Category Archives: Physics

Weird thermodynamics near surfaces can prevent condensation and make water more slippery.

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It is a fundamental of science that that the properties of every pure one-phase material is totally fixed properties at any given temperature and pressure. Thus for example, water at 0°C is accepted to always have a density of 0.998 gm/cc, a vapor pressure of 17.5 Torr, a viscosity of 1.002 centipoise (milliPascal seconds) and a speed of sound of 1481 m/s. Set the temperature and pressure of any other material and every other quality is set. But things go screwy near surfaces, and this is particularly true for water where the hydrogen bond — a quantum bond — predominates.

its vapor pressure rises and it becomes less inclined to condense or freeze. I use this odd aspect of thermodynamics to keep my platinum-based hydrogen getter catalysis active at low temperatures where they would normally clog. Normal platinum catalysts are not suitable for hydrogen removal at normal temperatures, eg room temperature, because the water that forms from hydrogen oxidation chokes off the catalytic surface. Hydrophobic additions prevent this, and I’d like to show you why this works, and why other odd things happen, based on an approximation called the  Van der Waals equation of state:

{\displaystyle \left(p+{\frac {a}{V_{m}^{2}}}\right)\left(V_{m}-b\right)=RT} (1)

This equation described the molar volume of a pure material, V_{m}, of any pure material based not the pressure, the absolute temperature (Kelvin) and two, substance-specific constants, a and b. These constants can be understood as an attraction force term, and a molecular volume respectively. It is common to calculate a and b from the critical temperature and pressure as follows, where Tc is absolute temperature:

{\displaystyle a={\frac {27(RT_{c})^{2}}{64p_{c}}}}, {\displaystyle b={\frac {RT_{c}}{8p_{c}}}.} (2 a,b)

For water Tc = 647 K (374°C) and 220.5 bar. Plugging in these numbers, the Van der Waals gives reasonable values for the density of water both as a liquid and a gas, and thus gives a reasonable value for the boiling point.

Now consider the effect that an inert surface would have on the effective values of a and b near that surface. The volume of the molecules will not change, and thus b will not change, but the value of a will change, likely by about half. This is because, the number of molecules surrounding any other molecule is reduced by about half while the inert surface adds nothing to the attraction. Near a surface, surrounding molecules still attract each other the same as before, but there are about half as many molecules at any temperature and pressure.

To get a physical sense of what the surface does, consider using the new values of a and b to determine a new value for Tc and Pc, for materials near the surface. Since b does not change, we see that the presence of a surface does not affect the ratio of Tc and Pc, but it decreases the effective value of Tc — by about half. For water, that is a change from 647 K to 323.5K, 50.5°C, very close to room temperature. Pc changes to 110 bar, about 1600 psi. Since the new value of Tc is close to room temperature, the the density of water will be much lower near the surface, and the viscosity can be expected to drop. The net result is that water flows more readily through a teflon pipe than through an ordinary pipe, a difference that is particularly apparent at small diameters.

This decrease in effective Tc is useful for fire hoses, and for making sailing ships go faster (use teflon paint) and for making my hydrogen removal catalysts more active at low temperatures. Condensed water can block the pores to the catalyst; teflon can forestall this condensation. It’s a general trick of thermodynamics, reasonably useful. Now you know it, and now you know why it works.

Robert Buxbaum August 30, 2021

Blue diamonds, natural and CVD.

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The hope diamond resides in the Smithsonian. It really is a deep blue. It has about 5 ppm boron.

If you’ve ever seen the Hope Dimond, or a picture of it, you’ll notice a most remarkable thing: it is deep blue. While most diamonds are clear, or perhaps grey, a very few are colored. Color in diamonds is generally caused by impurities, in the case of blue diamonds, boron. The Hope diamond has about 5 ppm boron, making it a p-semiconductor. Most blue diamonds, even those just as blue, have less boron. As it turns out one of the major uses of my hydrogen purifiers hydrogen these days is in the manufacture of gem -quality, and semiconductor diamonds, some blue and some other colors. So I thought I’d write about diamonds, colored and not, natural and CVD. It’s interesting and a sort of plug for my company, REB Research.

To start off, natural diamond are formed, over centuries by the effect of high temperature and pressure on a mix of carbon and a natural catalyst mineral, Kimberlite. Diamonds formed this way are generally cubic, relatively clear, and inert, hard, highly heat conductive, and completely non-conducting of electricity. Some man made diamonds are made this way too, using high pressure presses, but gem-quality and semiconductor diamonds are generally made by chemical vapor deposition, CVD. Colored diamonds are made this way too. They have all the properties of clear diamonds, but they have controlled additions and imperfections. Add enough boron, 1000 ppm for example, and the diamond and the resulting blue diamond can conduct electricity fairly readily.

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Seeds of natural diamond are placed in a diamond growth chamber and heated to about 1000°C in the presence of ionized, pure methane and hydrogen.

While natural diamond are sometimes used for technical applications, e.g. grind wheels, most technical-use diamonds are man-made by CVD, but the results tend to come out yellow. This was especially true in the early days of manufacture. CVD tends to make large, flat diamonds. This is very useful for heat sinks, and for diamond knives and manufacturers of these were among my first customers. To get a clear color, or to get high-quality colored diamonds, you need a mix of high purity methane and high purity hydrogen, and you need to avoid impurities of silica and the like from the diamond chamber. CVD is also used to make blue-conductive diamonds that can be used as semiconductors or electrodes. The process is show in the gif above from “brilliantearth”.

Multicolored diamonds made by CVD with many different dopants and treatments.

