Everyday quantum physics

Modern engineering more and more deals with photons one at a time. A photon is a packet, or quantum, of electromagnetic energy. As such it obeys quantum physics, which can seem rather strange compared to Newtonian physics. I'd like to examine the everyday effects of quantum physics as exemplified in a standard red light photon. The standard photon was chosen because it can be produced by a Helium-Neon laser, an easy to make tool which puts out only the standard photons, nothing else.
This standard red photon is exactly 632.99 nanometers long and has an energy of 1.959 electron-volts. This gets us immediately into quantum effects.

Size and energy work backwards here. A photon of twice the energy - 4 electron-volts - has half the wavelength, 315 nM. This is uv-b (ultraviolet-b) radiation, energetic enough to tan you, or do skin damage. Shorter wavelengths are x-rays, with energy to go clear through you. A photon of twice the wavelength of our standard red one is infrared, and has half the energy.

As a quantum, a photon is an all or nothing thing. The photon either interacts, delivering all of its energy, or it does not, and it keeps all of its energy. A photon 670nM long, with slightly less energy than our standard one, will interact with a chlorophyll-a molecule and deliver its energy to a single electron. The standard photon does NOT energize the electron with a little left over, it just bounces off the chlorophyll molecule and delivers no energy at all.

Atoms are much smaller than our standard photon. A hydrogen atom is about 0.1 nM in diameter. When an electron inside an atom jumps to emit the standard photon, what comes out is over 5000 times the size of the atom emitting it. This makes where and when it comes up extremely uncertain when compared to the atom itself. When a red light photon is absorbed by chlorophyll, all of its energy is suddenly crammed into a space less than 1/5000th its size. The photon has to hit just right to do this, resulting in uncertainty in when and whether it interacts. We can only deal with these uncertainties in the mathematics of probability, called statistical quantum mechanics. As discussed in an earlier post, nobody has a feel for statistics, so where and when photon-matter interactions occur can produce some big surprises.

In summary, a photon is a quantum of energy that has all-or-nothing interactions. While the smaller they are, the larger their energy, they are much larger than the matter they interact with, so their interactions are probabilistic.

Human dominance of biology

Many people suffer from the false image of a vast 'natural' world compared to a miniscule human influence. This is the reverse of the actual situation. The sun is the primary natural source of energy and variability, but it changes slowly. The overwhelming human influence on the planet is due to our success as a species and our ability to manipulate energy which have, in the last 200 years or so, yielded a large-animal population - us - at least 5 times larger than any previous species bigger than a cat has achieved. The only times the planet's biosphere has seen this rapid a change in the past have involved cataclysmic events like large meteor strikes.

Humans, at 6 plus billion and rising, are the commonest large animals on the planet. The next most commmon mammals are domestic livestock that total another 3 billion or so. Even pets, at 50 million dogs and 70 million cats in North America greatly outnumber the whitetail deer, the commonest large wild mammal at 15 million.
The total wild waterfowl population of North America is 70 million birds. North American poultry production is 14 million tons per year - over 100x as much. We, with our livestock, are overwhelmingly the large animal population of the world. We will thus overwhelm all other large animals in our influence on the world.

Since animals eat plants, it shouldn't be a surprise that the majority of land vegetation is planted and harvested by humans. Something that really brings this home, though, is the animation of primary production available at http://earthobservatory.nasa.gov/Newsroom/NPP/Images/npp_20012002_sm.mpg

Rainfall gets used for agriculture, manufacturing, and to wash down our habitation areas. All non-human usage combined about equals these totals. http://www.globalchange.umich.edu/globalchange2/current/lectures/freshwater_supply/freshwater.html

We are the dominant large animal life, the dominant plant life user, and the single largest users of fresh water. In addition we control energy out of proportion to other animal usage- several horsepower per person. Total CO2 output now providing this energy overwhelms natural sources,but to look at the energy itself take a look at the night sky view at
http://images.google.com/imgres?imgurl=http://www.phoenix5.org/gallery/earthlightsFull.jpg&imgrefurl=http://www.phoenix5.org/gallery/earthlights1500.html&h=296&w=591&sz=18&tbnid=VEumcq6aKN4J:&tbnh=66&tbnw=131&start=14&prev=/images%3Fq%3Dearth%2Bat%2Bnight%26hl%3Den%26lr%3D%26sa%3DG
and realize that this light is just wasteage from a small portion of our energy usage.

