing that complicates particle physics is that unstable particles can decay in different ways, with different particles as outcomes. The different outcomes have everything to do with quantum uncertainty, which will come up again later on.

A muon most often decays into a muon neutrino, electron antineutrino and an electron, below left. The decay is carried out by the massive W- weak force boson particle. The massive W- boson itself is unstable and it decays into the electron antineutrino and the electron. Note for interest's sake: the arrow for the electron antineutrino runs backward through time (downward) because it is an antimatter particle.

A more massive tau particle can decay in many different ways, directly below. Some of the most common outcomes are shown in the diagram below. Like the muon, it decays through the W- boson. Most decay diagrams for tau decay are drawn with time flowing left to right instead upward. The tau is massive enough to produce quarks - particles that make up protons and neutrons in atomic nuclei.

Muons and taus have a lot of mass so they can only be created in very high-energy particle collisions. Mass and energy are equivalent, a fact that is experimentally verified every day in particle colliders.

Neutrinos come in three analogous flavours – the electron neutrino, the muon neutrino and the tau neutrino. For some mysterious reason, all three neutrino flavours are stable. Like the charged leptons, there is very good evidence now that the neutrino flavours differ in mass with the tau neutrino being most massive, just as the tau itself is most massive of the charged lepton family. However, even the tau neutrino's mass can only be a very tiny fraction of an electron's mass. The "weird" comes in because every neutrino slowly oscillates between all three flavours as it travels through space. The proof of this is a big part of the Nobel Prize. The very fact that it must oscillate between three different masses is proof that the particle has mass. Otherwise the designation of flavour would be meaningless for the neutrino as they are all stable.

The idea that neutrinos oscillate is not new, but the proof is. It was predicted back in 1959. The Standard Model, however, predicts that neutrinos are massless. Finding that they have mass means an adjustment to the Standard Model is in order. The Standard Model is an incredibly successful and useful model that explains how subatomic particles interact with the four fundamental forces. Massive particles such as top quarks, tau neutrinos and the Higgs boson were all recently discovered in accelerators, where they were created in very high-energy collisions. The Standard Model predicted the mass and behaviours of each one of them, a powerful verification. Some people might say that the Standard Model comes close to the theory of everything in physics, but it does have limitations. It doesn't unify the theory of gravity with the other three fundamental forces into one truly unified theory. And it didn’t predict neutrino oscillation or mass.

Could there be a fourth neutrino? Are neutrinos their own antimatter particles? What do neutrinos have to do with the overabundance of matter overantimatter in the universe? Are neutrinos dark matter? Does the neutrino get its mass from a Higgs interaction or through some other mechanism (warning: this link is very technical)? The answers to these and other related questions might move science beyond the Standard Model toward a more unified theory. The questions themselves mean that the neutrino is far more than a sideline curiosity.

Proof that the neutrino oscillates between flavours and has mass comes from two separate but concurrent research collaborations, one in Canada and the other in Japan. Below, we explore their research findings. Both collaborations emphasize a common modus operandi in research: almost any question you can think of is answerable if you can find the right approach.


The now-permanent SNO (Sudbury NeutrinoObservatory) in Ontario, Canada, houses a giant sphere of heavy water (called deuterium) very deep underground. Deuterium is a water molecule that has a neutron in its nucleus along with the proton. The tank is so heavily shielded from radiation that only neutrinos stream through the apparatus. As solar neutrinos are most abundant around Earth, it serves as a perfect detector for them. The neutrinos can't be detected directly. However, electrons are part of the weak interaction, and these particles are quite easy to detect. Photomultiplier tubes all over the sphere detect the visible Cerenkovradiation produced by high-speed electrons in the water. This electromagnetic radiation is the eerie blue light you may have seen in photos of underwater nuclear reactors.

Cerenkov radiation in a TRIGA reactor pool at the Idaho National Laboratory 
It is created when a charged particle such as an electron travels through a medium faster than light can travel through it. When it does, it creates a blue-light shockwave in the water.