To make a CVD diamond, you place 15 to 30 seed- diamonds into a vacuum growth chamber with a flow of methane and hydrogen in ratio of 1:100 about. You heat the gas to about 1000°C (900-1200°C) , while ionizing the gas using microwaves or a hot wire. The diamonds grow epitaxially over the course of several days or weeks. Ionized hydrogen keeps the surface active, while preventing it from becoming carbonized — turning to graphite. If there isn’t enough hydrogen, you get grey, weak diamonds. If the gas isn’t pure, you get inclusions that make them appear yellow or brown. Nitrogen-impure diamonds are n-semiconductors, with a band gap greater than with boron-blue diamonds, 0.5-1 volts more. Because of this difference, nitrogen-impure diamonds absorb blue or green light, making them appear yellow, while blue diamonds absorb red light, making them blue. (This is different from the reason the sky is blue, explained here.) The difference in energy, also makes yellow diamonds poor electrical conductors. Natural, nitrogen-impure diamonds fluoresce blue or green, as one might expect, but yellow diamonds made by CVD fluoresce at longer wavelengths, reddish (I don’t know why).

The blue moon diamond, it is about as blue as the hope diamond though it has only 0.36 ppm of boron.

To make a higher-quality, yellow, n-type CVD diamonds, use very pure hydrogen. Bright yellow and green color is added by use of ppm-quantities of sulfur or phosphorus. Radiation damage also can be used to add color. Some CVD diamond makers use heat treatment to modify the color and reduce the amount of red fluorescence. CVD pink and purple diamonds are made by hydrogen doping, perhaps followed by heat treatment. The details are proprietary secrets.


Orange-red phosphorescence in the blue moon diamond.

Two major differences help experts distinguish between natural and man-made diamonds. One of these is the fluorescence, Most natural diamonds don’t fluoresce at all, and the ones that do (about 25%) fluoresce blue or green. Almost all CVD diamonds fluoresce orange-red because of nitrogen impurities that absorb blue lights. If you use very pure, nitrogen-free hydrogen, you get clear diamonds avoid much of the fluorescence and yellow. That’s why diamond folks come to us for hydrogen purifiers (and generators). There is a problem with blue diamonds, in that both natural and CVD-absorb and emit red light (that’s why they appear blue). Fortunately for diamond dealers, there is a slight difference in the red emission spectrum between natural and CVD blue diamonds. The natural ones show a mix of red and blue-green. Synthetic diamonds glow only red, typically at 660 nm.

Blue diamonds would be expected to fluoresce red, but instead they show a delayed red fluorescence called phosphorescence. That is to say, when exposed to light, they glow red and continue to glow for 10-30 seconds after the light is turned off. The decay time varies quite a lot, presumably due to differences in the n and p sites.

Natural diamond photographed between polarizers show patterns that radiate from impurities.

Natural and CVD also look different when placed between crossed polarizers. Natural diamonds show multiple direction stress bands, as at left, often radiating from inclusions. CVD diamonds show fine-grained patterns or none at all (they are not made under stress), and man-made, compression diamonds show an X-pattern that matches the press-design, or no pattern at all. If you are interested in hydrogen purifiers, or pure hydrogen generators, for this or any other purposes, please consider REB Research. If you are interested in buying a CVD diamond, there are many for sale, even from deBeers.

Robert Buxbaum, October 19, 2020. The Hope diamond was worn by three French kings, by at least one British king, and by Miss Piggy. A CVD version can be worn by you.

How not to make an atom bomb

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There are many books on how the atom bomb was made. They are histories of the great men who succeeded at site Y, Los Alamos, usually with a sidelight of the economics and politics in the US at the time. It’s sometimes noted that there was an equally great German group working too, and one in Japan and in Russia, that they didn’t succeed, but it’s rarely discussed what they did wrong. Nor does anyone make clear why so many US scholars were needed. What did all those great US minds to do? The design seems sort-of obvious; it appears in the note Einstein sent to Roosevelt, so what were all these people thinking about all that time, and why did the Germans fail? By way of answer, let me follow the German approach to this problem, an approach that won’t get you anywhere, or anywhere that I’ve seen.

It seems that everyone knew that making a bomb was possible, that it would be fearsomely powerful, and that it would be made using a chain reaction in uranium or plutonium. Everyone seems to have understood that there must be a critical mass: use less and there is no explosion, use more and there is one. The trick was how to bring enough uranium together make the thing go off, and as a beginning to that, there is the concept of “a barn.” A barn is a very small unit of area = 10−24 cm², and a typical atom has a cross-section of a few barns. Despite this, it is generally thought to be very easy to hit an atom at the nucleus, that is, at the right spot, as easy as hitting the board side of a barn (hence the name). The cross section of a uranium atom is 600 barnes at room temperature, or 6×10−22 cm². But each cubic centimeter of uranium holds .5 x 1023 atoms. Based on this, it comes out that a thermal neutron that enters a 1 cm cube of uranium has a virtual certainty of hitting an atom — there are 3 cm² of atoms in a 1 cm² box. You could hardly miss.

Each uranium atom gives off a lot of energy when hit with a neutron, but neutrons are hard to come by, so a practical bomb would have to involve a seed neutron that hits a uranium atom and releases two or more neutrons along with energy. The next neutron has to hit another nucleus, and it has to releases two or more. As it happens uranium atoms, when hit release on average 2.5 neutrons, so building a bomb seems awfully easy.

But things get more difficult as the neutron speeds get greater, and as the atoms of uranium get hotter. The cross-section of the uranium atom goes down as the temperature goes up. What’s more the uranium atoms start to move apart fast. The net result is that the bomb can blow itself apart before most of the uranium atoms are split. At high speed, the cross -section of a uranium atom decreases to about 5 barnes you thus need a fairly large ball of uranium if you expect that each neutron will hit something. So how do you deal with this. For their first bomb, the American scientists made a 5 kg (about) sphere of plutonium, a man-made uranium substitute, and compressed it with explosives. The explosion had to be symmetrical and very fast. Deciding how fast, and if the design would work required a room full of human “computers”. The German scientists, instead made flat plates of uranium and slowed the neutrons down using heavy water. The heavy water slowed the neutrons, and thus, increased the effective size of the uranium atoms. Though this design seems reasonable, I’m happy to say, it can not ever work well; long before the majority of the reaction takes place, the neutrons get hot, and the uranium atoms fly apart, and you get only a small fraction of the promised bang for your bomb.

