E2science

Why is blueschist significant?

There was a time when geologists thought the Earth's crust was more or less stable. We take plate tectonics so much for granted these days that it's hard to remember that until about 60 years ago just about the only action geologists accepted in the Earth's crust was the bubbling up of masses of igneous material in orogenic events, to form batholiths, or in volcanic events. There is a (ahem) mountain of (cough) rock-solid evidence for plate tectonics, which, quibbling about details aside, is as well accepted a theory as that of evolution or relativity. Blueschist was there in the beginning, however, and was an important datum in establishing the behavior of subduction zones.

What is schist in general?

Schist is a widespread metamorphic rock. It has been subjected to extremes of pressure, temperature, or both, within the earth. These extremes can do several things to rocks; in the case of schist, they cause a recrystallization of the minerals within the rock, which tend to reform in planes perpendicular to the direction of compression. In addition, schists are usually micaceous, exhibiting the luster characteristic of flakes of mica, and often also contain needle-like amphibole crystals (like actinolite). Blueschist forms in a very special environment, however, and is for that reason a strong evidence of plate tectonics.

How does blueschist form?

The oceanic crust forms out of long cracks from which mafic (manganese and iron-rich) rock extrudes; the extruded material moves away from the central ocean fissures something like a conveyor belt (this is the metaphor I was taught in college). Junk from the ocean and sediments from the land rain down more or less thickly on this oceanic crust as it moves toward the continents. Now, the continents float, because they are marginally lighter than the mafic material, while the oceanic crust hits the edge of the continents and bends down, back toward the mantle.

As it sinks, it heats up and big "bubbles" of melted oceanic crust boil up to erupt in andesite-producing volcanoes along the coast like the Cascades in North America. I was taught that these volcanoes can be fairly violent in their eruptions because the oceanic material has a lot of water locked up in it, and when pressure is released . . . .

But none of this was clear to geologists when plate tectonics was being debated, because there was no technology to image sinking oceanic crust. (Now it can be done, and the sonic image of subducting oceanic crust is one of the triumphant justifications of the theory.) Blueschist, on the other hand, develops as the crud on top of the oceanic crust literally gets scraped off and smashed by the "impact" with the continent.

Blueschist has as its signature mineral glaucophane, a beautiful blue amphibole which forms in high pressure/comparatively low temperature environments, and it pops up in outcrops as a highly metamorphosed rock in seas of somewhat less metamorphosed greenschists and serpentinites along (for example) the west coast of the United States, particularly in the coastal ranges of California and Oregon. (The areas which have experienced just the right high/pressure low temperature metamorphism are called "blueschist facies" precisely because of the characteristic presence of this rock there.)

Proponents of the plate tectonic theory pointed out that blueschists couldn't form in very deep (hot) places, because it is intense pressure, but not heat, that produces blueschists (high heat would cause different minerals to form in the schist). Occam's razor pointed to plate tectonics and the relentless pressure of the scraping of crustal plates of an entire planet--near the surface--as the most economical model to explain the widespread presence of heat-sensitive metamorphic rocks like the blueschists along the California coast (and here and there elsewhere on the planet where conditions have been right).

Blueschists are somewhat harder than the rocks they are normally associated with and often weather out of them as outcroppings. In the Bay Area they are called "knockers." I picked up a few pieces--which I treasure as being somehow significant in the history of science--on the Oregon coast in Bandon (they dynamited a nearby blueschist outcrop to provide hard stone for their jetty).

URLs.

Blueschist photos: http://geology.about.com/library/bl/images/blblueschist.htm. (Including some beautifully colored specimens.)
Greenschist: http://geology.about.com/library/bl/images/blgreenschist.htm.
Course lecture by a pro at Tulane: http://www.tulane.edu/~sanelson/eens211/contact&regional_metamorph.htm.
Tomography of the Japanese subduction zone: http://epsc.wustl.edu/classwork/classwork_210a/transparencies/wysession/w06.jpg.

References.

Alt, David, and Hyndman, Donald. 1978. Roadside Geology of Oregon. (See pp. 97-98 on the blueschist specimens in Bandon, Or.)
----------. 1984. Roadside Geology of Northern California. (See pp. 13-24 on the California coastal range and its oddities.)
Press, Frank, and Siever, Raymond. 1982. Earth (third edition). (See pp. 375-391 on metamorphism, 386 on blueschists in particular.)