The shock wave is analogous to the sonic boom you can hear when a supersonic jet flies overhead as well as the familiar boom of thunder. Both are sound shock waves. This is a light shock wave, and you might be wondering how anything travels faster than light. Light travels at its maximum velocity (light speed) in a vacuum. According to the theory of special relativity this is the speed limit of the universe. No particle can travel faster. Photons interact with matter so even though the individual photons of the beam don't change speed, they are busy bouncing off deuterium electrons. These interactions mean it takes longer for a beam of light to travel from one point to another through the water even though individual photons always travel at light speed. This is the same phenomenon as the 170,000 year-old sunlight example earlier.

There are two possible reactions between neutrinos and the deuterium in the tank. They are both types of weak interactions, and they happen only very rarely. Even though billions of neutrinos travel through the huge tank of water every minute, the vast majority of solar neutrinos pass right through the tank undetected, even though they have enough energy to interact.

Charged Current Interaction

It is the hydrogen isotope that distinguishes deuterium (heavy water) from ordinary light water. Each hydrogen atom nucleus in a deuterium molecule has a proton and a neutron, whereas each hydrogen atom in a light water molecule contains just a proton. The neutrino converts the neutron in the (heavy) hydrogen nucleus into another proton through the process of beta minus radioactive decay, shown below. A proton is composed of two up quarks and a down quark (udu). A neutron is composed of two down quarks and an up quark (udd). The electron has a lot of energy and it travels fast enough through the water to leave a tiny Cerenkov light cone in its wake.

The neutrino is absorbed in this process (not shown in the diagram) and transformed into its lepton relative, which could in theory be an electron, muon or tau particle depending on what flavour neutrino interacted. The process happens through the exchange of a charged W- boson. The W- boson in the diagram is shown rapidly decaying into a high-speed electron.

Almost every neutrino streaming through the deuterium is of solar origin. Solar neutrinos don't have enough energy to convert into the mass of a massive muon or tau particle. It takes lots of energy to convert into a high mass particle. In fact, it takes a powerful collider to create a muon through this interaction and the only the most powerful colliders can produce
the very massive tau. Therefore, tau and muon neutrinos can't take part in this reaction, but electron neutrinos can. Solar electron neutrinos have enough energy to transform into electrons, which have much smaller mass than muons or taus. The fast electron carries off almost all of the neutrino's original energy, which is about 5 – 15 MeV (million electron volts). The creation of the electron is detectable as a cone of blue Cerenkov light.

Neutral Current Interaction

In this case, instead of converting the deuterium atom's neutron into a proton, the neutrino breaks the nucleus up into a proton and a neutron and then it continues on with less energy. Unlike the charged current interaction, all three flavours of neutrinos can take part in this interaction. The free neutron is eventually captured by another deuterium nucleus (creating a tritium nucleus). When this happens, a gamma photon of around 6 MeV is produced. Some of the free neutrons released will travel right through the vessel walls and into the light (single proton) water that surrounds the vessel, where they are captured. The single proton of the light water nucleus, being of similar mass to the neutron itself, absorbs most of the neutron's energy, so that a photon of just 2MeV is produced. These photons are under the threshold of the detectors (which is 2.2 MeV) so they are automatically, and conveniently, eliminated from the experiment. The 6-MeV photon, meanwhile, collides with an electron in another deuterium atom through a process called Compton scattering. The electron is knocked free from the atom with great force so it moves at high velocity.  It is detected by its own emission of Cerenkov radiation.

In this detector, high-speed electrons, gamma photons, and free neutrons can all be detected by the sensitive photomultiplier tubes. By carefully analyzing the direction and magnitude of signals across the photomultiplier tubes, researchers can distinguish between neutral current interactions (carried out by all flavours of neutrino) and charged current interactions (carried out only by electron neutrinos). They can then compare the two contributions of solar neutrino radiation.

Importance of the Data

The fusion reaction in the Sun produces only one flavour of neutrino. Four hydrogen nuclei are fused into alpha particles (helium-4 nuclei), creating electron neutrinos, positrons, and gamma photons.

First, two hydrogen-1 nuclei fuse into a helium-2 nucleus (a very unstable isotope of helium that contains just 2 protons in the nucleus), releasing a gamma photon:

Second, a beta-plus decay reaction occurs, in which a proton is converted into a neutron, so helium-2 converts to hydrogen-2, with the release of a positron (an anti-electron) and an electron neutrino:

These two reactions can be written as one formula. The overall two-part process releases 0.42 MeV of energy:

In a separate process, the positron will annihilate immediately with an electron nearby, releasing additional energy in the form of two additional gamma photons.