How fast do you need to go to get things right? Assume you want to fusion 4 kg of uranium, or 1 x 1025 atoms. In that case, hitting atoms has to be repeated some 83 times. In tech terms, that will take 83 shakes (83 shakes of a lamb’s tail, as it were). This requires getting the ball compressed in the time it takes for a high speed neutron to go 83 x 3 cm= 250 cm. That would seem to require 1 x 10-7 seconds, impossibly fast, but it turns out, you can go somewhat slower. How much slower? It depends, and thus the need for the computers. And how much power do you get? Gram for gram, uranium releases about 10 million times more energy than TNT, but costs hardly more. That’s a lot of bang for the buck.

Robert Buxbaum, Mar 29, 2020.

Ladder on table, safe till it’s not.

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via GIFER

Two years ago I wrote about how to climb a ladder safely without fear. This fellow has no fear and has done the opposite. This fellow has chosen to put a ladder on a table to reach higher than he could otherwise. That table is on another table. At first things are going pretty well, but somewhere about ten steps up the ladder there is disaster. A ladder that held steadily, slips to the edge of the table, and then the table tips over. It’s just physics: the higher he climbs on the ladder the more the horizontal force. Eventually, the force is enough to move the table. He could have got up safely if he moved the tables closer to the wall or if he moved the ladder bottom further to the right on the top table. Either activity would have decreased the slip force, and thus the tendency for the table to tip.

Perhaps the following analysis will help. Lets assume that the ladder is 12.5′ long and sits against a ten foot ledge, with a base 7.5′ away from the wall. Now lets consider the torque and force balance at the bottom of the ladder. Torque is measured in foot-pounds, that is by the rotational product of force and distance. As the fellow climbs the ladder, his weight moves further to the right. This would increase the tendency for the ladder to rotate, but any rotation tendency is matched by force from the ledge. The force of the ledge gets higher the further up the ladder he goes. Let’s assume the ladder weighs 60 lbs and the fellow weighs 240 pounds. When the fellow has gone up ten feet up, he has moved over to the right by 7.5 feet, as the diagram shows. The weight of the man and the ladder produces a rotation torque on the bottom of 60 x 3.75 + 240 x 7.5 = 1925 foot pounds. This torque is combatted by a force of 1926 foot pounds provided by the ledge. Since the ladder is 12.5 feet long the force of the ledge is 1925/12.5 = 154 pounds, normal to the ladder. The effect of this 154 lbs of normal force is to push the ladder to the left by 123.2 lbs and to lift the ladder by 92.4lbs. It is this 123.2 pounds of sideways push force that will cause the ladder to slip.

The slip resistance at the bottom of the ladder equals the net weight times a coefficient of friction. The net weight here equals 60+240-92.4 = 217.6 lbs. Now lets assume that the coefficient of friction is 0.5. We’d find that the maximum friction force, the force available to stop a slip is 217.6 x 0.5 = 108.8 lbs. This is not equal to the horizontal push to prevent rotation, 123.2 lbs. The net result, depending on how you loot at things, is either that the ladder rotates to the right, or that the ladder slips to the left. It keeps slipping till, somewhere near the end of the table, the table tips over.

Force balance of man on ladder. Based on this, I will go through the slippage math in gruesome detail.

I occasionally do this sort of detailed physics; you might as well understand what you see in enough detail to be able to calculate what will happen. One take home from here is that it pays to have a ladder with rubber feet (my ladders do). That adds to the coefficient of friction at the bottom.

Robert Buxbaum, November 6, 2019.

Water Towers, usually a good thing.

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Most towns have at least one water tower. Oakland county, Michigan has four. When they are sized right, they serve several valuable purposes. They provide water in case of a power failure; they provide increased pressure in the morning when people use a lot of water showering etc.; and they allow a town to use smaller pumps and to pump with cheaper electricity, e.g. at night. If a town has no tower, all these benefits are gone, but a town can still have water. It’s also possible to have a situation that’s worse than nothing. My plan is to show, at the end of this essay, one of the ways that can happen. It involves thermodynamic properties of state i a situation where there is no expansion headspace or excess drain (most towers have both).

A typical water tower — spheroidal design. A tower of the dimensions shown would contain about 1/2 million gallons of water.

The typical tower stands at the highest point in the town, with the water level about 170 feet above street level. It’s usable volume should be about as much water as the town uses in a typical day. The reason for the height has to do with the operating pressure of most city-level water pipes. It’s about 75 psi and each foot of water “head” gives you about 0.43 psi. You want pressures about 75 psi for fire fighting, and to provide for folks in apartment buildings. If you have significantly higher pressures, you pay a cost in electricity, and you start losing a lot of water to leaks. These leaks should be avoided. They can undermine the roads and swallow houses. Bob Dadow estimates that, for our water system the leakage rate is between 15 and 25%.

Oakland county has four water towers with considerably less volume than the 130 million gallons per day that the county uses. I estimate that the South-east Oakland county tower, located near my home, contains, perhaps 2 million gallons. The other three towers are similar in size. Because our county’s towers are so undersized, we pay a lot for water, and our water pressure is typically quite low in the mornings. We also have regular pressure excursions and that leads to regular water-boil emergencies. In some parts of Oakland county this happens fairly often.

There are other reasons why a system like ours should have water towers with something more like one days’ water. Having a large water reserve means you can benefit from the fact that electric prices are the lowest at night. With a days’ volume, you can avoid running the pumps during high priced, day times. Oakland county loses this advantage. The other advantage to having a large volume is that it gives you more time to correct problems, e.g. in case of an electric outage or a cyber attack. Perhaps Oakland thinks that only one pump can be attacked at one time or that the entire electric grid will not go out at one time, but these are clearly false assumptions. A big system also means you can have pumps powered by solar cells or other renewable power. Renewable power is a good thing for reliability and air pollution avoidance. Given the benefits, you’d expect Oakland county would reward towns that add water towers, but they don’t, as best I can tell.

Here’s one way that a water column can cause problems. You really need those pressure reliefs.