What we do, as the overwhelming variable in present-day earth's environment, is the most influencial factor in the world we will live in. Since no projection of earth's human population shows it as dropping, our influence will continue to be overwhelming for the forseeable future. The world is not human habitation spotted through a wilderness. It is cities, suburbs, farms and ranches with occasional parklands.

Human influence on atmospheric CO2

This will be an evaluation of how much CO2 humans put into the atmosphere, showing how easily obtainable facts and a little math can dispel a lot of superstition. I strongly urge you to go through the calculations yourself.

How much CO2 is in the atmosphere?
as of the year 1800, about 280 ppm (parts per million), as of 2000, about 370 ppm http://earthguide.ucsd.edu/globalchange/keeling_curve/01.html
How much is that? Here we can take advantage of a couple of neat tricks. First, as we know from barometric pressure, the atmosphere over our heads weighs as much as a column of water 10 meters deep, so the atmosphere weighs the same as a layer of water 10 meters deep covering the earth. Second, the kilometer was originally defined as 1/10,000 of the distance from the equator to the pole, so figuring earth's area uses simple numbers that are easy to remember. Finally, a cubic meter of water weighs a metric tonne. Do the math and you find that the atmosphere weighs 5.03*10e15 tonnes. Times 370 parts per million means there were 1.87*10e12 tonnes of CO2 in the atmosphere as of the year 2000.
Since fossil fuels are mostly carbon, this amount is usually expressed by its carbon content. With carbon having an atomic weight of 12 and oxygen 16, the carbon content of CO2 is 12/44 of this total or 510 billion tonnes of carbon in the atmosphere as CO2.
how much are we putting in?
I always go to the CIA factbook first for geopolitical and economic data
http://odci.gov/cia/publications/factbook/index.html
gives oil and natural gas production , at 75 million barrels/day and 2.6 trillion cubic meters/year
http://www.eppo.go.th/ref/UNIT-OIL.html gives conversions, so oil is 3750 million tonnes/year, and natural gas is 2300 million tonnes/year. Natural gas (CH4) is 3/4 carbon, while oil is about 11/13, so the carbon content is 3190 and 1750 respectively for a total of 4940 million tons of carbon a year from oil and natural gas.
http://www.eia.doe.gov/emeu/aer/txt/ptb1114.html gives coal at 5227 million short tons/year or about 4700 tonnes. Using an average carbon content of 50% this is 2350 million tonnes
Total carbon usage, then, is just over 7.300 billion tonnes per year as of 2001.
According to these back-of-the-envelope calculations, we're putting out CO2 equal to about 1.4% of the atmospheric total every year, and this has increased the total in the atmosphere by a little over 1/3 since the industrial revolution.

Simple history of the universe

Everything, including the spaces between that we now see in a sphere 13.7 billion light-years across was contained in a pinpoint 13.7 billion years ago. As far as we can tell, it wasn't all there was, and the rest of what there was was similarly compressed. This superhot pinpoint expanded and cooled through exotic states until about 700,000 years after the big bang, where matter had condensed out and energy was low enough for atoms to form. At this point the universe became transparent with a temperature of 3000 kelvins. It was cool enough for matter and physics as we know it today to happen, with most of the energy in the universe transformed into atoms of hydrogen and helium. The leftover 3000k thermal radiation wavelength stretched along with the universe, and we see the leftover as the cosmic background radiation at about 3 kelvin today. In addition to this normal matter and energy, there seems to be dark mass, which interacts gravitationally equally to normal matter but which we haven't seen except for gravitational effects that indicate that it's about 90% of the known universe, and dark energy, that seems to be associated with how big space has gotten.
In normal and dark matter, gravity causes clumping, forming stars when the hydrogen eventually falls together tightly enough to light off a fusion reaction because of the gravitational packing and heating. This fusion reaction can produce all the light elements. If a big enough star is formed, a supernova can result in higher grade fusion that can almost instantaneously form all of the heavier elements.
Later stars in the aggregations called galaxies sweep up the remnants of earlier explosions and you get something like the solar system.
In solar systems, most of the matter clumps into the star, which lights off your fusion furnace. In our solar system this happened about 4.5 billion years ago. The rest of the matter condenses into planets and smaller pieces. These get cold enough for chemistry to happen. In at least one case, life has resulted.