Third, the hydrogen-2 nucleus fuses with a hydrogen-1 nucleus, creating a stable helium-3 nucleus, a gamma ray and more energy:

Fourth, two helium-3 nuclei can fuse to create a stable helium-4 nucleus, a hydrogen-1 nucleus and more energy:

4 hydrogen-1 nuclei are required to create one helium-4 nucleus. Each reaction written above is doubled, up to the last equation. All of these reactions form a chain reaction that releases a net energy of almost 27 MeV when each helium-4 nucleus is created. 2% of that energy is carried off by the electron neutrinos (two of them are created for each helium-4 created).

Two electron neutrinos are produced for every reaction and they fly right out of the Sun at approximately light speed in every direction, including Earth. Early neutrino detectors detected only about a third of the number of neutrinos expected from the ongoing fusion reaction. This unexpected observation was called the solar neutrino problem. At first, scientists nervously suspected that something was wrong with the Sun's reaction rate. Perhaps it was slowing down. Advances in sun science, however, indicated through other independent observations that the Sun was burning exactly as expected, so there must be some other explanation for the strangely low neutrino detection.

By the 1970's and 1980's, physicists were growing deeply suspicious that neutrinos have three different flavours, just as the charged leptons do. To have different flavours, they would have to have mass; otherwise they would all be identical. At the same time, experiments showed that neutrinos must travel exactly or nearly exactly at light speed, and if traveling at light speed, they must be massless. Otherwise they are breaking the rules of special relativity. To complicate matters more, in 2011 the OPERA Experiment at CERN measured neutrinos travelling slightly faster than light speed. No one really knew what to do with the unexpected data, and about a year later, the researchers declared their results were an anomaly – that neutrinos do travel at light speed or very close to it but not over it. Using newly upgraded detectors in 2012, Fermilab's MINOS detector clocked neutrinos traveling at essentially light speed. The difference in velocity between photons and neutrinos was calculated to be less than 0.0006%. The proof that neutrinos have mass would not be found by measuring their speed, but those results did mean that neutrino mass must be very, very small.

Meanwhile, some observational hints that neutrinos do indeed have different flavours (and therefore mass) were coming in. In 1987, a supernova was detected at the Kamiokande Neutrino Observatory. There was a very slight difference in the time of arrival of the few neutrinos that came from that far-away supernova, a suggestion that not all neutrinos are the same. More massive neutrinos should travel slower than less massive ones if they are produced with the same energy, and these results hinted that was the case. However, few neutrinos were observed and the timers used at that time were not precise enough to call it definitive proof.

Super-Kamiokande Collaboration

Along with the SNO data, convincing evidence finally came in 1998 from the now-called Super-Kamiokande collaboration. Scientists there observed solar neutrinos as well as neutrinos created in the upper atmosphere by cosmic ray collisions.

Earth is bombarded by cosmic muons as well as neutrinos. These muons come from cosmic rays striking Earth's upper atmosphere. Supernovas, massive black holes and possibly other cataclysmic events create cosmic rays, most of which are super-fast moving protons. These protons strike atomic nuclei in the upper atmosphere with great force. They come from all directions. A highly unstable pion particle (an up quark/down antiquark pair) is produced during each collision, which quickly decays into a muon and a muon neutrino. The muon itself then rapidly decays in the atmosphere but the muon neutrino travels through the Earth if it is pointed in the right direction. Atmospheric electron neutrinos are also produced in cosmic ray interactions. The Super-Kamioknade observatory is deep underground and filled with ultra-pure light water rather than heavy deuterium. It can detect the direction of atmospheric neutrinos traveling through the inner detector tank. It is sensitive enough to distinguish between muon neutrinos and electron neutrinos by their interactions with the light water (as Cerenkov radiation), but it can't detect tau neutrinos. Neither neutrino source has enough energy to create very massive Tau particles.

