Artificial aliens?

 kw: book reviews, nonfiction, science, biology, physics, cosmology, genetics, first contact

To put Sara Imari Walker's last question first, will first contact with a true alien occur in a laboratory? Dr. Walker's book Life as No One Knows It: The Physics of Life's Emergence is a heady brew of ideas. She has a wonderful kind of mind that looks at things from angles others would never imagine existed, and she has managed to find a number of kindred souls with a similar talent.

Dr. Walker and her colleagues propose Assembly Theory, a new view of evolution in which technology has become an agent of evolutionary change, and "selection" takes on a meaning that would mightily bemuse Darwin. Her explanations make sense. I don't yet understand enough about assembly theory to attempt an explanation. I must content myself with a few bullet points gleaned from the third chapter ("Life is what?"; intended to be pronounced with a distinct upward lilt, as, "Life is WHAT??"). These items do not describe life, but rather objects. Objects as the new theory envisions them:

• Objects are finite and distinguishable
• Objects are breakable (I would have said, "can be disassembled")
• Objects exist more than once
• Objects are lineages
• Objects form via selection

Some objects are living things. Some are not. A wooden table of the kind I built long ago to hold my mouse pad next to my desk is an example. I constructed it using nine pieces of wood, eight large wood screws, 24 small nails, and some glue. The top is plywood, which itself was fabricated by someone else before I bought it from a lumberyard and cut it to size. We can inventory the statements. 

• My little mouse-pad table is finite (less than a meter tall) and is distinct from other items of furniture in this room, some purchased (and thus built by someone else) and others built here, by me.
• It can be taken apart, by removing the fasteners and breaking the glue joints (no doubt tearing wood in the process). I don't plan to do so.
• I have made other similar tables, which I suppose qualifies at "exists more than once." Worldwide, there are many tables of many designs, but all related in general shape and function.
• Is it a lineage? The idea of "table", generalized from "supporting platform" is certainly a lineage, going back to the first table or table-like platform built by a human or prehuman creature.
• "Selection" in such a case means that the I selected to make a table rather than a cantilevered shelf hung off my desk, or other possible means of supporting my mouse pad.

Consider a screwdriver. The author writes, "An evolutionary chain of objects is necessary to assemble screwdrivers into existence." In other words, the forebears of screwdrivers include machine shops, mining and metals productions facilities, and creatures like us to think them up. In the case of living things, the "lineage" of everything alive today goes back about 3.9 billion years. All known life comes from life. What came before?

This is the crux of the matter for assembly theory. The theorists use these concepts to imagine life as we don't know it, life as no one knows it.

Side question: Can objects be produced by other objects that are not living? They can, which is apparently where all nonliving and never-previously-living things arose. For example, a planet such as Earth was assembled from dust, rocks, etc., under the influence of gravity and electromagnetism and sundry other possible forces. Also, natural, nonliving actions produce raindrops and snowflakes in clouds, sand and gravel from rocks, and so forth. 

However, the production of objects by nonliving processes yields objects with very few unique parts. Living objects tend to be much more complex, as do many of their products. Thus this conjecture, stated at least a couple of times in the book, "Life is the only thing in the universe that can make objects with many unique parts." The author notes that many kinds of minerals don't form in the absence of life. I recall taking a class in minerology, in which the professor stated, "There are about 1,000 mineral species known in the earliest rocks, before there was much life on Earth. There are now more than 4,000 minerals, and most of them can only form because there is life on Earth." Today the number of catalogued minerals is almost 7,000, and that may grow to more than 10,000 as busy geologists keep finding new stuff.

This principle yields the basis of the author's "assembly index", a measure of the minimum number of steps needed to produce an object. This gets us away from looking for life that is too chemically similar to "Earthlings" (from microbes and viruses to whales and forests, with us in the mid-range). If the assembly index of numerous objects collected on an exoplanet is large enough, we could conclude that life most likely produced them. The critical number is, according to the author, fifteen.

Frankly, I don't know how assembly index is calculated. I read that the assembly index of the molecule ATP is fifteen. This molecule has 47 atoms. Perhaps the calculation allows the synthesis to begin with smaller molecules that natural processes have already produced: water, carbon dioxide, ammonia, phosphorus oxide, and perhaps even small hydrocarbons such as ethane (ethane can result from abiotic, or nonliving, processes, but in the presence of a living biosphere we never observe it).

Therefore, the number 15 seems to be a good "filter" to discern objects produced by life.

A second prong in the approach by proponents of assembly theory is the development of a "chemputer", a semi-automated way to sort of "3d print" molecules, designed to have certain properties, in an attempt to produce a chemical system that takes on the attributes of life: reproduction, ingestion of supplies, elimination of wastes, relationships (very broadly construed), for example. Were such an effort to succeed, using large numbers of chemputers to explore the "assembly space" of small-to-medium sized molecules, there might indeed be alien life produced in the laboratory. It would be as alien as anything we might find on a planet far away, perhaps even more so. 

The key to grasping assembly theory is the claim that all things life can build are historically contingent. We can see this in the visible relatedness between the wide range of animals known as "tetrapods". They all have four limbs. The mythical flying horse Pegasus cannot evolve from a horse, because to do so would require adding two new limbs (to become wings) to a body that already works well with four limbs. The intermediate steps required don't make sense (and let's ignore the physics of wings long enough to support a half-ton animal). In fact, mammalian hexapods in general aren't likely to arise, because the competition from extremely well-adapted tetrapods has already pretty much filled all available ecological niches for critters bigger than a cockroach…on land, at least.

Historical contingency is a key concept. Finger-and-toenails didn't evolve all at once. They descended from claws. Claws came from something else. All living things trace back to a single-celled creature called LUCA, the Last Universal Common Ancestor. LUCA may not be the first cell. At one time other living things could have existed alongside LUCA that may have had quite different chemistry and cellular mechanisms. But only LUCA has descendants: us, and every living thing in the biosphere of Earth.

Our chain of imagined forebears stops with LUCA. Our knowledge is further constrained, because it is extremely unlikely that any creature now living is descended without change from LUCA. When I say "extremely unlikely", that middle E needs to be drawn out, "Extreeeeeeeeeeeemely!" Meaning, utterly impossible unless the universe is truly infinite, with an infinite number, not just of planets, but of biospheres. Even if we somehow track back the chain of biochemical contingency to "show" us a robust model of LUCA, the chain stops there.

I like the idea of the chemputer. But I don't hold out much hope. The assembly space of "small molecules" is too big. For example, if we "restrict" ourselves to the twenty most common elements, all of which are found in known life, and all of which are likely to be in any possible kind of life, and further, we call a molecule "small" if it has fifty or fewer atoms (just a tad bigger than ATP), the number of possible chemical species (most of them quite chemically unstable) is close to ten-to-the-power-of-65. A 66-digit integer. How large is that number? The number of stars in the visible universe is thought to be a 22- or 23-digit number. Could the average number of planets be as great as ten? Even if that were so, the number of planets in all the galaxies in the visible universe is no larger than the largest 24-digit number. It is hard to think about 66-digit numbers in any useful way. 

Dr. Walker dreams of being the researcher in the cartoon above, "meeting" the first true alien in the laboratory. I hope her dream comes true. But I think it more likely that we'll come across something, somewhere, soon, that proves life as we don't yet know it does in fact exist.