Now for an example of the sort of things that can go wrong in a water tower with no expansion relief. Every stand-pipe is a small water tower, and since water itself is incompressible, it’s easy to see that a small expansion in the system could produce a large pressure rise. The law requires that every apartment hose water system has to have expansion relief to limit these increases; The water tower above had two forms of reliefs, a roof vent, and an overflow pipe, both high up so that pressure could be maintained. But you can easily imagine a plumber making a mistake and installing a stand pipe without an expansion relief. I show a system like that at left, a 1000 foot tall water pipe, within a skyscraper, with a pump at the bottom, and pipes leading off at the sides to various faucets.

Lets assume that the pressure at the top is 20 psi, the pressure at the bottom will be about 450 psi. The difference in pressure (430 psi) equals the weight of the water divided by the area of the pipe. Now let’s imagine that a bubble of air at the bottom of the pipe detaches and rises to the top of the pipe when all of the faucets are closed. Since air is compressible, while water is not, the pressure at the bubble will remain the same as the bubble rises. By the time the bubble reaches the top of the pipe, the pressure there will rise to 450 psi. Since water has weight, 430 psi worth, the pressure at the bottom will rise to 880 psi = 450 + 430. This is enough to damage pump and may blow the pipes as well. A scenario like this likely destroyed the New Horizon oil platform to deadly consequences. You really want those pressure reliefs, and you want a competent plumber / designer for any water system, even a small one.

Robert Buxbaum, September 28- October 6, 2019. I ran for water commissioner is 2016.

Let’s visit an earth-like planet: Trappist-1d

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According to Star Trek, Vulcans and Humans meet for the first time on April 5, 2063, near the town of Bozeman, Montana. It seems that Vulcan is a relatively nearby, earth-like planet with strongly humanoid inhabitants. It’s worthwhile to speculate why they are humanoid (alternatively, how likely is it that they are), and also worthwhile to figure out which planets we’d like to visit assuming we’re the ones who do the visiting.

First things first: It’s always assumed that life evolved on earth from scratch, as it were, but it is reasonably plausible that life was seeded here by some space-traveling species. Perhaps they came, looked around and left behind (intentionally or not) some blue-green algae, or perhaps some more advanced cells, or an insect or two. A billion or so years later, we’ve evolved into something that is reasonably similar to the visiting life-form. Alternately, perhaps we’d like to do the exploring, and even perhaps the settling. The Israelis are in the process of showing that low-cost space travel is a thing. Where do we want to go this century?

As it happens we know there are thousands of stars with planets nearby, but only one that we know that has reasonably earth-like planets reasonably near. This one planet circling star is Trappist-1, or more properly Trappist 1A. We don’t know which of the seven planets that orbit Trappist-1A is most earth-like, but we do know that there are at least seven planets, that they are all roughly earth size, that several have earth-like temperatures, and that all of these have water. We know all of this because the planetary paths of this star are aligned so that seven planets cross the star as seen from earth. We know their distances from their orbital times, and we know the latter from the shadows made as the planets transit. The radiation spectrum tells us there is water.

Trappist 1A is smaller than the sun, and colder than the sun, and 1 billion years older. It’s what is known as an ultra-cool dwarf. I’d be an ultra cool dwarf too, but I’m too tall. We can estimate the mass of the star and can measure its brightness. We then can calculate the temperatures on the planets based their distance from the star, something we determine as follows:

The gravitational force of a star, mass M, on a planet of mass, m,  is MmG/r2, where G is the gravitational constant, and r is the distance from the star to the planet. Since force = mass times acceleration, and the acceleration of a circular orbit is v2/r, we can say that, for these orbits (they look circular),

MmG/r2 = mv2/r = mω2r.

Here, v is the velocity of the planet and ω is its rotational velocity, ω = v/r. Eliminating m, we find that

r3 = MG/ω2.

Since we know G and ω, and we can estimate M (it’s 0.006 solar masses, we think), we have a can make good estimates of the distances of all seven planets from their various rotation speeds around the star, ω. We find that all of these planets are much closer to their star than we are to ours, so the their years are only a few days or weeks long.

We know that three planets have a temperatures reasonably close to earths, and we know that these three also have water based on observation of the absorption of light from their atmosphere as they pass in front of their star. To tell the temperature, we use our knowledge of how bright the star is (0.0052 times Sol), and our knowledge of the distance. As best we can tell, the following three of the Trappist-1 planets should have liquid surface water: Trappist 1c, d and e, the 2nd, 3rd and 4th planets from the star. With three planets to choose from, we can be fairly sure that at least one will be inhabitable by man somewhere in the planet.

The seven orbital times are in small-number ratios, suggesting that the orbits are linked into a so-called Laplace resonance-chain. For every two orbits of the outermost planet, the next one in completes three orbits, the next one completes four, followed by 6, 9 ,15, and 24. The simple whole number relationships between the periods are similar to the ratios between musical notes that produce pleasant and harmonic sounds as I discussed here. In the case of planets, resonant ratios keep the system stable. The most earth-like of the Trappist-1 planets is likely Trappist-1d, the third planet from the star. It’s iron-core, like earth, with water and a radius 1.043 times earth’s. It has an estimated average temperature of 19°C or 66°F. If there is oxygen, and if there is life there could well be, this planet will be very, very earth-like.

The temperature of the planet one in from this, Trappist-1c, is much warmer, we think on average, 62°C (143°F). Still, this is cool enough to have liquid water, and some plants live in volcanic pools on earth that are warmer than this. Besides this is an average, and we might the planet quite comfortable at the poles. The average temperature of the planet one out from this, Trappist-1e, is ice cold, -27°C (-17°F), an ice planet, it seems. Still, life can find a way. There is life on the poles of earth, and perhaps the plant was once warmer. Thus, any of these three might be the home to life, even humanoid life, or three-eyed, green men.

