Why are Lakes and Rivers in the Canadian Rocky Mountains so Brilliantly Turquoise Blue?

An investigation into geology, history, and optics

I've always wondered what exactly is going on with these lakes and rivers. I was surprised to find so little written online to explain their colour. I did find a lot of people asking the same question, however. There are a few good answers, ranging from simple to very complex. I relied on them for my answer and I direct you to them here:

1) Ben Gadd, an Earth Science specialist and licensed interpretive guide, resides in Canmore, Canada. He offers an excellent not-too-technical treatment of the question in his book called Handbook of the Canadian Rockies. The geology in this book is challenging but really good if you want to know how the Canadian Rocky Mountains came to be (we call them simply The Rockies here). You can sense his passion for this gorgeous natural part of Canada.

2) An online article called Glacial Lake Colour – Get The Right Story. Nadine Fletcher, a mountain guide, offers the perfect introduction to glacial lake colour. She also mentions an out-of-print book as her source in the article, if you are lucky enough to find a copy.

3) If you want to go deep, you will find the 1988 scientific paper called Colours Of Glacial Water by Eyvind Aas and Jim Bogen (you have to pay to access it online) to be probably the best scientific answer available. It's not an easy read but physicists will appreciate it.

4) Wikipedia has a few good but brief entries to check out. Try Color of Water, Rock Flour and Glacial Lake.

5) Hyperphysics.com does a great job of explaining the concepts of light scattering. Usually applied to atmospheric optics, these are also the basic scientific principles behind glacial lake and river colour. As you will discover in this article, the answer takes you into a lesson about optics.

Introduction

Numerous lakes and rivers in the Rocky Mountains of Western Canada (my favourite stomping ground) are an otherworldly turquoise-blue hue. It's an opaque yet brilliantly bright colour that looks as if someone is continuously dumping huge vats of food colouring upstream. It is as if someone has painted the riverbeds and lake bottoms turquoise. And they are so luminescent at times that they appear as if they are under-lit as well. It is equally mysterious that rivers, which are obviously shallower than the lakes (you can see man-sized boulders peaking out of them), often appear just as brightly turquoise as the lakes, many of which are hundreds of metres deep.

A great example of this colour is Peyto Lake in Banff National Park (below) seen from a viewpoint on the Icefields Parkway. Once you see this colour yourself, you never forget it.

Tobias Alt; Wikipedia

You will likely see this particular turquoise only in the Rocky Mountains of Western Canada. These lakes and rivers are glacially fed bodies of water. There are many others around the world as well, but each glacial source tends to be unique. This means that the colours of the waters that melt from them likewise tend to be unique.

For example, Tasman Lake, a glacial water-fed lake in New Zealand, is muddy grey-green, as seen below.

It's a very young lake (around 25 years old) and it formed as ponds of glacial meltwater merged from fast-retreating Tasman Glacier. A submerged glacial ice apron projects into the lake (not visible) and icebergs periodically break off it to float across the lake.

Green, from my research, seems to be the more common glacial lake colour. A good example of a green glacial lake is the unnamed proglacial lake made of the meltwater from Schoolroom Glacier in Wyoming, US, seen below.

The water is held in a cradle of rocks and rock debris (called a moraine) left behind by the retreating glacier) (you can see the edge of the glacier in the upper right corner). Lakes formed by the damming action of moraines, or from ice dams, are called proglacial lakes. Both Tasman Lake and this unnamed lake are proglacial lakes.

Explanations for Rocky Mountain Lake Turquoise: A Stewpot of Anecdote and Science

I have heard several anecdotal explanations for the turquoise colour of our Rocky Mountain glacial lakes and rivers. One explanation is that the water surface reflects the blue of the sky. Frankly this is the laziest explanation. This is true, but it is just one small contribution to the colour, and it's blue not turquoise. If you look at the sky's reflection in the Peyto Lake photo above, you can see that the blue sky's reflection is a true blue colour on the lake, different from its more greenish turquoise inherent colour. The reflection of sunlight on lake water can make all lakes look blue at least at certain times of day on sunny days when the surface is calm and reflective. The luminescent turquoise of glacial lakes appears much different, and it doesn't require an intensely sunny day, although it appears more brilliant on bright sunny days. On stormy early summer afternoons, and there are many in the Rockies, lakes turn dark and foreboding and glacial rivers in particular seem to take on an almost eerie milky light blue.