Muon neutrinos are detected when one of them interacts with a water nucleus and creates an energetic muon. The muon interacts strongly with matter, so it travels only a short distance before it loses energy and is absorbed. However, before it is lost, the muon creates a Cerenkov signal that has a very sharp cone shape. This Cerenkov signal can be distinguished from the electron neutrino signal, which is a diffuse circle of light. In the latter case, a shower of electrons and positrons are created all at once, each one with its own light cone, so it is diffuse rather than sharp. These two different signatures offer firm evidence for the presence of at least two different flavours of atmospheric neutrinos. Solar neutrinos are also expected to pass through the detector but these neutrinos can be distinguished from the ones produced in the atmosphere because they have significantly less energy.

The researchers found that upward going muon neutrinos, those that were generated on the other side of Earth and traveled through Earth into the detector, were half as numerous as downward going muon neutrinos (those that didn't go all the way through Earth). Knowing that the abundance should be the same in both directions (cosmic radiation is uniform all around Earth), this meant that somehow the muon neutrinos changed into some undetectable form in the time it took to travel through Earth. Those undetectable neutrinos are expected to be tau neutrinos.

The oscillation of muon neutrinos into tau neutrinos is called the Mikheyev–Smirnov–Wolfensteineffect (MSW) or matter effect. Electrons in matter change the energy level of neutrinos (this happens through weak force interactions as you would expect). It is a coherent forward scattering effect that is similar to the refractive index of light traveling from air into denser water. This means that the neutrino effective mass changes when it is traveling in matter.

By combining the SNO and the Super-Kamiokande data, researchers were able to estimate that electron neutrinos made up a third of the solar neutrino population, and they had good evidence that neutrinos oscillate at least between muon and tau flavours. These numbers agreed very well with computer models of the Sun that rely on other independent lines of solar data. Electron neutrinos, the first and easiest kind to detect, make up one third of the total solar neutrino radiation. The data proves that neutrinos oscillate between flavours.

There are two mechanisms through which neutrinos oscillate. They oscillate as they travel through a vacuum (due to a quantum mechanical effect) and they oscillate according to the MSW mechanism as they travel through matter. Researchers believe now that even though only electron neutrinos are created by solar fusion, all three types of neutrino exit the Sun's surface. The solar core is very dense so through the MSW mechanism, oscillations are thoroughly. As they travel to Earth they oscillate across the vacuum of space as well. By the time solar neutrinos reach Earth's detectors, they are composed of an equal mixture of electron, muon and tau neutrinos.

Oscillation and Mass

Neutrino oscillation is important because it proves that neutrinos have mass. Physicists expect very slight differences in mass between tau, muon and electron neutrinos. The current Standard Model picture of neutrinos as massless light-speed particles is now more complicated. The neutrino's mass must be very small, and the difference between the masses of the three flavours must be very small. Every Standard Model interaction that involves neutrinos holds up when neutrino mass is assumed to be zero, so neutrino mass must be so small it's impact on those interactions is insignificant.

The question of what the neutrino flavour masses are is not easy to answer. Measuring particle mass isn't simple to start with. You can't set an electron on a scale to measure its mass, for example. To get an electron's mass, you can measure its charge versus its mass as it accelerates around a magnetic field. More charge means it creates more magnetic force, higher acceleration, and therefore more curvature in its path. More mass means less acceleration and a smaller curvature. To get charge per electron, there are several devices you can use to measure the current produced by a known number of electrons. When you get the charge/mass ratio and the charge, you can calculate the mass per electron. Electrons interact with the electromagnetic force and that makes these calculations possible. Neutrinos refuse to interact with everything except the weak force and only occasionally (as well as gravity to a negligible extent) so their masses can't be calculated kinematically in the same way.