Visiting Trappist-1A won’t be easy, but it won’t be out-of hand impossible. The system is located about 39 light years away, which is far, but we already have a space ship heading out of the solar system, and we are developing better, and cheaper options all the time. The Israeli’s have a low cost, rocket heading to the moon. That is part of the minimal technology we’d want to visit a nearby star. You’d want to add enough rocket power to reach relativistic speeds. For a typical rocket this requires a fuel whose latent energy is on the order mc2. That turns out to be about 1 GeV/atomic mass. The only fuel that has such high power density is matter-antimatter annihilation, a propulsion system that might have time-reversal issues. A better option, I’d suggest is ion-propulsion with hydrogen atoms taken in during the journey, and ejected behind the rocket at 100 MeV energies by a cyclotron or bevatron. This system should work if the energy for the cyclotron comes from solar power. Perhaps this is the ion-drive of Star-Trek fame. To meet the Star-Trek’s made-up history, we’d have to meet up by April, 2063: forty-four years from now. If we leave today and reach near light speed by constant acceleration for a few of years, we could get there by then, but only as time is measured on the space-ship. At high speeds, time moves slower and space shrinks.

This planetary system is named Trappist-1 after the telescope used to discover it. It was the first system discovered by the 24 inch, 60 cm aperture, TRAnsiting Planets and PlanetesImals Small Telescope. This telescope is operated by The University of Liége, Belgium, and is located in Morocco. The reason most people have not heard of this work, I think, has to do with it being European science. Our news media does an awful job covering science, in my opinion, and a worse job covering Europe, or most anything outside the US. Finally, like the Israeli moon shot, this is a low-budget project, the work to date cost less than €2 million, or about US $2.3 million. Our media seems committed to the idea that only billions of dollars (or trillions) will do anything, and that the only people worth discussing are politicians. NASA’s budget today is about $6 billion, and its existence is barely mentioned.

The Trappist system appears to be about 1 billion years older than ours, by the way, so life there might be more advanced than ours, or it might have died out. And, for all we know, we’ll discover that the Trappist folks discover space travel, went on to colonize earth, and then died out. The star is located, just about exactly on the ecliptic, in the constellation Aquarius. This is an astrological sign associated with an expansion of human consciousness, and a revelation of truths. Let us hope that, in visiting Trappist, “peace will guide the planets and love will steer the stars”.

Robert Buxbaum, April 3, 2019. Science sources are: http://www.trappist.one. I was alerted to this star’s existence by an article in the Irish Times.

Great waves, small circles, and the spread of ideas.

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Simplified wave motion, GIf by Dan Russel (maybe? I think?).

The scientific method involves looking closely at things. Sometimes we look closely for a purpose — to make a better mouse-trap, say. But sometimes it’s just to understand what’s happening: to satisfy curiosity, to understand the way the world works, or to answer a child. Both motivations bring positive results, but there is a difference in how people honor the product of these motivations. Scientific knowledge developed for curiosity is considered better; it tends to become the model for social understanding, and for art and literature. Meanwhile, science developed for a purpose is considered suspect, and often that suspicion is valid. A surprising amount of our knowledge was developed for war: for the purpose of killing people, destroying things, and occupying lands.

Waves provide a wonderful example of science exploration that was developed mostly for curiosity, and so they have become models of social understanding and culture — far more so than the atom bomb and plague work discussed previously.

Waves appear magical: You poke a pond surface with a stick, and the influence of that poke travels, as if by magic, to all corners of the pond. Apparently the initial poke set off something, and that sets off something else, and we’ve come to use this as a model for cultural ideas. Any major change in music, art, or cultural thought is described as a wave (and not as a disease). The sense of wave is  that a small push occurs, and the impact travels across a continent and across an ocean. The Gifs above and below shows how this happens for the ordinary wave — the one with a peaked top. As shown, the bits of water do not move with the wave. Instead they just circulate in a small circle. The powerful waves that crosses an ocean are composed of many small circles of water rolling in the general direction of the wave. With ideas too, I think, one person can push a second, and that second a third, each acting in his or her own circle, and a powerful transmission of ideas results. Of course, for a big wave, you need a big circle, but maybe not in cases of reflection (reflected waves can add, sometimes very destructively).

simplified wave movement

In the figures I’ve shown, you will notice that the top of the circle always moves in the same direction as the top of the wave. If the wave moves to the right, the circle is clockwise. There are also Rayleigh waves. In these, the top of the wave is not peaked, but broad, with little indents between ripples. For Rayleigh wave the motion is not circular, but elliptical, and the top of the ellipse moves in the opposite direction to that of the wave. These waves go slower than the normal waves, but they are more destructive. Most of the damage of earthquakes is by the late-arriving Rayleigh waves.

If regular waves are related to fast-moving ideas, like rock n roll, Rayleigh waves might be related to slower-traveling, counter-intuitive ideas, paradigm shifts: Religions, chaos, entropy, feminism, or communism. Rayleigh waves are mostly seen in solids, and the destructive power of counter-intuitive ideas is mostly seen in rigid societies.

Then there are also pressure waves, like sound, and wiggle waves (transverse waves). Pressure waves travel the fastest, and work in both solids and liquids. Wiggle waves travel slower (and don’t travel in liquids). Both of these involve no circles at all, but just one bit of material pushing on its neighbor. I think the economy works this way: bouncing springs, for the most part. Life is made up of all of these, and life is good. The alternative to vibration, I should mention, is status. Status is a form of death. There is a certain sort of person who longs for nothing more than an unchanging, no-conflict world: one government and one leadership. Avoid such people.

Robert Buxbaum, February 10, 2019

Why the earth is magnetic with the north pole heading south.

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The magnetic north pole, also known as true north, has begun moving south. It had been moving toward the north pole thought the last century. It moved out of Canadian waters about 15 years ago, heading toward Russia. This year it passed as close to the North pole as it is likely to, and begun heading south (Das Vedanga, old friend). So this might be a good time to ask “why is it moving?” or better yet, “Why does it exist at all?” Sorry to say the Wikipedia page is little help here; what little they say looks very wrong. So I thought I’d do my thing and write an essay.

The motion of the magnetic (true) north pole over the last century; it's nearly at the north pole.

Migration of the magnetic (true) north pole over the last century; it’s at 8°N and just passed the North Pole.