Besides the reflection "answer," it is true that any water in general looks blue en masse. The colour comes from the water molecules themselves. The molecules tend to absorb the red, orange, yellow and green wavelengths within the full spectrum of white sunlight striking them, while they reflect the shorter blue wavelengths back to your eyes. This is called Rayleigh scattering, more on this mechanism in a moment. The water in an indoor pool that is lit by white ceiling lights but not sunlight looks blue for this reason. The deeper the water is, the bluer it looks (there are more molecules reflecting blue light).

An additional source of lake colour can come from suspended organic material, which most lakes have. This includes all the living organisms suspended in the water column. These organisms will reflect the sunlight that strikes them back upwards. The sunlight must pass through water of varying depths to reach them first, so this means that the light that strikes these particles is mostly blue light. Some organisms, especially diatoms, act like little mirrors. The light they reflect upward to your eyes is also blue. Algae often have their own intrinsic colour, and at high enough concentration (an algal bloom) they will change the colour of a lake to deep green, blood red or even bright pink depending on the species.

Shown below,  an intense cyanobacterial bloom turned Lake Erie turquoise and green in 2011. These organisms are technically bacteria, not algae (a unicellular plant).

This pink bloom is caused by a algal species of dinoflagellate. Some dinoflagellates are bioluminescent. They glow eerie blue in the water at night.

Marufish – Flickr;Wikipedia

Algae are not at play in glacial turquoise lakes, however. Glacial lakes and rivers are cold and very low in organic matter, although super-tough Watermelon algae, tiny ice worms and ice springtails can be present in glaciers. Is glacier water safe to drink? If the ice has a pink tinge don't drink from a glacier's snout as it has Watermelon algae, which is said to be a laxative.  I couldn't find any evidence that the animals are toxic if ingested. Is the rock flour itself okay to ingest? Glacial snout water will clog up a coffee filter in no time, and consider too that this stuff acts like fine sandpaper. A laxative sandpaper drink wouldn't be my choice.

Besides suspended organisms, chemicals and ions dissolved in water can colour it. The natural presence of copper was once an explanation for the turquoise colour of the glacial water. Decades ago as a teenager I was told this "fact." Perhaps folklore lingering from the late 1800's mining rush in the Canadian Rockies explains why it was natural to point to copper as the reason behind turquoise water. Copper can exist in rock as pure (insoluble) metallic ore and it can also exist in soluble compound form such as copper sulphate, copper chloride, etc. Many copper compounds are blue-green or bright blue when the copper ions (usually Cu⁺⁺) dissolve in water. Copper ions are naturally found in lake and river water in the Rocky Mountains, but their concentration is generally at or just over the current detection limit of 0.001 mg/L. This concentration number comes from a study done along Athabasca River (a Rocky Mountain glacial river) in 1995. The concentration is lowest upstream near its glacial source and increases downstream because of contributions from human development. The tiny amount of copper dissolved in glacial water comes from the weathering of mountain rock, which contains trace amounts. It is not high enough to colour the water a detectable amount.

The Canadian Rocky Mountains do (or did) contain some minable solid copper ore deposits. Quartz-carbonate veins in the limestone and dolostone rock of the mountains contain copper. These veins are found in fractures in the rock, where the copper-bearing quartz-carbonate forced its way up from deep underground. The fractures come from faults and mechanical shear zones in the sedimentary rocks that formed as they were folded and deformed during mountain building.