Magic in disguise

 kw: book reviews, nonfiction, science, physics, magical thinking

If people think about it at all, they might imagine that an astronomer's work bears some resemblance to this beguiling image. Dr. Felix Flicker takes advantage of this impression in his new book The Magick of Physics: Uncovering the Fantastical Phenomena in Everyday Life. His focus is on quantum physics and quantum mechanics, which still seem magical to me and nearly everyone. (The image came from a Pinterest pin, which pointed to Kai Fine Art, a digital art aggregating site.)

Just for fun, consider this picture, an architect's rendering of the Extremely Large Telescope being built at the site of the Paranal Observatory in Chile. The center of the Milky Way is in the southern sky, so a lot of big telescopes are in use or in the works to study that part of the sky. The high plains of Chile are high and dry, with very clear sky, so they are a great place for astronomy.

A real astronomer works nowhere near the telescope, unless a new detector is being added to its arsenal. Usually, the work is done from an office at lower altitude, directing the actions of the instrument over an Internet connection. Ah, science! These days far too much of it is done in an office, at the keyboard. The primary mirror of the ELT has an area of 0.3 acres, and its focal length is about 120 feet. Most suburban houses, and the lot they sit on, could comfortably fit inside, stacked two or three deep! Note: That's inside the telescope, not just inside the (much larger) dome, which is the size of a small stadium, rolling roof and all.

Reading through, I realized how disconnected I am from contemporary culture. It isn't just that I'm old; I've never been well integrated into the culture around me. I took notes. The author mentions at least 30 books, TV shows and movies, clearly expecting them to be familiar. Several more classic works such as Tao Te Ching (Daodejing) are given the same treatment, while other subjects, classic or modern, are at least given a bit of introduction. Of the 30, I had never heard of 14, I had seen or read at most three, and the rest were just names I'd heard before. The author is really, really trying to be "with it" (does anyone say that any more?).

Dr. Flicker is particularly interested in the ways quantum physics gets into various areas of everyday life, "the middle realm" (not microscopic, not cosmic). For example, polarization is a quantum phenomenon—and so is reflection off a pane of glass: which photon bounces, and which one passes through, is a "quantum choice". The interaction of light with most surfaces causes the reflected light to be at least partly polarized. These pictures illustrate it:

The picture at the right was taken through a polarizer, the lens of my sunglasses. The purpose of the glasses is to reduce glare; the company logo near the top of both pictures shows the effect. If you look closely in the right picture, it reads "Craftsman", upside down. The blue effect on the body of the mower is because the polarizer is less effective for blue light, so some gets through. Metal objects, such as the throttle lever at center left, don't polarize scattered light, only insulating materials such as plastic, rubber (the tires) and asphalt.

Our eyes can detect polarized light, just a little. The author describes how to activate the Haidinger Effect, or Haidinger's Brush, which allows us to see whether light is polarized, and determine its direction. So far, the method hasn't worked for me, but I'll look into it more. Seeing polarization is useful in a sunlit environment, because the light scattered from the sky is polarized. The effect is strongest 90° from the Sun. If you are wearing polarizing sunglasses, look at the sky with the Sun off you your right or left, and tilt your head (or remove the glasses and turn them). The sky will be darkest when the top of the glasses points toward or away from the Sun. There is no explanation in classical mechanics for polarization, but we use it frequently. The screen on your phone or computer or TV uses polarization to regulate the colors on the screen. Photographers use a rotating polarized lens to adjust the darkness of the sky in landscape photography.

One discussion that puzzled me was about Maxwell's Demon (illustrated by a friend of the author). The idea is this: a box has a divider with a hole in it, and a sliding gate that can let through molecules of a gas. Gas molecules at any temperature have a range of velocities. The gate is controlled by a demon that watches the molecules, letting the faster molecules pass from left to right, and the slower molecules pass in the opposite direction, but blocking them otherwise. This heats up the right side (making it toasty warm for the demon) and cools the other. What is missing from the book? The fact that seeing takes energy. How does the demon detect a molecule's speed and direction? 

This may puzzle us because we don't realize the energy needed for us to see the house across the street. Light from the Sun bounces off the house and to our eyes. Millions of photons pass through the pupils of our eyes every second, to be detected in our retinas. Houses and eyes and retinas are big and heavy compared to photons of light. The molecules the demon is watching are very small and light. At least two or three photons must bounce off a molecule and into the demon's eyes, in the span of a few billionths of a second, for the demon to determine its path in time to open or close the gate.

A little math fun: The kinetic energy of an atom of argon or a molecule of oxygen or other gas at the freezing point of water, 0°C, is about 0.035 eV (1 eV is an electron-volt). The energy of a visible photon—let's pick a reddish one at a wavelength of 620 nm—has an energy of about 2 eV. If it bounces off an oxygen molecule, the molecule will receive a kick about 50 times greater than the energy it already has. It would pop off in a new direction with a velocity commensurate with a temperature of 10,000°C or more. The chance of such a photon-molecule collision is very low. It would take such a bright light shining into the chamber for the demon to "see" the molecules that he would enjoy a truly toasty environment! However, his seeing would be useless, because the molecules would scatter about such that he couldn't gather any useful information about sorting them by velocity.

Photons that wouldn't affect the molecules very much would need to have a very low energy, as low as 0.01 eV. That corresponds to a wavelength of 124 microns. The demon's eyesight would then be rather blurry; these far-infrared photons are almost microwaves. It couldn't see sharply enough to know whether the molecule would go through the hole if the gate were pulled back.

I was happy to see something on page 236, that the environment "measures" what quanta are doing. A tenet of quantum theory is that a quantum has no fixed location or velocity until a measurement is taken, whereupon its position and velocity become known, within the bounds of accuracy imposed by Heisenberg uncertainty. The Copenhagen Interpretation of quantum mechanics insists that the measurement must be by an intelligent agent, such as an experimenter in a laboratory. I consider that point of view to be nonsense. Fortunately, our author never mentions the CI, so while he may "believe" it, at least he doesn't press it upon us.

Consider what happens in your eye. Back to the millions of photons per second that enable us to see. As a single photon with a wavelength of 620 nm travels from the red roof on the house across the street to your eye, it doesn't matter if it is a wave or a particle. It makes the trip in a ten-millionth of a second (from the photon's point of view, were it to have one, no time at all would pass). Upon arriving at the cornea, the photon behaves as a quantum particle, with a 5% probability of bouncing off. Let us assume it enters, at a slightly deflected angle because of refraction (also quantum effect). A few mm further on, passing through aqueous humor behind the cornea, it encounters the lens, which is denser. There, assuming it doesn't reflect, it is refracted again, and yet again when it passes from the lens to the vitreous humor that fills most of the eye. In bright light the pupil of your eye is about 2 mm in diameter. This causes a slight deflection of the photon's path because of diffraction, but in the eye, the difference is smaller than the size of a detector cell, so we can neglect it. About 20mm behind the lens, the photon encounters a rod or cone cell in the retina, where it is absorbed, and its energy is deposited in the cell, with a probability depending on the color sensitivity of that cell. If the cell is R type this red photon is probably absorbed; a little lower probability if it is G type, and much lower if it is B type or if it is a rod cell, which is also blue sensitive, and can't see 620 nm photons at all. In the space of less than 25 mm this photon "acts like" a wave at some points, and like a particle at others. There are at least five interactions, and all are described by different quantum mechanical computations. Which is the "measurement"?