I am not a professional geologist. I checked this information, but I may have gotten something wrong, alas!

I want to put in a bid for equality here! Everyone has heard of Mach number 1, but who ever heard about Ma=0.3? Who ever heard about Ma=0.97?

These numbers are almost as significant as Ma=1.000, but no-one ever gets to hear about them. Why not? Because that fucking unity, that isolated and arrogant number one got in the way, and made everyone think unity is the only Mach number to think about. Well let me tell you, they're Wrong!

In case you were wondering, the speed of sound in air at sea level on a normal kind of day is about 330 m/s, or 750 mph, or about 1200 kph. The speed of sound slows down at higher altitudes, because the pressure and temperature drop as you go higher in the atmosphere.

So driving along in your car at 120 kph will get you a Mach number of about 0.1. Speeding along in a train at 300 kph will get a Mach number of 0.25. Taking off in Concorde at 412 kph will get you up to a Mach number above 0.3, and that is where things start to get interesting.

At Ma=0.3, in air, the first signs of compressibility set in. We start to see the very first indications that air behaves differently from water. We all know that when you pump up a tyre, you can fill it with air, and then pump in more air, with no appreciable change in volume, but can you do that with water? Nope! Water is incompressible, and that makes a huge difference when you start to push things through it at high speed.

When you are driving along in your car at 120kph, air seems to be incompressible, because when you push at such a slow speed, the air has plenty of time to get out of he way. There is nothing—such as viscosity or inertia—holding it back, so if something is forced to travel through air at these low speeds, the air behaves just like water, and everything is fairly straightforward and easy to predict.

As your aircraft speeds up, and the Mach number gets to around 0.3, however (around 100m/s or 400 kph), the air molecules simply cannot get out of the way fast enough, so we start to see the first signs of changes in density in the air around the aircraft.

Get up to double that speed: Ma =0.6, and the compressibility becomes noticeable, but nothing really to worry about. As you speed up (relative to the air), the Mach number climbs to 0.7… 0.8…0.9 and still there is not much change in the flight performance. Around Ma=0.9 we are approaching the limit of subsonic flight, so this is the aerodynamic speed limit applied to modern, commercial airliners. That is about 1100 kph at ground level, but more like 900 kph (airspeed) at typical cruising altitudes of 37000 ft/11000m.

When the bulk Mach number gets up to around 0.95, things start to get even more interesting. This is called the trans-sonic zone, but was once called the sound barrier, A normal aircraft wing works by using geometry to make the air speed up over the top of the wing and slow down underneath. By the wonders of the Bernoulli effect, that creates a pressure differential, which gives some lift.

Now, imagine that the aircraft is flying forward at Ma=0.95 or slightly more. The air speeds up slightly over the wing, so the local airspeed might start approaching Ma=1.

What happens then?

At low speeds, the wing is rushing through the air, making a noise. This noise is sent out in all directions, radiating out from the source as a series of sound waves: little compressions and relaxations in the air pressure. However, the sound can only travel forward at the local speed of sound. This means that the sounds will pulse forward at around 330 m/s as viewed from a stationary observer, but will be less than that for someone looking out from the moving wing.

If the wing is moving forward at Ma=0.5, it will move forward 50 cm in the time the sound waves have gone forward by 1m. At Ma=0.9, the wing will go 90 cm in the time the sound waves travel 1m. At Ma=0.99, then the wing is so close behind the sound waves that even after travelling 1m, the wing is only 1 cm behind the sound wave. All the noise and pressure waves generated in the last 1m of travel are packed into a space1 cm long.

With just a little more speed, the wing catches up with the sound waves, and all the compressions get packed into zero space, That shows itself as a shock wave. A little zone of space where the pressure changes suddenly from one value to another. A discontinuity in the pressure field surrounding the aircraft.

Shock waves are strange things. Nature normally abhors discontinuities, and we humans have to work very hard to create them. They absorb a lot of energy, and as a consequence, a shock wave creates huge amounts of drag on an aircraft, a bit like suddenly launching a sail out of the top of the wing.