Composition of the Canadian Rocky Mountains

These geology terms might be new for many readers so I offer here a brief amateur lesson in Rocky Mountain geology (I can mostly thank Ben Gadd's book for my understanding): The Rocky Mountains are made of sedimentary rock. This rock was slowly deposited over time as layers of sediment built up on the floor of a shallow ancient inland sea. Later, as the plates of Earth's crust separated, shifted and collided, those plates pushed against this rock, folding it into mountains, like bunching up a rug on a floor. Limestone (CaCo₃) and dolostone (CaMg(Co₃)₂) are sedimentary rocks composed of calcium carbonate. Dolostone is similar in chemical composition to limestone except that it has the addition of magnesium (Mg). These rocks, along with two other sedimentary rocks, sandstone (formed when sand grains cement together over time) and shale (formed from much finer grained silt and clay), make up almost all of the Rocky Mountains. Quartz (silicon dioxide or SiO₂), part of the copper bearing quartz-carbonate veins mentioned earlier, is a very common mineral that either crystallizes from magma or precipitates from very hot hydrothermal veins. Quartz, hard and very resistant to weathering, is commonly found as crystals in sedimentary rocks such as sandstone, shale and in carbonate rocks such as limestone and dolostone. Beach sand itself is composed mostly of granules of quartz and calcium carbonate.

Key Differences Between the Canadian and American Rocky Mountains

Fracture zones filled with copper-rich quartz/carbonate veins are not common in the Rocky Mountains, at least not near the surface. However, some were accessible enough in the far northern part of the Rockies to be minable. There was once a productive copper mine (Churchill Copper Mine, discovered in 1943 and most productive between 1970 and 1975) in that region.

The copper rush (or more accurately a silver/gold/copper rush) took place earlier, ramping up in the late 1800's in the Canadian Rockies. Copper Mountain, a popular ski resort in the Rocky Mountains, was named after a prospector that suspected vast copper ore was present within its rock (it wasn't). There was also a frenzied copper rush at Silver City located at the foot of Castle Mountain (along with wild rumours of gold and silver, hence the name). There were minute amounts of copper and silver ores found there but not enough to be commercially viable. Just as quickly abandoned as it formed, only a marker now indicates the area where Silver City once stood.

The mining hysteria originated in the American Rocky Mountains, which extend southward from our border. Prospectors found a wide variety of valuable minerals and metals in their American extension of the North American Cordillera. It was natural to expect more of the same north of the border. Unknown at the time, however, there is a key difference between the two regions. The Canadian Rocky Mountains are composed of layered sedimentary rock that underwent mild metamorphism, while the American extension of Rockies is mostly of metamorphic and igneous origin (this is rock such as gneiss (metamorphic) and granite (igneous).

Rock of deep volcanic origin (igneous) and rock formed under tremendous heat and pressure (metamorphic) tend to be where gems are formed and where metallic ores and precious metals are deposited. The American part of the Rocky Mountains was reformed from a mountain range that existed 300 million years ago. Unlike the present American Rocky Mountains, this ancient range was built by volcanic activity. In contrast, the Rockies to the north, in Canada, were formed from sedimentary rock laid down at the bottom of a large shallow sea that existed around that same time and earlier. Both of these types of rock bunched up into the Rocky Mountains around 80 million years ago, as the Pacific continental plate pushed into the North American continental plate.

Sites in the Canadian Rockies are rich in rare Cambrian marine fossils. These creatures lived around 500 million years ago, long before any plants or animals lived on dry land. As animals died their bodies were covered in fine silt (the raw material for shale rock), which prevented oxygen from seeping into them and decaying them. For this reason even some soft body tissues are beautifully preserved, offering one of the best windows in the world into our first ancient multicellular creatures. The fossils are still intact after all this time because the Cambrian sedimentary rock in this zone, called the Stephen Formation, was protected by an adjacent ancient cliff of hard-to-compress limestone (called the Cathedral Formation) nearby. This means that the fossil-rich Stephen Formation was never heated or squeezed intensely during mountain-building later on. Besides the beautiful glacial lakes and rivers, another reason to come and visit our Rocky Mountains is to take a guided Burgess Shale hike in Yoho National Park to see them for yourself. The Burgess Shale formation is a world-famous UNESCO site.