Your first assumption of the cause of the earth’s magnetic field would involve ferromagnetism: the earth’s core is largely iron and nickel, two metals that permanent magnets. Although the earth’s core is very hot, far above the “Curie Temperature” where permanent magnets form, you might imagine that some small degree of magnetizability remains. You’d be sort of right here and sort of wrong; to see why, lets take a diversion into the Curie Temperature (Pierre Curie in this case) before presenting a better explanation.

The reason there is no magnetism above the Curie temperature is similar to the reason that you can’t have a plague outbreak or an atom bomb if R-naught is less than one. Imagine a magnet inside a pot of iron. The surrounding iron will dissipate some of the field because magnets are dipoles and the iron occupies space. Fixed dipole effects dissipate with a distance relation of r-4; induced dipoles with a relation r-6. The iron surrounding the magnet will also be magnetized to an extent that augments the original, but the degree of magnetization decreases with temperature. Above some critical temperature, the surrounding dissipates more than it adds and the effect is that the original magnetic effect will die out if the original magnet is removed. It’s the same way that plagues die out if enough people are immunized, discussed earlier.

The earth rotates, and the earth's surface is negatively charged. There is thus some room for internal currents.

The earth rotates, and the earth’s surface is negatively charged. There is thus some room for internal currents.

It seems that the earth’s magnetic field is electromagnetic; that is, it’s caused by a current of some sort. According to Wikipedia, the magnetic field of the earth is caused by electric currents in the molten iron and nickel of the earth’s core. While there is a likely current within the core, I suspect that the effect is small. Wikipedia provides no mechanism for this current, but the obvious one is based on the negative charge of the earth’s surface. If the charge on the surface is non-uniform, It is possible that the outer part of the earth’s core could become positively charged rather the way a capacitor charges. You’d expect some internal circulation of the liquid the metal of the core, as shown above – it’s similar to the induced flow of tornadoes — and that flow could induce a magnetic field. But internal circulation of the metallic core does not seem to be a likely mechanism of the earth’s field. One problem: the magnitude of the field created this way would be smaller than the one caused by rotation of the negatively charged surface of the earth, and it would be in the opposite direction. Besides, it is not clear that the interior of the planet has any charge at all: The normal expectation is for charge to distribute fairly uniformly on a spherical surface.

The TV series, NOVA presents a yet more unlikely mechanism: That motion of the liquid metal interior against the magnetic field of the earth increases the magnetic field. The motion of a metal in a magnetic field does indeed produce a field, but sorry to say, it’s in the opposing direction, something that should be obvious from conservation of energy.

The true cause of the earth’s magnet field, in my opinion, is the negative charge of the earth and its rotation. There is a near-equal and opposite charge of the atmosphere, and its rotation should produce a near-opposite magnetic field, but there appears to be enough difference to provide for the field we see. The cause for the charge on the planet might be due to solar wind or the ionization of cosmic rays. And I notice that the average speed of parts of the atmosphere exceeds that of the surface —  the jet-stream, but it seems clear to me that the magnetic field is not due to rotation of the jet stream because, if that were the cause, magnetic north would be magnetic south. (When positive charges rotate from west to east, as in the jet stream, the magnetic field created in a North magnetic pole a the North pole. But in fact the North magnetic pole is the South pole of a magnet — that’s why the N-side of compasses are attracted to it, so … the cause must be negative charge rotation. Or so it seems to me.  Supporting this view, I note that the magnet pole sometimes flips, north for south, but this is only following a slow decline in magnetic strength, and it never points toward a spot on the equator. I’m going to speculate that the flip occurs when the net charge reverses, thought it could also come when the speed or charge of the jet stream picks up. I note that the magnetic field of the earth varies through the 24 hour day, below.

The earth's magnetic strength varies regularly through the day.

The earth’s magnetic strength varies regularly through the day.

Although magnetic north is now heading south, I don’t expect it to flip any time soon. The magnetic strength has been decreasing by about 6.3% per century. If it continues at that rate (unlikely) it will be some 1600 years to the flip, and I expect that the decrease will probably slow. It would probably take a massive change in climate to change the charge or speed of the jet stream enough to reverse the magnetic poles. Interestingly though, the frequency of magnetic strength variation is 41,000 years, the same frequency as the changes in the planet’s tilt. And the 41,000 year cycle of changes in the planet’s tilt, as I’ve described, is related to ice ages.

Now for a little math. Assume there are 1 mol of excess electrons on a large sphere of the earth. That’s 96500 Coulombs of electrons, and the effective current caused by the earth’s rotation equals 96500/(24 x3600) = 1.1 Amp = i. The magnetic field strength, H =  i N µ/L where H is magnetizability field in oersteds, N is the number of turns, in this case 1, µ is the magnetizability. The magnetizability of air is 0.0125 meter-oersteds/ per ampere-turn, and that of a system with an iron core is about 200 times more, 2.5 meter-tesla/ampere-turn. L is a characteristic length of the electromagnet, and I’ll say that’s 10,000 km or 107 meters. As a net result, I calculate a magnetic strength of 2.75×10-7 Tesla, or .00275 Gauss. The magnet field of the earth is about 0.3 gauss, suggesting that about 100 mols of excess charge are involved in the earth’s field, assuming that my explanation and my math are correct.

At this point, I should mention that Venus has about 1/100 the magnetic field of the earth despite having a molten metallic core like the earth. It’s rotation time is 243 days. Jupiter, Saturn and Uranus have greater magnetic fields despite having no metallic cores — certainly no molten metallic cores (some theorize a core of solid, metallic hydrogen). The rotation time of all of these is faster than the earth’s.