Let's look further at diffraction. As an amateur astronomer I am deeply familiar with it. Diffraction limited optics are the goal of telescope makers, and the greater the width of the primary lens or mirror, the less diffraction is experienced. For example, the little telescope my father and I made 65 years ago has a three-inch mirror. I usually use it with a magnification of 30x or 60x. At 60x, the planet Jupiter appears to be about 2/3 of a degree across, or a little bigger than the Moon appears without magnification. The maximum useful magnification is 120x, because of diffraction. Here is why. Three inches is 76 mm. The wavelength of light usually used to determine visual acuity is 550 nm, or 0.00055 mm. Their ratio is 1:138,000 or 0.00000724, which is the tangent of 0.000414 degrees, or 0.0249 arc minutes or 1.49 arc seconds. About 1.5 arc seconds is the resolving power of a 3 inch diameter telescope. Human vision varies, such that the smallest separation between two points that someone can see is between one and three arc minutes, or between 60 and 180 arc seconds. Divide these two numbers by 1.5 and we find 40 and 120. For someone with very sharp vision, even using my telescope at 60x, they'll see the image as slightly blurry, while other people need 60x, or 90x, or 120x to see everything the instrument can show.

If a telescope has a larger mirror, the details it can show will be smaller, in exact proportion. Thus, a 30-inch diameter telescope could see (or "resolve") details as small as 0.15 arc seconds...BUT! The atmosphere messes things up. Except in very rare cases, a telescope on Earth cannot resolve better than 1/3 of an arc second. So an amateur astronomer will rarely buy or make a telescope larger than 14 inches. This is why professional astronomers either use telescopes outside the atmosphere (Hubble and Webb, for example), or they use costly "adaptive optics" that can mostly compensate for the vagaries of atmospheric distortion.

With that windy explanation behind us, I can get to the point. A photon is typically millions of times smaller than the largest telescope mirrors, yet it can "detect" the size of the mirror, and its path after entering the instrument is modified a little as a consequence. This is also true of a hole of any size is placed in the path of light going from anywhere to anywhere else. If you have a searchlight on the Moon (where there is no atmosphere) with a beam 36 inches wide, and half a mile away you place a board with a 24-inch circular hole in it, and then a further half mile away you put a screen, the bright area on the screen will not have a sharp edge. It will be a little blurry because the "diffraction limit" of a 24 inch hole is 0.186 arc seconds, or a ratio of 1.1 million to 1. Divide a half mile by 1.1 million: 0.0024 feet or 0.029 inch, about 3/4 of a millimeter. It isn't much but it's visible. If you put a lens with a diameter of 24 inches and a focal length of half a mile in the hole, it would focus the light to a point about 3/4 mm across. Back to the question above: where was the measurement made? The 2-foot hole participated in the measurement, as did the eye that observed the screen.

A consequence of such reasoning is this: Every quantum interaction is affected by the whole Universe. No matter how big a "hole" a photon passes through, or how far it is from the "edge", its path is affected. No matter what kind of quantum weirdness we want to measure, we can't perfectly isolate the interaction from the "environment" (everything else). In all our experiments, we just reduce "outside influences" to an acceptable minimum that allows the phenomenon we want to examine to occur.

Dr. Flicker writes in terms of wizards and spells, taking advantage of a humorous milieu to help us understand how things like "holes" can move through a semiconductor as though they were electrons with a positive charge, but are not positrons, which would energetically annihilate nearby electrons; things like fractional charges exhibited in some instruments, that have nothing to do with the 1/3 and 2/3 of an elementary charge that our Standard Model theory posits for quarks; things like MRI machines (that used to have the word "nuclear" in their name but that scared the public), which work because of superconductivity, a quantum effect we don't understand well but have learned to employ.

I hope you enjoy the humor and the allegories (each chapter begins with an allegorical story). I sure did. Physics is a long-held love of mine, and I like this fresh take on it.

I must make a few corrections (sorry, Doc!). On page 186, we read that a diode, a rectifier, "detects" an AM radio signal, converting the oscillating radio-frequency voltage to direct current. A key word is missing: the radio signal is converted to fluctuating direct current. In AM radio the audio frequencies cause the carrier wave's strength (amplitude) to fluctuate. When the rectified signal goes into earphones, the steady direct current is ignored, and the audio frequencies activate the earphone speakers, so we can hear the audio that has now been separated from the radio-frequency carrier wave.

On pages 190 and 191, explaining transistors: the example mentions adding arsenic (a Group V element) to silicon to make it n-type (negative, because it has added electrons), and adding germanium to make it p-type. Germanium is Group IV, the same as silicon. One must instead use a Group III element such as gallium (I am sure that is what the author meant!). Gallium "robs" the silicon of electrons, making it p-type (positive). 

Can and Can't versus Did or Didn't

kw: book reviews, nonfiction, physics, constructor theory, counterfactuals

When I saw the title of The Science of Can and Can't: A Physicist's Journey Through the Land of Counterfactuals, by Chiara Marletto, I was intrigued. I wondered whether it would be a diatribe against pseudoscience (where we most frequently encounter the word "counterfactual") or an explanation of something new. Thankfully, it is the latter.

Dr. Marletto is a disciple of Dr. David Deutsch, and together they are trying to reformulate physics. That's a tall order, but it's about time. A couple of generations have passed since the clash between the General Theory of Relativity and Quantum Theory became evident…perhaps it is better to say, the best explanations of these two theories definitely clash. It is not known whether the General Relativistic principles and Quantum principles indeed clash, or somehow mesh. If they clash, one must eventually be superseded, or both.

Studying the subject on the side I found that Dr. Deutsch presented his earliest ideas on the subject under the title Constructor Theory. I suggest reading the Wikipedia article Constructor Theory before reading the book, to get a grounding there. Then the book will be easier going. For a deeper dive, see the Constructor Theory web site.

Strangely, the words "constructor theory" do not appear in the book. Instead, the subject that previously had less emphasis has taken center stage: "Counterfactuals." I hope a better term can be found, but it may not be possible. Here is why I think so.

As an adjective, counterfactual refers to something that is not true, it is "contrary to fact." As a noun, a counterfactual is a conjecture about what might happen if something were changed, "Could a kangaroo jump if its tail were removed?" Whether the animal can still jump, you don't have a kangaroo any more, but a ruined kangaroo.

As used in the book, "counterfactual" partakes of the latter meaning, but does not extend it to "ruined" systems. Rather, a counterfactual is a statement about what is provably possible and what is provably impossible about a system, and Dr. Marletto calls it the Science of Can and Can't. Though this is never stated, it is placed in apposition to physics theory as a Science of Did and Didn't. We develop hypotheses by doing experiments and making observations about what Did happen and what Didn't happen. One or more hypotheses can be tested until we have a sufficient collection of happenings, or failures to happen, to enable us to propose a theory, or an explanation for the successes and failures of our experiments and observations. Based on the theory we can make predictions about the outcomes of experiments not yet done. Doing those experiments, assuming we have the means to do so, will either tend to confirm or refute the theory.

How does this relate to a counterfactual (or whatever it will eventually be called)? The counterfactual states what is possible or not possible for the system. It goes beyond the observations. Therefore, "counterfactual" is taken to mean, "Facts to be discovered in the future are expected to conform to this." It is a more powerful idea than it sounds at first. However, because of the on-the-street connotation of "counterfactual = false", I hope a different term can be devised. I tried to think of terms including the Latin root "potens-", for potential, because a counterfactual expresses the potential range of effect for a system, and sets its limits also. I didn't get far. Don't hold your breath; it isn't easy to find a euphonious term for this powerful concept.