This Geology Lesson Leads To Rock Flour, Our Secret Ingredient

In terms of our turquoise colour investigation, we can now rule out organic matter, dissolved copper, and the sky's reflection as the source. This leaves a perhaps unexpected or perhaps inevitable source: rock flour. If you have never heard of rock flour you are not alone. Rock flour, or glacial flour, consists of very fine-grained particles of rock. Like grains of wheat ground under a grindstone mill, the surfaces of mountains were ground fine as enormously heavy rock-hard glaciers crept slowly along the surface during the last ice age (yes glacial ice is a fluid – it will flow very slowly downhill due to gravity). Rock flour particles are tiny and come in all shapes. Some can be rough-edged. A layer of these particles underneath a heavy creeping glacier thoroughly sands down the landscape.

Rock flour was deposited throughout the Rockies. You can see it mixed in with larger rock debris at the snouts of glaciers today. The entire North American Cordillera was glaciated in the past. Extremely thick continuous sheets of ice covered almost all of Canada during the last interglacial period, while the southern American Rockies were, and some still are, covered with local glaciers. The Big Pine glacial lakes, for example, exist as far south as southern California. These lakes located in the Sierra Nevada exist at the southern end of the Rocky Mountains. They exhibit a lovely emerald green colour thanks to their rock flour content.

Rock dust, as you can guess, is composed of the mountain's rock, so here in Canada it is rich in limestone, dolostone, sandstone and shale. Most of the particles are so small that they can stay in suspension in glacial meltwater for a long time. The water very close to the snout (leading edge) of a glacier can be so heavily loaded with rock flour that it appears milky white or milky light grey. In rivers downstream and in glacial lakes, however, suspended rock flour magically turns the water luminous turquoise. This is where the science of optics comes in.

Rock Flour Optics

Colour is all about visible light. Visible light is a small portion of the electromagnetic (EM) spectrum of energy that humans can see. The energy of EM radiation increases as wavelength decreases. Visible light wavelengths range from 380 nm (violet) to 750 nm (red). Green, in the middle of the optical spectrum, is around 540 nm (these wavelengths are in the nanometre or billionths of a metre range). This screenshot of Wikipedia's entry will help you compare colour wavelengths as you read on.

The Intrinsic Blue Colour of Water: Rayleigh Scattering

I snuck in a little intro to light scattering, called Rayleigh scattering, earlier on. Rayleigh scattering contributes blue colour to pure water. Now we can fully explore how it works. This contribution has to do with how the water molecule vibrates in its liquid state. If you wiki Rayleigh scattering you find it is defined as "the (dominantly) elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation." This is a good working definition we can expand upon.

Individual atoms and molecules are the right size to produce this phenomenon. They have a diameter smaller than one tenth of an optical wavelength. When sunlight strikes a molecule of water, for example, it doesn't change its physical state but it does act on the electrical charges in the molecule (the charged electrons). Visible light is EM radiation. It is a traveling oscillating electric field. This oscillating field acts on the molecule's charges, making them oscillate at the same frequency. In effect it turns the molecule into a tiny EM radiating dipole. It is now a tiny oscillating electric field, so it radiates its own EM radiation as scattered visible light. We don't need to know a lot of complex math to understand this but the following relationship is key: The amplitude of the scattered light is proportional to the inverse square of its wavelength. This means that small visible wavelengths (blue wavelengths) will produce the most intense scattered light. The scattering process itself, in other words, is most effective at short wavelengths, or toward the blue end of the visible spectrum. As an example, the scattering of sunlight off air molecules at 400 nm is almost 10 times greater than it is at 700 nm. This is why the sky, full of small nitrogen, oxygen and other molecules, looks blue when sunlight shines through it.