Robert E. Buxbaum, February 3, 2019. I have two pet peeves here. One is that none of the popular science articles on the earth’s magnetic field bother to show math to back their claims. This is a growing problem in the literature; it robs science of science, and makes it into a political-correctness exercise where you are made to appreciate the political fashion of the writer. The other peeve, related to the above concerns the game it’s thoroughly confusing, and politically ego-driven. The gauss is the cgs unit of magnetic flux density, this unit is called G in Europe but B in the US or England. In the US we like to use the tesla T as an SI – mks units. One tesla equals 104 gauss. The oersted, H is the unit of magnetizing field. The unit is H and not O because the English call this unit the henry because Henry did important work in magnetism.  One ampere-turn per meter is equal to 4π x 10−3 oersted, a number I approximated to 0.125 above. But the above only refers to flux density; what about flux itself? The unit for magnetic flux is the weber, Wb in SI, or the maxwell, Mx in cgs. Of course, magnetic flux is nothing more than the integral of flux density over an area, so why not describe flux in ampere-meters or gauss-acres? It’s because Ampere was French and Gauss was German, I think.

Disease, atom bombs, and R-naught

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A key indicator of the speed and likelihood of a major disease outbreak is the number of people that each infected person is likely to infect. This infection number is called R-naught, or Ro; it is shown in the table below for several major plague diseases.

R-naught - communicability for several contagious diseases, CDC.

R-naught – infect-ability for several contagious diseases, CDC.

Of the diseases shown, measles is the most communicable, with an Ro of 12 to 18. In an unvaccinated population, one measles-infected person will infect 12- 18 others: his/her whole family and/ or most of his/her friends. After two weeks or so of incubation, each of the newly infected will infect another 12-18. Traveling this way, measles wiped out swaths of the American Indian population in just a few months. It was one of the major plagues that made America white.

While Measles is virtually gone today, Ebola, SARS, HIV, and Leprosy remain. They are far less communicable, and far less deadly, but there is no vaccine. Because they have a low Ro, outbreaks of these diseases move only slowly through a population with outbreaks that can last for years or decades.

To estimate of the total number of people infected, you can use R-naught and the incubation-transmission time as follows:

Ni = Row/wt

where Ni is the total number of people infected at any time after the initial outbreak, w is the number of weeks since the outbreak began, and wt is the average infection to transmission time in weeks.

For measles, wt is approximately 2 weeks. In the days before vaccine, Ro was about 15, as on the table, and

Ni = 15w/2.

In 2 weeks, there will be 15 measles infected people, in 4 weeks there will be 152, or 225, and in 6 generations, or 12 weeks, you’d expect to have 11.39 million. This is a real plague. The spread of measles would slow somewhat after a few weeks, as the infected more and more run into folks who are already infected or already immune. But even when the measles slowed, it still infected quite a lot faster than HIV, Leprosy, or SARS (SARS is a form of Influenza). Leprosy is particularly slow, having a low R-naught, and an infection-transmission time of about 20 years (10 years without symptoms!).

In America, more or less everyone is vaccinated for measles. Measles vaccine works, even if the benefits are oversold, mainly by reducing the effective value of Ro. The measles vaccine is claimed to be 93% effective, suggesting that only 7% of the people that an infected person meets are not immune. If the original value of Ro is 15, as above, the effect of immunization is to reduce the value Ro in the US today to effectively 15 x 0.07 = 1.05. We can still  have measles outbreaks, but only on a small-scale, with slow-moving outbreaks going through pockets of the less-immunized. The average measles-infected person will infect only one other person, if that. The expectation is that an outbreak will be captured by the CDC before it can do much harm.

Short of a vaccine, the best we can do to stop droplet-spread diseases, like SARS, Leprosy, or Ebola is by way of a face mask. Those are worn in Hong Kong and Singapore, but have yet to become acceptable in the USA. It is a low-tech way to reduce Ro to a value below 1.0, — if R-naught is below 1.0, the disease dies out on its own. With HIV, the main way the spread was stopped was by condoms — the same, low tech solution, applied to sexually transmitted disease.

Image from VCE Physics, https://sites.google.com/site/coyleysvcephysics/home/unit-2/optional-studies/26-how-do-fusion-and-fission-compare-as-viable-nuclear-energy-power-sources/fission-and-fusion---lesson-2/chain-reactions-with-dominoes

Progress of an Atom bomb going off. Image from VCE Physics, visit here

As it happens, the explosion of an atom bomb follows the same path as the spread of disease. One neutron appears out of somewhere, and splits a uranium or plutonium atom. Each atom produces two or three more neutrons, so that we might think that R-naught = 2.5, approximately. For a bomb, Ro is found to be a bit lower because we are only interested in fast-released neutrons, and because some neutrons are lost. For a well-designed bomb, it’s OK to say that Ro is about 2.

The progress of a bomb going off will follow the same math as above:

Nn = Rot/nt

where Nn is the total number of neutrons at any time, t is the average number of nanoseconds since the first neutron hit, and nt is the transmission time — the time it takes between when a neuron is given off and absorbed, in nanoseconds.

Assuming an average neutron speed of 13 million m/s, and an average travel distance for neutrons of about 0.1 m, the time between interactions comes out to about 8 billionths of a second — 8 ns. From this, we find the number of neutrons is:

Nn = 2t/8, where t is time measured in nanoseconds (billionths of a second). Since 1 kg of uranium contains about 2 x 1024 atoms, a well-designed A-bomb that contains 1 kg, should take about 83 generations (283 = 1024). If each generation is 8 ns, as above, the explosion should take about 0.664 milliseconds to consume 100% of the fuel. The fission power of each Uranium atom is about 210 MeV, suggesting that this 1 kg bomb could release 16 billion Kcal, or as much explosive energy as 16 kTons of TNT, about the explosive power of the Nagasaki bomb (There are about 38 x10-24 Kcal/eV).

As with disease, this calculation is a bit misleading about the ease of designing a working atomic bomb. Ro starts to get lower after a significant faction of the atoms are split. The atoms begin to move away from each other, and some of the atoms become immune. Once split, the daughter nuclei continue to absorb neutrons without giving off either neutrons or energy. The net result is that an increased fraction of neutrons that are lost to space, and the explosion dies off long before the full power is released.