Current evidence suggests a neutrino's mass that is at least half a million times less than that of its next lightest lepton relative, the electron. (The link is technical but it explains possible approaches to extend the Standard Model to accommodate neutrinos with mass.) Experiments such as the Super-Kamiokande look for effects that rely on differences in mass between neutrino flavours. Neutrino oscillations are sensitive not to absolute mass but to only to differences in the squares of the masses (this is due to the formulas used). For example, in 2006, the MINOS experiment carefully measured oscillations in a muon neutrino beam. They found the difference in the squares of the masses between the two heaviest neutrino flavours to be 0.0027 eV2. (I'm not sure why MINOS didn't share the 2015 Nobel Prize but they, along with 1300 other physicists, did share the $3 million 2015 Breakthrough Prize For Particle Experiments awarded a few months later.) This result agrees with the results from the Super-Kamiokande experiment. Since that value is the difference of two squared masses, at least one mass should be at least 0.04 eV. You can also set mass limits on the neutrino based on its estimated gravitational effects (knowing its abundance) on large mass objects such as galaxies. You can get it also from a very well accepted fixed ratio between neutrinos and photons created in the Big Bang, according to the Standard Model. These limits give an estimated upper limit of 0.3 eV for the total of all three neutrino flavours combined. To note, however, none of these estimates can tell us whether the lightest electron neutrino has mass or not. It could be massless.

Theoretical Description of Oscillation and Mass

This part is more technical but if you are wondering how a single particle can oscillate between different masses, this is for you. At first thought it doesn’t seem possible.

To really examine the relationship between neutrino oscillation and mass, one needs to get into quantum mechanics (This link is an optional place to get acquainted with the theory in general. It won't mire you down in technical talk). Here, I try to limit the quantum detail to what you need to know for neutrino mass. We tend to think of a particle, like an electron, as having a definite position, momentum, and mass, like a tiny solid ball flying through space. This picture is inaccurate. The electron, like all particles, behaves according to quantum mechanics, and quantum mechanics has the uncertainty principle built into it. This means we can't know everything about the electron at the same time. The certainty of one value leads to uncertainty of another one. It's like playing whack-a-mole. This means we need a word to describe the one quality that can be pinned down at a time. In this case, we could measure the electron's position, as a precise coordinate in space. That would be its position eigenstate. Meanwhile, we can't know what its momentum or velocity right at that same moment is. If we use the same logic, we can pin down the resting masses of the three generations of charged leptons – the electron, the muon and the tau – and they are eigenstates because they can be pinned down to precise values.

The neutrino is fundamentally different and the reason for this is complex. It has to do with the fact that it has so little mass. Like the charged leptons, the three neutrino flavours have three mass eigenstates. The difference is that, for the neutrino, these mass eigenstates are a coherent superposition. The three mass eigenstates of the charged leptons (by virtue of same complex math) are called a decoherent superposition. In simple terms, the calculations hint that the charged leptons are just too massive to oscillate. They come in three distinct particles, each with its own specific mass. In contrast, it's not quite accurate to call any of the neutrinos distinct particles with specific masses.

Wave/particle duality in quantum mechanics makes this a bit easier to visualize. A particle with a certain energy/mass is also a wave of a certain frequency. It's strange to think of an electron as a wave but it is. In fact, entire atoms can act just like waves too under the right circumstances. The electron, muon and tau neutrino flavours are superimposed waves corresponding to the three different mass eigenstates. It is coherent, which means the three waves exist at once. If the waves are in phase with each other, the different neutrino flavours are indistinguishable. As a neutrino travels through space the waves superpose in different ways. The state, or phase, of the oscillation changes over long distances as the particle travels. Each superposition state corresponds to a specific flavour of neutrino. A tau-like superposition state collapses into a tau neutrino when it is measured. If the superposition is more electron-like then it collapses into an electron neutrino at that point.


The elusive weird little neutrino remains a mystery in many ways. Unless you are into nuclear physics or particle physics you could ignore it altogether. Despite this, it packs a big punch straight into the heart of the Standard Model, the model that explains particles and forces, which are the essential building blocks of the universe. Neutrino research and debate is going on as hotly as ever in laboratories around the globe. There are many questions that still need to be asked. The research might lead to a way beyond the Standard Model. Up until now, a lot of focus has been on discovering the particles that the Standard Model predicts. That is great in its own right but the neutrino points out weak spots in the model that if worked on could lead to answers about dark matter, dark energy, the ongoing mystery of how gravity fits into the big picture of physics, and perhaps it can even tell us why the universe seems to have far more matter than antimatter in it, a question that continues to perplex theorists. 