In our case we are examining Rayleigh scattering in a liquid. A water molecule (H₂O) never sits still. In technical terms it is a tiny harmonic oscillator. It can vibrate in three different ways. It can vibrate along each of its two oxygen hydrogen (OH) bonds, and the molecule itself can rotate back and forth. However, it can only rotate when it is free in the gas state as water vapour (this rotation is called a v₂ vibration). As a liquid in our case, molecules are too close together to rotate freely. This leaves OH stretching oscillations (acting like tiny vibrating elastic bands) and there are two kinds possible, shown below left. Blue spheres represent hydrogen atoms and yellow sphere represents oxygen. The bonds are shown as black lines (each black/striated triangle pair is a non-bonding lone electron pair).

Each of these two fundamental modes of vibration has a frequency. V₁ (top) is 3650 cm^-1 and v₃ (bottom) is 3755 cm^-1. The absorption of EM radiation at these vibrations is in the invisible infrared part of the spectrum. The strongest reflected wavelength (the true colour of pure water if we could see it) is ultraviolet, which is also invisible. This is the fundamental mode of vibration of those two OH bonds. None of this contributes to the visible colour of pure water. This reflected UV radiation, by the way, is not the shorter wavelength high energy UV solar radiation that causes skin cancer and cataracts.

So why is water blue then? The water molecule not only has fundamental modes of vibration, it has harmonic modes as well (just as in music). A significant harmonic mode is v₁ + 3v₃, which equals 14,318cm^-1. This frequency corresponds to a wavelength of 698 nm, which is visible red. The water molecule absorbs red, so the colours it reflects are disproportionally on the blue end of the visible spectrum. Water therefore has an intrinsic blue colour.

Difference Between Rayleigh and Mie Scattering

When light strikes any molecule, some wavelengths are absorbed and others scatter off it. This is a size-dependent phenomenon that operates only on very small size objects such as molecules. It works for particle sizes up to one tenth the wavelength of the light. Much larger objects such as water droplets in clouds make clouds look white. Light scattering for them is mostly independent of wavelength in the visible range. Incoming white sunlight scatters off them as white light. The mechanism responsible here is Mie scattering.

For example, look up at a sunny sky when the sunlight is angled from the South (if you're in the northern hemisphere). If you look over to the north, you see the most intense blue colour. If you look more toward the south, near where the Sun is shining, the sky progressively looks whiter. This happens because the contribution of Rayleigh scattering decreases in favour of increased Mie scattering. This effect is more pronounced when there is a lot of particulate matter (larger than atomic size) in the sky. Smoke blown in from forest fires often makes the entire sky look white. To see the difference between Mie scattering and Rayleigh scattering in easy diagram form, click this Hyperphysics link.

Both Mei and Rayleigh scattering are examples of light scattering off a small object such as a molecule (Rayleigh) or dust grain (Mie). In both cases, light scatters elastically, which means that the energy (wavelength or frequency) of the light is not changed during the process. To describe how light interacts with larger objects, you move on to ray optics. These processes include reflection, refraction, and diffraction, where light is described as rays rather than as an oscillating EM wave. Ray optics are also at work in glacial lakes and rivers (the partial reflection of a blue sky in a glacial lake is an example).

Neither Rayleigh Nor Mie Scattering Make Glacial Water Turquoise

Rayleigh scattering does not contribute to the brilliant turquoise colour of glacial water. There is a common misconception that rock flour particle sizes generally match the wavelength of the blue-green light component in the Sun's light spectrum, so they reflect blue-green light like tiny Rayleigh scattering machines in the water. Remember, Rayleigh scattering operates when particle size is, at most, a tenth of visible wavelength size. On the other hand, Mei scattering occurs most predominantly when particle size roughly matches wavelength size. The smallest rock flour particles approach visible wavelength size but many are larger. The finest particles tend to be between 2 um (micrometres, or millionths of a metre) and 100 um. Most rock flour particles are larger than a typical optical wavelength. To compare, red, the longest visible wavelength, comes in at 698 nm, or 0.698 um, under the size of most rock flour particles, but probably not all. For Rayleigh scattering to work, particle size must be less than one tenth the size of a visible wavelength. Mei scattering, however, works in this range. The problem is that Mei scattering reflects (white) sunlight back as white, not turquoise, light. It certainly contributes to the brightness or brilliance of glacial lakes, however.