Computers are very helpful in the analysis of bombs and plagues, as are smart people. The Manhattan project scientists got it right on the first try. They had only rudimentary computers but lots of smart people. Even so, they seem to have gotten an efficiency of about 15%. The North Koreans, with better computers and fewer smart people took 5 tries to reach this level of competence (analyzed here). They are now in the process of developing germ-warfare — directed plagues. As a warning to them, just as it’s very hard to get things right with A-bombs, it’s very hard to get it right with disease; people might start wearing masks, or drinking bottled water, or the CDC could develop a vaccine. The danger, if you get it wrong is the same as with atom bombs: the US will not take this sort of attack lying down.

Robert Buxbaum, January 18, 2019. One of my favorite authors, Issac Asimov, died of AIDS; a slow-moving plague that he contacted from a transfusion. I benefitted vastly from Isaac Asimov’s science and science fiction, but he wrote on virtually every topic. My aim is essays that are sort-of like his, but more mathematical.

Of God and gauge blocks

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Most scientists are religious on some level. There’s clear evidence for a big bang, and thus for a God-of-Creation. But the creation event is so distant and huge that no personal God is implied. I’d like to suggest that the God of creation is close by and as a beginning to this, I’d like to discus Johansson gauge blocks, the standard tool used to measure machine parts accurately.

jo4

A pair of Johansson blocks supporting 100 kg in a 1917 demonstration. This is 33 times atmospheric pressure, about 470 psi.

Lets say you’re making a complicated piece of commercial machinery, a car engine for example. Generally you’ll need to make many parts in several different shops using several different machines. If you want to be sure the parts will fit together, a representative number of each part must be checked for dimensional accuracy in several places. An accuracy requirement of 0.01 mm is not uncommon. How would you do this? The way it’s been done, at least since the days of Henry Ford, is to mount the parts to a flat surface and use a feeler gauge to compare the heights of the parts to the height of stacks of precisely manufactured gauge blocks. Called Johansson gauge blocks after the inventor and original manufacturer, Henrik Johansson, the blocks are typically made of steel, 1.35″ wide by .35″ thick (0.47 in2 surface), and of various heights. Different height blocks can be stacked to produce any desired height in multiples of 0.01 mm. To give accuracy to the measurements, the blocks must be manufactured flat to within 1/10000 of a millimeter. This is 0.1µ, or about 1/5 the wavelength of visible light. At this degree of flatness an amazing thing is seen to happen: Jo blocks stick together when stacked with a force of 100 kg (220 pounds) or more, an effect called, “wringing.” See picture at right from a 1917 advertising demonstration.

This 220 lbs of force measured in the picture suggests an invisible pressure of 470 psi at least that holds the blocks together (220 lbs/0.47 in2 = 470 psi). This is 32 times the pressure of the atmosphere. It is independent of air, or temperature, or the metal used to make the blocks. Since pressure times volume equals energy, and this pressure can be thought of as a vacuum energy density arising “out of the nothingness.” We find that each cubic foot of space between the blocks contains, 470 foot-lbs of energy. This is the equivalent of 0.9 kWh per cubic meter, energy you can not see, but you can feel. That is a lot of energy in the nothingness, but the energy (and the pressure) get larger the flatter you make the surfaces, or the closer together you bring them together. This is an odd observation since, generally get more dense the smaller you divide them. Clean metal surfaces that are flat enough will weld together without the need for heat, a trick we have used in the manufacture of purifiers.

A standard way to think of quantum scattering is that the particle is scattered by invisible bits of light (virtual photons), the wavy lines. In this view, the force that pushes two flat surfaces together is from a slight deficiency in the amount of invisible light in the small space between them.

A standard way to think of quantum scattering of an atom (solid line) is that it is scattered by invisible bits of light, virtual photons (the wavy lines). In this view, the force that pushes two blocks together comes from a slight deficiency in the number of virtual photons in the small space between the blocks.

The empty space between two flat surfaces also has the power to scatter light or atoms that pass between them. This scattering is seen even in vacuum at zero degrees Kelvin, absolute zero. Somehow the light or atoms picks up energy, “out of the nothingness,” and shoots up or down. It’s a “quantum effect,” and after a while physics students forget how odd it is for energy to come out of nothing. Not only do students stop wondering about where the energy comes from, they stop wondering why it is that the scattering energy gets bigger the closer you bring the surfaces. With Johansson block sticking and with quantum scattering, the energy density gets higher the closer the surface, and this is accepted as normal, just Heisenberg’s uncertainly in two contexts. You can calculate the force from the zero-point energy of vacuum, but you must add a relativistic wrinkle: the distance between two surfaces shrinks the faster you move according to relativity, but measurable force should not. A calculation of the force that includes both quantum mechanics and relativity was derived by Hendrik Casimir:

Energy per volume = P = F/A = πhc/ 480 L4,

where P is pressure, F is force, A is area, h is plank’s quantum constant, 6.63×10−34 Js, c is the speed of light, 3×108 m/s, and L is the distance between the plates, m. Experiments have been found to match the above prediction to within 2%, experimental error, but the energy density this implies is huge, especially when L is small, the equation must apply down to plank lengths, 1.6×10-35 m. Even at the size of an atom, 1×10-10m, the amount of the energy you can see is 3.6 GWhr/m3, 3.6 Giga Watts. 3.6 GigaWatt hrs is one hour’s energy output of three to four large nuclear plants. We see only a tiny portion of the Plank-length vacuum energy when we stick Johansson gauge blocks together, but the rest is there, near invisible, in every bit of empty space. The implication of this enormous energy remains baffling in any analysis. I see it as an indication that God is everywhere, exceedingly powerful, filling the universe, and holding everything together. Take a look, and come to your own conclusions.

As a homiletic, it seems to me that God likes friendship, but does not desire shaman, folks to stand between man and Him. Why do I say that? The huge force-energy between plates brings them together, but scatters anything that goes between. And now you know something about nothing.

Robert Buxbaum, November 7, 2018. Physics references: H. B. G. Casimir and D. Polder. The Influence of Retardation on the London-van der Waals Forces. Phys. Rev. 73, 360 (1948).
S. Lamoreaux, Phys. Rev. Lett. 78, 5 (1996).