This concept, that "Can and Can't" goes beyond "Did and Didn't" leads to the key focus of the book. Systems that have been considered outside the realm of "good physics", such as information theory and thermodynamics, can be analyzed using counterfactuals. The author claims that, using counterfactuals, exact statements can be propounded, while using traditional physics, the statements are approximations. Info theory and thermo and a few other systems larger than quanta are analyzed in the book, to discern the qualities that make them unique. For example, what was earlier called a Constructor is called in the book a Catalyst, generalizing the chemical term to mean any system that induces a change to another system and is either not changed or is returned to its initial condition afterward. Thus a thermodynamic engine can transform heat energy into motion but is not changed in the process; it is, in the most general terms, a catalyst for such a conversion.

The simplest system (in one view) treated is Information. A system such as a switch, or transistor, or coin (to be flipped) can carry information, and larger aggregates of such items can carry more information. Information has two counterfactual properties, Set and Copy. Turning a lamp on or off, or setting a coin to show heads or tails, is a Set operation. Information transfer refers to performing a Copy operation, so that the information is duplicated. When you see a lamp's light appear it causes a change in your brain: When the lamp was the steeple lantern and the brain was Paul Revere's, he began his ride to announce, "The British are coming!" (and if a second lamp was on it indicated a coastal invasion). The information system of the lamps was Set to send a certain signal, and the information was Copied to Paul, who further copied it by announcing it, loudly, as he rode.

Why does this have anything to do with counterfactuals? Because there is nothing in particle physics, quantum mechanics, and so forth, that delimits information. Set and Copy are characteristics of systems bigger than the particles dealt with the the Standard Model and the Modern Synthesis.

One way I began to think about "standard physics" related it to the gears on a bicycle. If you have a 3-sprocket cluster at the pedal and a 6-sprocket cluster at the wheel, you can choose among 18 gears. That's a lot more than the single-speed bicycle I used as a child, or the 3-speed bicycle I used as a teen. But it still has limitations. If you want to study bicycle locomotion, your observations will be limited to the gears available.

Then, suppose you think, what kind of versatility could I have if there were many gears, thousands, perhaps? Keep thinking along those lines and you begin to wonder about a continuously variable "gear" system.

This Evans Cone Drive, patented in 1880 and used in machine shops for some decades thereafter (a few are still in use; this one is in Delaware at the Hagley Museum machine shop. I used it when I was a docent there), has a range of speeds of 16:1. The effective ratio is set by moving the leather belt right or left. This idea is behind the CVT transmissions used in Toyota Corollas, some BMW models, and a few other autos, plus many snowmobiles. This Drive has the counterintuitive quality that it yields an essentially infinite number of "gears" by doing away with the gears! Dear author, if you run across this review, and you like this example, you are free to use it.

It is early days for Constructor Theory. Drs. Deutsch and Marletto are just getting their feet wet. Perhaps a revolution in physics is on the horizon. They think so. This book might be the infant's cry of a new take on physics.

Elements - the rest of the stories

kw: book reviews, nonfiction, chemistry, physics, elements, stories

A perfectly ordinary spoon. It looks and feels like aluminum, just a bit heavier…unless you hold it too long. But the person who handed it to you urges you to immediately mix your coffee with it. In a matter of seconds, you have in your hand only the handle, which soon begins to melt and also drip into the coffee cup! What is this?

Gallium, which is chemically very similar to Aluminum, is nearly twice as dense, but still much less dense than stainless steel or silver. A spoon made of it feels light. Its melting point is 85.6°F (29.8°C), and your hand is several degrees warmer than that (unless you've just been outside throwing snowballs with bare hands). If you had held the spoon in your hand more than a few seconds, it would have begun to melt. Gallium and Mercury are the only two metals that you can touch when they are molten without getting a serious burn. There are hundreds of YouTube videos showing gallium spoons, and other objects, melting in warm water or into the hand of someone. It is not toxic, while mercury is very toxic.

Stories about gallium and other elements—all of them, in fact—fill the pages of The Disappearing Spoon: And Other True Tales of Madness, Love, and the History of the World From the Periodic Table of the Elements, by Sam Kean. "The Periodic Table!" you say, perhaps with a shudder. Shades of Junior-class Chemistry in High School rise up to haunt you.

The Periodic Table of the Elements isn't (only) an instrument of teen torture. It is very useful. Just to lay some groundwork, and to get it out of the way, here is a simple version as seen in the Gallium page of Wikipedia:

The version you most likely remember (or try to forget) probably had 18 columns, not 32, with a separate pair of lines below with elements running from La to Lu and Ac to Lr (or maybe only as far as Cm or Bk with the rest of the boxes blank). This table incorporates all the elements into a single table and adds the convenience of color coding of elements with similar, or related, chemical properties. Gallium (Ga) is highlighted, right below Aluminum (Al).

The chemical similarities between certain elements led to the development of the first Periodic Table by Dmitri Mendeleev in 1869. He was not the first to notice the similarities, but he was the first to use the "periods" (the columns in the table and their repeating nature) to predict the placement and chemical properties of several new elements. As these elements were discovered, one after another, the table was established, as was Mendeleev's fame.

Early chapters of The Disappearing Spoon outline Mendeleev's discovery and that of the first handful of elements, including the ones that confirmed that his table was trustworthy. Other chapters group the elements by the kinds of stories that swirl around them (or did when they were newly known). For example, Chapter 9, "Poisoner's Corridor: 'ouch-ouch'", begins with the sad story of cadmium (Cd) in a Japanese mine. Waste material rich in Cd and zinc (Zn) was a byproduct of the precious metals that the Shogun desired. Later, when Zn was found useful, the waste tailings were re-mined, of course without any protective measures. You'll see Cd in the table above, just below Zn, which is next to Ga. Being chemically similar, Cd is found with Zn, but it is not totally identical so acid roasting can separate the two metals. Cd-rich waste, now in water-soluble form, was cast away and got into the streams. People downstream who drank the water got "Itai-itai!" disease. "Itai" is Japanese for "Ouch!" Cd weakens the bones and later causes the kidneys to fail. Early death was nearly universal, either because of infection from compound fractures, or from kidney disease. Thallium (Tl) and Bismuth (Bi) have their own stories to tell, of chemical "improprieties". Strangely, in the right compound, Bi is not toxic, and is the basis for Pepto-Bismol! You can drink it to help an upset stomach. Tl, on the other hand, is horrific! Read about it.

Two other elements, Thorium (Th) and Americium (Am) poison in a different way. They are radioactive. They bracket the range of the more common radioactive elements. The most stable isotope of Thorium, Th-232, has a half-life of 14 billion years, nearly three times as long as Uranium-238. As metals, Th and U are safe to handle for short times (I have done so). Am-241 is much more dangerous than radium (Ra). Its half-life is 432 years, while that of Ra-226 is 1,600 years. However, while radium decays to radon (Rn), the radioactive gas that we try to keep out of our basements, americium decays to other metallic elements, which stay put. Thus it can be used in smoke detectors, so you probably have a few micrograms of Am-241 in your house!

Chapter after chapter, the author tells us story after story of how elements were discovered, and/or how they are used, and curious facts about them. The phrase "Mad as a Hatter" (and the Mad Hatter of Alice in Wonderland) indicate the gradual insanity caused by using mercury (Hg, for "hydrargium" or "liquid silver") to process felt for hat-making. And some new elements have been tried as love potions, with universal lack of success.

So, maybe you hated high school chemistry, or maybe, like me, you loved it. Regardless, the stories behind the elements, and their arrangement into the Periodic Table, are enjoyable. The book is well worth a read.