How Rock Flour Results in Turquoise Water: The Tyndall Effect

To understand the mysterious turquoise colour, we must move on to a different optical explanation called the Tyndall effect, or colloid scattering. As a mixture, a colloidal dispersion finds itself between a solution and a suspension. A solution is a homogenous mixture where a substance is dissolved in a solute. Particles in solution can be atoms, ions or molecules. They are smaller than 1 nm (0.001 um) across. A suspension consists of particles that can be evenly distributed if the contents are shaken or disturbed, but at rest the particles settle out. Medium to coarse rock flour in water (40 - 100 um rock flour particles) is a suspension. Very fine rock flour acts much like a colloid in the water. When it is mixed with water, the particles tend to stay evenly distributed throughout it for some time (but they will eventually settle out too). Colloidal particles tend to be around 1 micrometre (um) in diameter, which is a just bit larger than a visible wavelength.

The Tyndall effect is not a mechanism per se and, unlike Rayleigh and Mie scattering, it does not have a formal mathematical description. Instead, it simply describes how light tends to behave when it passes through particles suspended in a liquid.

This effect is not Rayleigh scattering but, like Rayleigh scattering, it is particle size dependent, and it is wavelength dependent. Longer-wavelengths tend to be transmitted through the colloid (suspension) and shorter wavelengths tend to be reflected by scattering. The underlying mechanism is, in fact, a special form of Mei scattering, which might seem a bit contradictory, as we are getting colour here. Colloidal scattering becomes mathematically equivalent to Mei scattering if the colloidal particles are perfectly spherical in shape. Rock flour particles are all kinds of shapes from roughly spheres to sharper fragments. Confusingly, as we talk about the Tyndall effect, the argument can seem reminiscent of Rayleigh scattering, as the following Tyndall effect analogy suggests. 

To get a feel for the Tyndall effect, think of the difference between (long) radio waves and (short) light waves. Radio waves can pass right through solid materials like walls in buildings because the length of the wave is much larger than the width of the wall. In order to absorb or reflect EM radiation, you need a charge oscillation that corresponds to the EM wavelength. In most materials, the oscillating charges in molecules can match visible EM radiation (clear glass is an exception so it is invisible to light). The radiation is absorbed and reflected (which wavelengths absorb and which wavelengths reflect determines what colour the wall appears). There are no charge oscillations big enough to correspond with radio waves so walls are transparent to them. Some metal walls are an exception. The electrons in metals form a mobile "sea" that can resonate with long radio wavelengths and reflect them.

Don't despair if this theory is confusing. Both Rayleigh and Mei scattering are simply mathematical constructions based on ideal (unreal) objects. In real life, with real objects such as a mixture of irregularly shaped rock particles in water, we use the best theoretical approximations we can. We get a close, but not perfect, fit for our situation. All light absorption/reflection/scattering/interference at all scales boils down to a simple process: EM photons matching the charge oscillations of electrons in atoms.

Colloidal scattering is most strongly observed when particle size is between 0.04 um and 0.9 um, slightly under visible wavelength range, and just under the size of very fine rock flour. While this isn't a perfect match, the effect is much more intense than Rayleigh scattering, and therefore significant. The reason for this can be obtained by comparing the diagrams for Rayleigh and Mie scattering. While the Rayleigh scattering intensity is uniform around the particle (same size arrows), Mie scattering intensity is highest away from the light source, available to reflect the light straight back from the upper surfaces of deeper particles. Why this is so has to do with interference effects that develop as particle size increases from Rayleigh particle size (the size of a chemical bond) to Mie particle size (a sphere). The reflective/absorptive surface area of the particle starts to have a significant effect. Technically speaking, wavelength interference develops through phase variations over the particle's surface.