Sir Arthur's magic orbit

As objects in space get further from the mass they are orbiting around, the orbit takes longer. The space shuttle and other objects in low earth orbit, can go around in about 90 minutes. The moon takes about a month to complete an orbit. Arthur C. Clarke, author of "2001, a Space Odyssey" noticed clear back in 1945 that we could take advantage of this fact to do a few special things with satellites. He noted that in an orbit at about 35,800 kilometers out a satellite would take 24 hours to go around the earth. Since the earth rotates in 24 hours, a satellite in orbit in the equatorial plane would appear to be stationary in the sky. This is the geosynchronous or Clarke orbit. If a satellite is in such an orbit a very narrowly focused telescope or antenna can be pointed at it without it leaving the field of view. You can use a lot of magnification, or antenna gain, because the satellite appears to stay put. The small carefully pointed antenna dishes used for direct-from-satellite TV work on this principle.
The orbit must be in exactly the equatorial plane or the satellite will appear to bob up and down, so the limited number of parking spots in Clarke orbit are extremely valuable and regulated by treaty. In addition the satellites aren't visible from polar areas due to the bulge of the earth getting in the way. In spite of these minor drawbacks, use of the Clarke orbit has brought worldwide wireless telephony, global data linkage for business, educational programming to poor rural areas worldwide and allowed millions of people to access programs their governments would prefer to censor, in general furthering communication and knowledge throughout the world.

This is magical enough, but recent advances in materials technology have generated new interest in an even more miraculous use that Clarke thought up for geosynchronous orbit. Take a satellite in geosynch orbit. Build towers below and above it, so that its center of mass stays at geosynch. The portion below center is traveling slower than orbital speed, so it tends to fall, pulling down. The portion above center is going faster than orbital speed and tends to fly outward. The system is stable, and is loaded in pure tension, so we can replace the towers with cables and it will remain 'tidally locked' in a straight line perpendicular to the orbit. We can even extend the bottom cable all the way to the surface of the earth, where it will have zero speed relative to the ground. If we anchor the bottom and add a little extra weight on the outer end we have a skyhook, or orbital elevator. We can grab onto the cable and pull ourselves upward to orbit for only the energy cost of doing so - pennies per pound instead of tens of thousands of dollars.!
The catch is that the cable has to be able to support its own weight. The best steel, for example, will break when you hang a vertical length of only 50 kilometers, far short of what we need. When Clarke used this idea in the science fiction novel "The Fountains of Paradise" he envisioned it as being built of diamond, the strongest material then known, and even then had to taper the cable severely - very fat at geosynch, tapering almost to a point at the ends. Constructing and setting the cable would be a nightmare, even if we could make that much diamond. Since a Mars-synchronous orbit requires 24 hours 40 minutes at an altitude of only 20,460 kilometers in the weaker Martian gravity field, it would actually be easier to build a skyhook for Mars than Earth.
We have recently invented a new form of carbon, the nanotube. This is a hollow filament only 10 atoms or so across, but capable of being made in macroscopic lengths. This material has awesomely better strength-to-weight than even diamond -so much better that a film less than a millimeter thick and tapering from 1/3 meter to only a meter wide could span earth-to-Clarke orbit and carry useful loads! There seems to be no reason we can't learn to make nanotubes in the quantities required, and we have boosters capable of carrying an entire skyhook like this to orbit, where we could simply unreel it.
There are people seriously planning on doing this in less than 20 years. The result will be an advance in space travel comparable to having replaced Columbus's ships within 100 years with a 6-lane freeway bridge across the Atlantic.
This seems a good point to introduce another idea that Sir Arthur C. Clarke thought up, known as Clarke's third law:

ANY sufficiently advanced technology is indistinguishable from magic.