I have to close with a quibble about near-homonyms and their misuse. Referring to metals such as Cd being dissolved into ground water, the author uses both "leech" and "leach", where only "leach" is proper. The other word refers to a parasitic animal, or your cousin who is always borrowing from you. Then, he describes the damage and illness caused by some elements as being "ravished". The right word is "ravaged". To ravish is to rape, though the word has other uses, but it is definitely not a synonym for ravage. And finally, describing physical characteristics of some animals, "waddles" appears. The author meant "wattles", the folds of skin on the neck of a turkey or an elderly person or dog. "Waddle" is a verb, not (or very rarely) a noun, and describes walking with a distinct swaying motion.

Well, let's forgive Sam Kean for such minor crimes. His writing is enjoyable and the stories he has unearthed are fascinating. I bought this e-book as part of a three book set, so it won't be long until I review the third (I already reviewed The Tale of the Dueling Neurosurgeons).

A lot of things time isn't

kw: book reviews, nonfiction, physics, time

Just over two years ago I reviewed an earlier book by Carlo Rovelli, Seven Lessons On Physics. That was a fun and interesting read, so I was happy to find a new book of his, The Order of Time. It is equally fun and interesting.

Let's first get to the bottom line: Nobody yet knows just what time IS. So of necessity, a lot of this book is about things that time is NOT. Understanding how time works, and perhaps to approach knowing what it is, constitutes Dr. Rovelli's life's work.

Now that we can make comparatively affordable (cheaper than an automobile) instruments that "measure time" to incredible accuracy, it is possible to obtain two of them, place one on the tabletop, and the other on the floor…Then, within perhaps a half hour, the one on the tabletop will show a slight positive difference in "what time it is", to the nearest picosecond or so. You can then switch their places. After a while, the one that is now on the tabletop will have caught up with the other, that is now running slower, and then will pass it by, so to speak. Why? The force of gravity is just a tiny bit greater at floor level than at tabletop level, and gravity slows time.

You can also take one of the "clocks" for a joyride, and when you return, it will have recorded the passage of a little less time than the one that remained behind. Motion slows time.

While we are at it, the equivalence of gravity and acceleration that underpins the General Theory of Relativity by Einstein indicates that acceleration also slows time. It's a bit harder to measure, since we don't have a simple way to divorce acceleration from velocity of motion. Even driving around with a hyper-precise clock, we don't know how to distinguish the change in what it measures that is due to the acceleration from that which is due to the speed(s) traveled.

The fact that time flows differently because of one's velocity, and one's position relative to a large mass, results in the necessity for the satellites used in the GPS system to correct the time their very precise clocks record. Otherwise, in just a day, your navigation device would be misplacing your calculated location by a few kilometers. These corrections, for both the speed of the satellite and its elevation (~22,000 km) above Earth, are sufficiently accurate that your device can know its location within a 5-to-10-meter radius, and a military-grade (and much more costly) device can determine its location within a centimeter or so. The radio signals that the satellites send travel about a foot (0.3m) in a nanosecond. Centimeter-level precision implies time accuracy of ~10 picoseconds, or trillionths of a second.

Back to the book. We have a number of practical and customary definitions of time, that allow us to go about our day-to-day work. Part I of the book draws us to realize that, to a physicist, time is changeable. Physics equations that include time and rate terms work in either direction. There is no "past", "future", or "present". Even the notion of Entropy, which is a physicist's description of the direction of time, is actually based on the "blurring" of our perceptions.

We may think we have pretty sharp vision. Indeed, since our visual cortex is nearly as large as the entire brain of a chimpanzee, our general vision is better than any other animal's (the very acute vision of a hawk is in a very small part of the bird's visual field). But how sharp is sharp? Human visual acuity ranges from 1/20 to 1/60 of a degree of arc. That means, if you hold something in your hand at "reading distance" of about 16 inches (40 cm), you'll be able to distinguish features on its surface as small as 1/60 inch, or perhaps 1/200 inch apart (0.4 to 0.13 mm). But we know we need a microscope to see "small stuff" like pollen grains (10-100 times smaller) or bacteria (even smaller). Special microscopes are needed to "see" atoms, which are smaller than a millionth of a millimeter.

So, we cannot see the molecules moving in a glass of water, but their motion gives the water its temperature. What we measure as a temperature of, say 20°C or 68°F, represents a certain average velocity of the molecules in the water. We don't see that. But the basic concept of entropy can be considered this way: moving energy through a system tends to make it less ordered. Thus, ice is very ordered, because the water molecules are in fixed relationships to one another. When ice melts, the molecules come "unglued" and can move about. Even a small glass of water contains, not just millions or billions, but billions of trillions of them. So there are a lot of ways for those molecules to be arranged, but they all look the same to us. In the glass full of ice, there was only one arrangement. We can't distinguish the motion; to us the glass of water just sits there. That is the blurring of our perception.

In the second part of the book the author describes a world without time; where there are no "things", just events. Not only do you and I not understand this, neither does he. Some very smart scientists have developed mathematical formulas that describe events with no time element. That doesn't mean we have any way to experience utter timelessness.

In Part III, he claims that "Time is Ignorance" (a chapter title). We can say that "Time is nature's way of keeping everything from happening at once", or "Time is a dimension" (as Relativity states). Whatever time "really is", we have our perceptions, which include a flow and direction of time, because that's what we need to survive. We evolved to perceive successions of events as time. We are pretty far from really knowing much more than that.

Relativity from a photon's point of view

kw: musings, special relativity, physics

I am between books, catching up on journal reading. Something has arisen in my thoughts from time to time, and this is as good a time as any to solidify it a little. The question: If a photon had consciousness, what would it experience?

I have read in numerous books and articles that Albert Einstein began the mental journey that led to the special theory of relativity by imagining he could ride along with a photon. Reading his own writings, though, we find that he was really thinking of riding a very fast railway carriage, and seeing how this might affect the photon's motion. Based on the Michelson-Morely experiment and on theoretical work by Lorentz, Fitzgerald and others, he concluded that no matter what speed he attained, the photon would zip by at the same speed, the one we define as c, the "speed of light". Then, taking the constancy of c as an axiom, he derived the special theory of relativity.

Supposing the photon could be endowed with the ability to observe on its own, what would it observe? Based on a wealth of experimental data, we can discuss the "career" of a photon in three sections:

1. Emission
2. Propagation
3. Absorption

Although we seldom think about the time it takes for a photon to be emitted, we can consider that the "wavicle" model implies a finite "size" that is similar to the wavelength, according to Feynman's probability-wave diagram (actually, when I saw Feynman draw this during a lecture, he only put in about 1½ or 2 cycles of the wave inside the envelope). Therefore, though we typically think of the emission as occuring "instantly"—if we think of it at all—it is reasonable to posit that it takes about the time required for one cycle to occur. In this discussion we will assume that everything occurs in a vacuum or near-vacuum, so that we don't need to consider refractive index or the reduction in the value of c within a material medium.

For a visible photon of wavelength 546.1 nm (the green Hg line), which has energy of 2.270 eV and a frequency of 549.0 THz, that emission might take 1.822x10^-15 sec, or 1.822 fs (femtoseconds). We may also assume that absorption occurs in a similar amount of time.

This photon-observer needs to have quick reactions indeed to observe anything at all during such brief periods of time! Will it, then, have more leisure for observation during propagation? No! According to the special theory of relativity, no matter the physical length of its journey, the time experienced by the photon will be zero; it will be unable to observe its own propagation.

From the photon's point of view, whether the photon was emitted by an electron transition at one end of the lab, and absorbed by inducing a similar transition at the other end, or the photon was emitted billions of years ago in a galaxy far, far away and today happens to arrive and produce an electron transition in the CCD attached to yon telescope, its experience is the same: less than 2 fs of emission immediately followed by less than 2 fs of absorption, after which it exists no longer. To us, one photon "was there" for a few nanoseconds and the other, for billions of years. The "experience" of the two photons, however, was identical: be emitted/be absorbed.