Colloidal particles are basically what we are dealing with when we talk about glacial water - rock particles that are small and light enough to suspend in water. An easy colloidal mixture to make at home is to suspend flour from the kitchen in a glass of water. Milled flour particles are between 1 and 100 um, according to engineeringtoolbox.com, pretty close to the particle range of rock flour (2 to 100 um). Wow! It looks a lot like blue glacial water (you have to get the concentration right for this effect).

Chris 73;Wikipedia Commons

Like the flour-water above, the smallest rock flour particles (around 2 um and just under) reflect most strongly in the visible blue range. They also display a fairly high irradiance ratio, meaning it’s a brilliant blue too. The irradiance ratio is the amount of light scattered backwards compared to the amount of light that continues down deeper into the water column. Particles around 20 um reflect more toward the green range and their irradiance ratio is quite low, about one tenth that of the smallest particles. Finally, large suspended particles (around 100 um) reflect equally across the visible spectrum, so white light shining down on them is reflected back up as white light. Like the smallest particles, their irradiance ratio is strong so they are highly reflective as well.

We can imagine what all these optical effects do when we think about water melting from a glacier's snout. There will be lots of rock flour right under the snout. This means that glacial water near its source, where the largest rock flour particles haven't had a chance to settle out yet, appears bright and milky white (or grey if the melting glacier has lots of dust/debris in it). A glacial lake with a very high concentration of suspended rock flour, including lots of medium size particles will look greener. A lake in which the larger particles have sifted out and only tiny particles remain will be the most intensely turquoise.

By the Tyndall mechanism alone, the inherent colour of the tiny rock pieces themselves has nothing to do with glacial lake colour. Tan, white and grey rock flours should produce similar effects. There could be other colour-enhancing effects at play, however. Think of the shallow clear brilliant turquoise water just off tropical beaches. The colour is especially vivid when seen from a plane directly above. In this case, we are likely dealing with a simpler effect. The sand and coral beneath these turquoise shallows is often roughly tan-coloured, like our rock flour. You can think of the ocean floor as a tan sheet having a high absorption coefficient for short wavelength (blue, indigo and violet) light. It in turn reflects some blue, green, yellow, orange and red light. If it wasn't underwater, these absorption/reflection effects would add up to what we see as the colour tan. The tan ocean floor eliminates some blue light by absorbing it and the water itself absorbs reds, oranges and yellows. What remains is blue-green, aqua or turquoise light, which makes these shallows look blue-green, aqua or turquoise. Water itself, as we learned, is intrinsically blue. That colour intensifies with the depth of the water column, so as the ocean deepens away from the shoal, the blue deepens and eventually gives way to the black colour of deep-ocean water.

Conclusion

As we've seen, glacial lakes can look turquoise, green, blue or milky white, depending on how much rock flour is suspended in them and especially how coarse those particles are. It also depends on what angle the Sun is shining. To see the most intense turquoise possible, look down at a glacial lake from a plane when the Sun is at its highest in the sky on a sunny clear day in late June. At this time, the light will be right for maximal turquoise reflection and the rock flour concentration should be at its highest from maximal melt.

Sometimes you can see layers of different colours in a glacial lake after a heavy rain as rainwater flows into it from rising rivers and streams, which change the rock flour concentration and distribution of grain size. Our glacial lakes and rivers change all the time, depending on rain, melt rate in the glaciers, how sunny it is, what angle you are viewing from and what time of day it is. Even when you know the science behind it, it still seems magical. In early spring, the magician has not yet arrived for the year. Glacial lakes have settled out over winter and they are dark blue just like other lakes. By mid-June at the peak of melt season, they turn intensely turquoise and they more or less tend to stay that way all summer long. The conversion to luminescent turquoise really seems more like magic than science, as this photo of Lake Louise proves.

You can see accumulated rock flour on the bank as it enters and becomes suspended in the glacial meltwater. Once suspended in deeper lake water, the magic happens. I have seen Lake Louise appear emerald green. Other times, it looks robin-egg blue, like the photo above, which has always been my favourite colour.

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.

SNO

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.

Conclusion

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.