As the first rocket-powered aircraft speeded up beyond Ma=0.95, small shock waves started forming over their convex exterior surfaces, and the drag increased dramatically. That slowed them down again to subsonic speeds. As the engineers built in more power, to push harder, the shock waves got bigger and more powerful, creating yet more drag on the aircraft, and shaking the aircraft as they formed, collapsed and re-formed along the outer surfaces of the plane.

With more power still, the craft can be pushed up to Ma =1.05, and out beyond the trans-sonic zone, into true supersonic flight. Once the aircraft has passed into the supersonic condition, a large, primary shock wave appears ahead of the craft, centred on the nose cone, with a secondary shock forming near the tail. Once the plane is up to this speed, it is always travelling in still air, and the bumps and lurches associated with trans-sonic speeds disappear.

Modern supersonic aircraft are designed quite differently from subsonic planes. In subsonic craft, all the surfaces are rounded and smooth, designed to allow smooth airflows around the body. For supersonic flight, pointy bits and sharp edges are the norm, in order to control the formation of shock waves. So the front of a subsonic Boeing 747 is a blunt, curvy shape, but the front of a Concorde is a sharp point, designed to ensure the shock wave originates at a pre-defined place.

When you run the tap in your washbasin, the stream of water hits the basin and spreads out in a very thin film of water moving at high speed. After a short distance, there is a line where the flow changes depth and travels more slowly. That wave front where the water changes from fast and shallow to slow and deep is an hydraulic jump. Although the jump in your washbasin is only a couple of millimetres high, these waves can reach three or four metres on a river.

They are fascinating and wonderful things: not only for surfers, who want to remain standing on their boards for a long, long time, but also for water engineers who need to control the flow and energy of their rivers and canals. One of the most spectacular natural examples is the bore on a river such as the Severn in the UK.

Canoeists are warned against them because of the extreme turbulence behind the wavefront, which does very unexpected things to people and boats. Canoeists drown in hydraulic jumps daily.

Next time you look at a river near a dam or a weir, look for the tell-tale signs of rapid, shallow flow. The first is the surface of the water is smooth, because the water is flowing faster than a surface wave can propagate. The second is that somewhere downstream is a standing wave where the flow changes from fast and smooth to deep and turbulent.

This phenomenon is governed by the Froude Number, which balances the inertial forces in a fluid against the gravitational forces. At any given Froude number, there are only two possible depths of water. One represents the depth ahead of the hydraulic jump, the other is the depth immediately behind the hydraulic jump. It is difficult to calculate the two permissible depths, except in a a smooth, regular, rectangular channel, but the keys are the Froude number, the cross-sectional area and the specific energy within the flowing fluid. Basically, the faster the fluid flows, the bigger the hydraulic jump.

If V² > gD, then the flow is fast and shallow (rapid flow). This is called super-critical flow, and is very aggressive and abrasive to a river bed

If V² < gD, then the flow is deep and probably turbulent. Sub-critical flow is much more benign

The case of a circular hydraulic jump, such as you might find in your washbasin, or when a jet of water hits a flat horizontal plate, is one of those problems which looks simple, but is very difficult to analyse properly

Looking at a large-scale application, such as a dam, the water flows a bit like the following diagram:

 ->------R 
  wwww= \\a
  #### | \\p    
  #### |  \\i 
  #### |   \\d 
  #### |    \\             sub-critical flow-> 
  #### |     \\flow_______JWWWWWWWWW  Flow direction ---------->
  #### |      ===============================

our "hydraulic jump" is represented by the letter "J". Engineers will shape the base of the dam (between the 'f' of flow and the J) so that the falling water is guided into a horizontal trajectory, ensuring the jump forms at the desired place.

Note 1 Thanks to Gorgonzola for, well, for being a hero Note 2 Thanks to Frankie for advice on canoing
Note 3 This piece written, formatted and edited in Dann's E2 offline scratchpad

CP violation is an effect in particle physics that has, of late, been of considerable interest. A CP-violating process is one which is not symmetric under the combined operations of charge conjugation (C) and parity reversal (P), collectively referred to as CP. The operation of charge conjugation replaces every particle with its respective antiparticle, and the operation of parity reversal reflects the system such that left and right are interchanged. CP violation is one of the cornerstones of the theory of baryogenesis, which describes how the universe came to be made of matter and not equal amounts of matter and antimatter. CP-violating interactions discriminate between matter and antimatter, a distinction that is rare in particle physics.