That is it! A photon of green light can at most experience 3-4 fs of emission and absorption. The rest of the universe is irrelevant to it. For a photon to have a longer "career", from its point of view, it would have to have a longer wavelength, a lot longer! For example, the power grid leaks a lot of 60 Hz (ultra-low-frequency) radio waves, photons with a wavelength of about 50,000 km and photon energies of 4.1x10^-15 eV. Such a photon might "experience" a time period of around 1/30 of a second. Pity the poor X-rays and gamma rays, with energies of thousands to millions, and even billions of eV! Their wavelengths are very short (from about a nanometer to a femtometer or less) and their frequencies are very high (from thousands to billions of THz). A one-billion-eV gamma ray photon is likely emitted in about 4 fs, and would most likely "experience" a total of less than 10^-23 seconds of existence.

Had Einstein actually spent his time thinking like a photon, I doubt much would have come of it. But instead, he thought of a very fast railway carriage observing a photon, which is much more interesting, and led to much more interesting results.

Wu Li: Circular reasoning to the max

kw: book reviews, nonfiction, physics, cosmology, buddhism, copenhagen interpretation, quantum mechanics

From time to time I have heard about The Dancing Wu Li Masters: An Overview of the New Physics, by Gary Zukav, since it was published in 1979. I had never read it until now. As a student of all the sciences, particularly the "hard" sciences (those amenable to experimental verification), since before 1960, I have at least a reading familiarity with physics, which is a hard science, and cosmology, which is not. Now having read the book, I find it contains no surprises, at least, none of a scientific nature. Of course, a lot has happened in physics and cosmology in the past nearly forty years.

The author, an admitted outsider to the field of physics, conceived of the book while on a retreat at Esalen along with a real mixed bag of folks including numerous scientists and science hangers-on (some would consider me more of a hanger-on, though I am a working scientist, even in "retirement" from a career in the sciences). Al Huang, who was teaching T'ai Chi at Esalen when Zukav was there, introduced him to the concepts of Wu Li. That is concepts, plural.

I have a great many Chinese friends. The Chinese languages, primarily Mandarin, the principal written Chinese language, abounds in homophones, words that sound the same, at least to a Westerner. Most basic Chinese words consist of one syllable, and very few require more than two syllables. Spoken Chinese sounds to us like a long string of only a few syllables repeated various ways, with a "sing-song" quality that means nothing. What Westerners miss is that the "sing-song" variations in tone are meaningful and are part of the proper pronunciation of Chinese words. Thus, the syllable "MA", depending on the tone, and its context in a sentence, has at least these meanings:

• Mother.
• When doubled, an affectionate term for Mother, just as in English, at least when pronounced with two flat tones.
• Horse, using a different tone.
• The verb "ride", when the context demands a verb rather than a noun, and using still another tone.
• The pronounced question mark that ends (nearly) all Chinese questions, spoken with a rising tone.

The familiar greeting "Ni Hao Ma" is a lot like the New Jersey, "How are ya?" The Chinese sentence, "Ma-ma ma ma ma", with the proper string of tones, means, "Is mother riding the horse?" (Chinese has no articles, so "the" is implied).

Depending on tone and context, "WU", pronounced "woo", has about 80 meanings, and "LI", pronounced "lee", has a great many, primarily focused on pattern. Different written Chinese characters (ideographs) are used for the various meanings of wu and li. In combination, the word wu li is the primary Chinese term for "physics". But when other combinations of ideographs with the same pronunciation (except for tones) are used, there are other meanings. In the context of this book, Al Huang gathered five. The literal meaning of the ideographs used for wu li meaning "physics" is "patterns of organic energy". The other four are "my way", "nonsense", "I clutch my ideas", and "enlightenment".

The book is structured around these five concepts, with each section containing two or three chapters. As I might have expected from a book inspired at Esalen, each chapter is numbered 1.

The "new physics" on which the book is centered is quantum mechanics and its relationship to Einstein's theories of relativity (special and general). The core message is the ambiguity of quantum phenomena—when any single "particle" is studied—coupled with the exactitude of the predictions the mathematical theories of quantum mechanics make regarding the statistics of interactions when many particles are subjected to the same set of conditions. The "scripture" of quantum mechanics is the Copenhagen Interpretation, that of Niels Bohr and his followers (I almost wrote "disciples").

Thus, for example, when light is shined through a pinhole, which spreads the beam by diffraction, and this beam is passed through a pair of narrow slits, an interference pattern emerges. This works best when monochromatic light is used, such as from a laser, but "near-mono" filtered light works well enough for visual purposes. The intensity in each part of the interference pattern can be exactly calculated by the Schrödinger wave equation, although the calculations are formidable; various simplifications of the wave equation yield very precise results with less arithmetical grinding.

I mentioned diffraction. This matter is first mentioned on pages 64-65 of the book. In the upper half of an illustration, a series of waves in a harbor are shown exiting a rather broad opening, and those that get through are shown going straight onward, with a sharp edge to their pattern. In the lower half, the opening of the harbor is smaller, and the waves exiting are shown as semicircular wave fronts spreading beyond the opening. There are two major errors here. Firstly, the upper pattern should show a little spreading at the edges of the "beam" of waves exiting the harbor (you can verify this using a wave tank, as I was shown decades ago in a Freshman physics class). In other words, diffraction occurs when waves pass through any opening of any width, not just very narrow ones. Secondly, for the lower wave pattern, the wavelength of the exiting waves is drawn as much shorter than the waves in the harbor.

In actuality, diffraction produces a nonzero probability of the waves at every angle. They seem to "go straight" through a larger opening only because the off-axis waves lose energy with angle very rapidly in such a case. When a wave front passes through an opening of a size similar to the wavelength, or smaller, there are significant amounts that are found at nearly every angle, making a much more divergent beam. Zukav seems to have been ignorant of this.

Interestingly, if a double-slit setup using extra-sensitive photographic film is set up, you can get a surprising result. The best photo film can record the capture of each photon, as long as the light is blue enough, meaning the photons are energetic enough. One silver halide grain is exposed by the capture of a single photon. If the light is dimmed enough that only a few photons per second pass through the apparatus, and you let it run for less than a minute before extracting the film and developing it, the developed film will have one or two hundred tiny exposed grains that are seemingly scattered at random over the film. If instead, you leave the film in place for an entire day, there will of course be many more exposed grains, tens of thousands of them. They will show a very clear interference pattern, identical in form to the one you could see when the light was shining brightly and tens of trillions of photons per second were passing through the apparatus.

Interference is a wave phenomenon. Photons are particles; each carries a specific amount of energy and has a specific momentum (these are all the same for monochromatic light). It took me and all my fellow students a long time to become comfortable with the fact that light has both wave and particle characteristics. Eventually we thought of a photon as a "wavicle", a small wave bundle, that could somehow "sense" that both slits were open and "interfere with itself", when passing through a two-slit apparatus. It seems that light behaves as a wave when wave "behavior" is demanded of it (the two slits), and as a particle when particle "behavior" is required (exposing a silver grain in the film).

Where does Gary Zukav take this, and several other experimental results of quantum mechanics, special relativity, and general relativity? Straight to the door of a Buddhist sanctuary. The language he uses is usually as ambiguous as the language physicists typically use to describe concepts like the "collapse" of a wave function when an "observation" is made. He compares some conclusions and statements of physicists to similar statements of Buddhist doctrine, though I could seldom recognize the resemblance. The core of the Copenhagen Interpretation, at least as it is explained in this book, is that the Observer is central. But, to date, nobody has adequately defined "Observer". That doesn't stop Zukav from equating the one-is-all-all-is-one that he believes the new physics is trending toward to Buddhist teachings of the pre-Christian era. I have a question or two about observers, or Observers.