Really simple evolution model

Evolution requires something that can almost perfectly copy itself. Adaptation requires a way for those copies to interact with their surroundings that affects their ability to make more copies. Given these conditions, evolution and adaptation are inevitable. You can prove it with a game requiring only a sheet of lined paper, a pen or pencil, and a coin. Here are the rules:
1) drawing is freehand.
2) draw two circles on the first line, approximately the same size.
3) flip the coin.
a) if it comes up heads, each circle gets one copy , as exact as you can draw it, on the next line.
b) if it's tails, the least circular (by eyeball) gets two copies of itself, mistakes and all, as exact as you can draw them, on the next line. The other(s) get one.
4) repeat.
5)Watch how quickly you evolve something that doesn't look at all like a circle. Rule 3b is an adaptation that yields reproductive advantage. Without rule 3b you will still evolve things that don't look like circles, but not as fast, and they won't crowd the line so much. If we replace rule 3 with a rule that says when the line gets full eliminate those copies that look most like circles there is a survival advantage. The combination will evolve faster than either alone.
This is an absurdly simple system where the figure can't even make a copy without you helping. Still, it evolves.
If you would like to get a better appreciation of how evolution works, there are many computer simulations that involve 'genes', 'competition', even 'sex' in addition to adaptation to modify evolution. http://www.alcyone.com/max/links/alife.html contains a number of fascinating links for simulated and computational evolution, at levels from grade school to cutting edge research.
Competitive advantage, 'survival of the fittest' , complex organisms, even life itself, are all results of evolution and adaptation that are frequently mistaken for necessary parts of the process. The discovery that much of our DNA is evolutionarily neutral, just 'along for the ride', was probably held back for quite some time because of our focus on 'survival of the fittest' and adaptive significance. We have evolved both straight and naturally curly hair, but neither is of any particular survival significance. If they were, adaptation would cause one to crowd out the other. Focusing on the simple model helps us remember that evolution does not have to follow our logic, we use our logic to find out what evolution does.

Statistics - NOT in simple models.

Statistics have no place in simple models because NOBODY has a 'feel' for statistics . We can illustrate this with a really simple statistical system, the coin flip. An honest coin gives 50-50 odds on each flip - either heads or tails. Consider though, what happens if we get 10 heads in a row. If they are betting, most people will shift their bet to tails, with the feeling that the coin has to come up tails more often in the next few flips to 'even things out'. In a trial of several thousand flips, though, you can expect 10 in a row of either heads or tails to occur multiple times. What has gone before has absolutely no effect on the current flip. The odds remain 50-50, but our feelings about the odds vary dramatically, even when we know they don't change.
Good statisticians know that expectations can influence not only our perception of the odds but even the way we report the events. This is why they go to extreme measures to set up 'double-blind' experiments, so the experimenters and the subjects don't know what to expect.
Feynman illustrated another problem with statistics, that of remembering only 'significant' results. His line was approximately:
"On the way in from the parking lot today I noticed the license plate ABR165. Now, consider the odds that THAT particular license would be there today. It's over 10 million to one!"
The point was that the license had to have SOMETHING on it. If we consider it significant, we note it and say "wow !" and otherwise we don't notice it. We never remember when we have a premonition that a phone call will be bad news about a relative and it turns out to be a telemarketer.
We set up simple models to force ourselves to look at what is actually happening without fooling ourselves. Statistics are an extremely powerful tool for checking reality, but the probability of self-delusion is so high that they are most useful in disproving a simple model, rather than setting one up.