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  2. I think this article is well-written. I'm learning more about neutrinos than I knew before. I'm not qualified to comment on that part of it but I did notice a mis-representation in these two phrases "heavy water (called deuterium) " &
    "deuterium is a water molecule that has a neutron in its nucleus along with the proton."

    On the contrary, I believe deuterium refers to the isotope of hydrogen that includes two main sub-atomic particles in its nucleus, a proton and a neutron (hence the deu prefix in the name) as opposed to the typical isotope of hydrogen that contains only a proton (and is about 99 times more prevalent in nature). I am quite sure the author knows too that heavy water is water (two hydrogens and an oxygen) that contains deuterium instead of normal hydrogen. I am not sure whether both hydrogens have to be deuterium flavor of hydrogen atoms to qualify as "heavy water". But my main point is that "heavy" water is still water, it still contains two hydrogens and one oxygen atom per molecule, it is just the isotopes of those hydrogen atoms that must be heavier than usual.

    1. Thank you Isaak! I absolutely mis-wrote myself in that statement. I indeed mean that deuterium (heavy water) differs from ordinary water ONLY in the nuclei of its two hydrogen atoms, which are an isotope that contains both a neutron and proton. The oxygen is the same in both types of water. I appreciate your good eye and will fix that shortly :-)

  3. Integral research about the rhythm of evolution: a hidden spiral-fractal pattern in universal dynamics!

    Dear Gale Martha,

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    In 1993, the journal of general evolution World Futures —Vol. 36, pp. 31-56—, edited by Ervin Laszlo, published my article entitled A hypothesis on the rhythm of becoming. Since then, I’ve continued this research about the rhythm of macro (phylogenesis) and microcosmical (ontogenesis) human evolution, and I’ve found spectacular confirmations. This work discovers, with surprising accuracy, a hidden spiral-fractal pattern of change in Big History that leads to a next point —Omega— of singularity and reveals the essential non-duality of the universe.

    I include a brief Addendum in which I expose some key points in the work of three researchers who have analyzed the phenomenon of evolutionary acceleration independently and from different perspectives —Russian astrophysicist Alexander D. Panov, French paleontologist Jean Chaline (in collaboration with Laurent Nottale and with Pierre Grou), and American computer scientist Carter V. Smith— whose proposals are fully in tune with the pattern of rhythms which I raise in my work. I think the result is overwhelming.

    I dare to send you an actual resume of my research of more than 34 years. You can find it in: “”, in English and Spanish versions, with optional PDF. I’m sure that, if you read it, you’ll be surprised by its results.

    Warm regards


    You can contact me at )

  4. Integral research about the rhythm of evolution: a hidden spiral-fractal pattern in universal dynamics!

    Dear Gale Martha,

    I just found your work “Fractal Universe”. I’m very interested in this topic. So I think maybe you’d also like to hear my integral research about the fractal rhythm of human evolution. I tell you.
    In 1993, the journal of general evolution World Futures —Vol. 36, pp. 31-56—, edited by Ervin Laszlo, published my article entitled A hypothesis on the rhythm of becoming. Since then, I’ve continued this research about the rhythm of macro (phylogenesis) and microcosmical (ontogenesis) human evolution, and I’ve found spectacular confirmations. This work discovers, with surprising accuracy, a hidden spiral-fractal pattern of change in Big History that leads to a next point —Omega— of singularity and reveals the essential non-duality of the universe.

    I include a brief Addendum in which I expose some key points in the work of three researchers who have analyzed the phenomenon of evolutionary acceleration independently and from different perspectives —Russian astrophysicist Alexander D. Panov, French paleontologist Jean Chaline (in collaboration with Laurent Nottale and with Pierre Grou), and American computer scientist Carter V. Smith— whose proposals are fully in tune with the pattern of rhythms which I raise in my work. I think the result is overwhelming.

    I dare to send you an actual resume of my research of more than 34 years. You can find it in: “”, in English and Spanish versions, with optional PDF. I’m sure that, if you read it, you’ll be surprised by its results.

    Warm regards


    You can contact me at )

  5. I was reading your article and wondered if you had considered creating an ebook on this subject. Your writing would sell it fast. You have a lot of writing talent.
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