Must an Observer have a self-aware mind? Can the photographic film described above be an observer, or has no observation been made until the film has been developed and a human (or other self-aware entity) has looked at it to see the pattern? If I understand the Gary Zukav presentation of the Copenhagen Interpretation, there is no "collapse" of the wave function into an actual "event" without an observer. It is as though, outside your peripheral vision, nothing exists until you pay attention to it. Taken to an extreme, it means there was no Universe until humans evolved to be the Observers to bring it into existence. This is the reason for the title of this post. If this is actually what Niels Bohr believed, I have to say to him and his disciples, as Governer Festus long ago said to the Apostle Paul, "Much learning has driven you insane!" Paul was not insane, but I think Zukav might be. More on this anon…

At the time The Dancing Wu Li Masters was being written, some "newer" new physics concepts were arising, such as the Quark/Gluon resolution of the Particle Zoo, and the theory of the Multiverse. To take up the former: It appears that the quark is truly fundamental. All the hadrons seem to be made up of various combinations of quarks and anti-quarks. However, it takes such enormous energies to generate interactions that give evidence of the existence of quarks—and they apparently cannot be brought into independent existence—that we may need to await a particle accelerate wrapped around the equator of the Earth to achieve energies sufficient to determine whether quarks do or do not have any substructure. Apparently, electrons have no substructure, so maybe they and quarks are as fundamental as it gets. But our experiments have reached "only" into the range of 10 to 100 TeV. What might be achieved with an energy a thousand times as great, or a million? Fears have been expressed already that the current experiments at CERN could trigger destruction of the Universe. Maybe the Multiverse is real, and we inhabit a surviving Universe that didn't get destroyed.

The notion of the Multiverse is simple. Rather than the wave function for a particle "collapsing" into some actual event, an entirely random outcome within the statistical framework described by the wave function, perhaps every possible outcome actually occurs, and a new Universe is spawned to contain each of those outcomes. This is simple enough if the "outcome" is that a particular photon passes through either the left slit or the right slit of a two-slit apparatus. Two universes result. I one of them, the photon passes to the left, and in the other, it passes to the right. But there is detail in the interference pattern, and when I have done the experiment with a laser pointer and a home-made pair of slits cut in aluminum foil, I could see more than twenty interference fringes. Now what? Did each photon create twenty or more universes to accompany each outcome? When the light is bright enough to see, trillions of photons per second are "in use"; the beam of my laser pointer emits 200 trillion photons or deep red light per second. Did I inadvertently create a few quadrillion new universes, just by shining my laser pointer through a pair of slits? Were new universes being created at the same rate even when I wasn't looking?

So what are the chances that the search for the Higgs boson at CERN caused the creation of truly enormous numbers of universes, nearly all of which were immediately destroyed, and we inhabit one of those that survived. I think you can see where such thinking can lead.

And some folks say that I am crazy to believe in God, a God who knows a level of physics (if it is called that) that can resolve this stuff, without the insanity of Multiverse speculations. I think it is fair to say that "modern physics" has reached a point of adding more and more epicycles to a group of theories that seem to produce very precise results, but that they are really analogous to pre-Copernican cosmology. Actually, Copernicus used epicycles also, because he thought orbits were based on circles. It took Kepler and others to work that part out.

Another item or two that have arisen in physics since 1979:

• On page 119 we read, "No one, not one person has ever seen an atom." If you are talking about direct visual sight without the use of a microscope, you could say the same thing about bacteria or viruses. But we have microscopes of several kinds that can show us what they look like in rather amazing detail. Since about 1981, highly refined transmission electron microscopes have been able to show atoms directly, and since the invention in 1982 of the scanning tunneling microscope and the atomic force microscope, we now have three methods for seeing where the atoms lie in a surface. Whatever point the author wished to make based on the above statement is now moot.
• Beginning on page 292 we find an illustration using polarized light. Simply put, when light is passed through a polarizer (such as the special plastic in some sunglasses), the light that emerges is now all vibrating in the same plane (for convenience, we use the electric vector as the "direction" of polarization, though the magnetic vector could be used equally well, and is at 90° to the electric vector. Zukav does not mention this). When you place a second polarizer with its polarizing axis at 90° to the first, it blocks all the light. If you rotate it to various angles, some of the light gets through, in accordance with an elliptical formula. Now, if you set the two polarizers so their polarization axes are at precisely 90° so that no light is getting through, then put a third polarizer between them, with its axis oriented at 45° to the other two, quite a lot of light gets through! This goes on for several pages and is presented as quite a mystery. Strangely, elsewhere in the book we find the tools to solve this mystery (I didn't look up page numbers):
• In a discussion of Feynman Diagrams and the S-Matrix (Scattering Matrix) we read that physicists consider every interaction to entail the destruction of all the impinging particles and the creation of new ones that exit the interaction locus at the appropriate angles with appropriate velocities. Thus, when a photon reflects off a mirror or any shiny surface, it is actually absorbed and a new photon is released at the appropriate angle. So they say. Refraction works similarly. Thus, the polarizer absorbs the incoming photons and releases a somewhat smaller number of photons, all with the appropriate polarization.
• As I recall, a polarizer made of stretched plastic film passes 38% of the original light. A Nicol prism can actually split light into two beams with nearly no loss, so that 50% exits with horizontal polarization at one angle, and 50% with vertical polarization at a different angle. This would make no sense according to the "picket fence" analogy, because very, very little of the original light could get through any polarizer: only that which is already polarized the "right" way. Thus, a Nicol prism, in particular, "tests" each photon, and either twists its polarization to match the nearest direction (and shifting its exit angle according to the one or the other), or annihilates the photon and emits one of appropriate polarization and exit angle.
• Polarizing plastic is less efficient, passing only light of one polarization, but obviously changing whatever the polarization was of most photons to match its orientation. Thus, what is happening with the 45° polarizer is this: it absorbs some photons entirely, and twists the polarization of the rest of them by 45°. Then when they reach the last polarizer, they are now subject to a further absorption or twisting, so that the "twisted ones" get through, with perhaps 5% of the original beam intensity. That is a lot more than the fraction of a percent that "sneaks through" the original set of crossed polarizers because plastic film polarizers are not perfect.
• So polarizing devices do not just passively allow certain photons to pass and block all others, but they change the polarization of the photons that they allow to pass.
• I cannot pass by the chance to mention circular polarization. A thin piece of calcite or quartz (or, indeed, any colorless crystalline material that does not have cubic molecular symmetry) rotates the polarization of the incoming light. What is more, if it is just the right thickness, it will produce circularly polarized light. This is sometimes thought of as two streams of photons that are related to one another. Think of a vertically polarized photon coupled with a horizontally polarized photon, and their "waves" are out of phase by a quarter of a wavelength. Then, in effect, their polarization will rotate as the go.

As interpreted by Gary Zukav, physics was becoming one with Buddhism. I wonder what he would make of today's situation, with the great popularity among physicists of cosmological string theories (at the moment, they can't decide which of the potential 10⁵⁰⁰ possible string theories to favor!), the supposed detection of increasing cosmological expansion that may lead to a "big rip" in which all things will be literally shredded to their composite quarks, and the theory of cosmological inflation (developed in the early 1980's) that supposes that the initial expansion of the big bang took off at several trillion trillion trillion times the speed of light for just a tiny fraction of a second, during which the Universe grew to a size somewhere between that of a grapefruit and a galaxy (nobody can pin that down too precisely).