The Discovery of CP Violation

Initially, it was believed that parity reversal was an exact symmetry of nature, i.e., that a mirror-image universe would evolve in exactly the same manner as this universe, only reflected across some plane. All theories of gravity and electromagnetism are exactly symmetric under parity reversal. However, it was discovered in the late 1950s, by C.S. Wu, that the weak nuclear force is not only asymmetrical under parity reversal but that the parity violation is maximal, meaning that some weak interactions have a particular preferred orientation and that corresponding interactions in the opposite orientation are not observed. These interactions, involving neutrinos, were then found to once again be symmetric if the parity reversal were followed by a charge conjugation. So, CP was postulated as being an exact symmetry of nature.

Alas, it was not to be. A few years later, it was discovered by Cronin and Fitch that CP was also violated, this time in the decay process of the neutral kaon. This came as a shock to the entire particle physics community, as their experiment was expected to be a routine confirmation of CP symmetry. Initially, there was an attempt to explain the results without resorting to CP violation but further experiments confirmed that a CP-violating interaction was occuring. Cronin and Fitch later won the Nobel Prize in Physics for their work.

The Role of the Kaon

The neutral kaon is not its own antiparticle, unlike the neutral pion, and so it is not unchanged under charge conjugation. Thus, when the CP operation is performed on a K⁰, the result will be a form of its antiparticle K⁰. This is clearly a different particle so the K⁰ are not eigenstates of the CP operator. Now kaons usually decay into pions, and from conservation of charge they will either be neutral pions or pairs of oppositely-charged pions. Both of these cases are eigenstates of CP and thus have a definite value (the 'eigenvalue') associated with them. Since CP is its own inverse, these eigenvalues must be either 1 or -1. If CP is an exact symmetry then the sign of its eigenvalue is conserved in particle interactions

So the conclusion is that when the kaon decays into pions it must have a definite CP eigenvalue and therefore must be in an eigenstate of CP. To create this, we combine equal parts of the K⁰ and K⁰ to form two new, CP-eigenstate particles, which can be called K₁ and K₂. K₁ has a CP eigenvalue of +1 and decays to two pions, and K₂ has a CP eigenvalue of -1 and decays to three pions. Each or the 'observed' kaons (K⁰ and K⁰) is a combination of K₁ and K₂ and oscillates between them as it propagates.

CP, however, is not an exact symmetry, and so occasionally a K₂ will decay into two pions. Thus, the eigenstates of the weak interaction are not the CP eigenstates K₁ and K₂ but slightly unequal combinations of the original K⁰'s called "K short" (K_S) and "K long" (K_L). The names refer to the fact that, since three pions have a greater mass than two pions, a decay into two pions will happen, on average, more rapidly than a decay into three pions.

The difference in lifetime between K_S and K_L was the key to the original observation of CP violation. Since the difference in their lifetimes is greater than two orders of magnitude, one can obtain a pure K_L beam simply by sending a K⁰ beam down a pipe and waiting for a certain distance before observing it. Moreover, the fraction of K_S remaining in the beam at a certain point should be calculable. CP violation was discoverd in the simple observation that far more two-pion events were appearing far down the beamline than could be explained by any remaining component of K_S, suggesting the existence of the process K_L -> 2π. Other experiments have confirmed this effect. For example, K_L decays more often to π^-μ⁺ than π⁺μ^-, which is a clear violation of charge conjugation symmetry.

Future

For many years, the kaon was the only case where CP violation was observed. In the last decade, however, CP violation was observed in neutral B mesons, by both the Belle collaboration in Japan and the BaBar collaboration at SLAC. The CP violation observed in B decays has been found to be mostly consistent with the predictions of the Standard Model. Currently, there are hopes to measure CP violation in neutrino oscillation, which may be more prominent an effect than in meson physics.

The CP operation combines with time reversal to form the CPT operation. The laws of quantum mechanics require that the laws of physics are symmetric under CPT, and this is borne out by experiment.