In my view, coupling physics theorizing with Buddhism is tantamount to solipsism. Let us accept as a first premise that what exists, does indeed exist, and go from there. Then the extreme versions of "New Physics" simply vanish, like an unobserved photon.

A peek into physics

kw: book reviews, nonfiction, physics, popular treatments

Physics is the intersection of mathematics with observations of nature. So a book that promised an entirely non-mathematical presentation of the deepest puzzles of physics was impossible for me to pass by. In Seven Brief Lessons on Physics, Carlo Rovelli aims not so much for non-physicists to understand the great theories of physics, but for them to become intrigued by them.

Optimistically enough, he begins with "The Most Beautiful of Theories", discussing Albert Einstein's two related theories of relativity, the Special Theory, which treats of the effects of relative motion on time and space, and the General Theory, which unifies space with gravity. He discusses the problems left unsolved by Newton's mechanics, and at least helps us get a glimpse of the way that these two theories resolve them, at least in part.

Many people think that Einstein's Nobel Prize was for one of this theories of relativity, but it was instead for his work on the Photoelectric Effect, with which he demonstrated that light is quantized, or made up of particles. Newton had thought this might be so, calling the particles "corpuscles", but had no way at the time to prove it one way or another. Albert Einstein did so, and then worked on quantum theory for many years. Today, many, at least many of those with some scientific training, are more or less comfortable with light's having both a wave nature and a particle nature. Not only that, but elementary particles such as protons are found to also have a wave nature, though it takes subtle apparatus to winkle out the evidence for it.

Eventually, Einstein was dissatisfied with quantum mechanics, not least because his theory of general relativity and the developing theory of quanta were in fundamental conflict. General relativity requires that space and time be continuous. All aspects of quantum theory require them to be "chunked". Is this just another duality we simply have to accept, like the particle-wave duality of light and even matter? Dr. Rovelli is clear: At the moment we don't know, and nobody is sure how to resolve the dilemma. I like that about him. He doesn't sweep the problems under the rug. They are just there, waiting for someone to hit upon the right approach to straighten them out.

Rather than discuss each of the following chapters, I think it best to leave folks with the following picture of the way light behaves as it enters our eyes and is perceived. Once light is on its way to us, either directly from a source such as the sun or an artificial lamp, or indirectly after bouncing off something, whether it travels as a wave or as a stream of particles is not important. But as it reaches the cornea of the eye, and before that the very thin film of tears on the cornea, it behaves as a wave and is refracted. There is no equation in quantum mechanics which can adequately describe refraction. This shows us that quantum theory is still not complete. During the tenth of a nanosecond that the light is traveling through the eyeball, it is refracted several times, as it passes from one thing to the next: the tear film, the cornea, and aqueous humor in the front of the eye, the crystalline lens behind the iris, the vitreous humor that fills the rest of the eye, and a very thin film of liquid between that and the retina. At the retina, all of a sudden, the light behaves like a stream of particles. The "color" of light depends on the kinetic energy of those particles, the photons, the quanta of light. The cone cells in our retina come in three varieties (for most of us). The cones that respond only to a range of higher energy photons stimulate the color "blue", those that respond best to lower-energy photons stimulate "red", and those with a medium energy preference stimulate the color "green". Thus the particular mix of variously-energetic photons in the beam of light striking a particular patch of cone cells stimulates a color response, which may differ quite a lot from the response of the next patch over, depending on the energy mix of photons that reach that spot.

An interesting side note is that the solution to a quantum mechanical event requires an "observer", and in a simple way, we humans are typically considered the observers. But if phenomena such as diffraction occur when none of us is watching, as we think is true, then the "observer" is actually the whole of the universe, which responds at some level (usually a very, very, very low level) to every quantum event. So we aren't really the "observers" of quantum theory, but those who have figured out that whatever happens in the universe seems to matter to all the universe. At that point physics begins to border on metaphysics. By definition, science gets left behind if we go further.

The other matters covered in the book, cosmology and the shape of space, the resolution of the "particle zoo" that first emerged from our early cyclotrons and synchrotrons, what black holes might really represent, and where we fit into all of this, are each treated succinctly. Dr. Rovelli revels in the beauties of natural science as studied by theorists. His little book is a "good college try" at helping some of the rest of us respond to that beauty.

The Roach Motel for everything

kw: book reviews, nonfiction, physics, black holes, history of science

In 1905 Albert Einstein published four small monographs in scientific journals. Their subjects were

• The Photoelectric Effect, in which the color of the light, and thus its frequency, were directly related to the voltage of electrons emitted from a sensitive surface, and depending on the "activation potential" of various surfaces, there was a threshold below which no emission could occur. This proved that light is quantized as particles now called Photons.
• Brownian Motion, in which tiny, lightweight items such as pollen grains, suspended in water and viewed through a microscope, are seen to jiggle continuously. He showed that this is a statistical effect of jostling by molecules of water, the first empirical evidence for the existence of atoms and molecules.
• Special Relativity, in which he established that the speed of light and all effects of the interaction of light with spacetime are the same as measured in any non-accelerating reference frame, regardless of that frame's velocity with respect to any other. This implies that everything except light is variable when measured between reference frames moving at differing velocities, particularly mass, length, and the passage of time.
• Mass-Energy Equivalence, expressed in the formula E=Mc², in which he showed that Maxwell's laws imply that as energy is added to a system its mass increases. The parameter c is a large number, 300,000 km/s, and its square is thus so huge that simply heating a kg of iron, for example, between 0°C and the melting point of the iron, will only increase its mass by something like a few billionths of a billionth of a gram. But the equation as stated provides a hint, later well defined by the scientists of the Manhattan Project, that nuclear reactions which confer a reduction of mass yield enormous energy release.

Guess which of these discoveries led to Einstein receiving the Nobel Prize in 1922? It is the Photoelectric Effect, which laid a foundation for Quantum Physics, by effectively discovering the Photon, the first quantum particle to be so defined.

Ten years later, Einstein published articles on his General Theory of Relativity, usually just called General Relativity, which extended Special Relativity to accelerating motion and, in particular, to motions in a gravitational field. The set of equations at the core of the theory show that gravity is a consequence of curvature in spacetime caused by mass. As John Wheeler states it, "Mass tells Spacetime how to curve, and Curved Spacetime tells Mass how to move."

It wasn't long before scientists, striving to find exact solutions to the theory's equations, determined that the end point of gravitational collapse was a singularity. This had been hinted at by scientists as far back as 1783, when John Mitchell first calculated the mass needed for a Sol-sized star to prevent the escape of light, and thus be rendered invisible to a (safely) distant observer.

The events along the way between 1783 and 1915, and those since, form the structure of Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved by Marcia Bartusiak. The author's aim is not to discuss the physics of black holes to any great extent—though a certain amount is necessary—but to trace the history of the idea, from an idea that made classical physicists queasy to the modern understanding of the way black holes have shaped the universe. That "queasiness" led to general relativity being neglected for most of fifty years. Finally, improvements in astronomical instruments and methods forced recognition that such "supercollapsed" objects as black holes might indeed be real.

The first astronomical object to be generally accepted as a black hole is Cyg X-1, in the constellation Cygnus (the Swan), which weighs about 15 times as much as the Sun. It and a blue supergiant star orbit one another closely, with a period of 5.6 days. The supergiant sheds mass in irregular fashion, and some of the gas is drawn into an accretion disk circling the black hole, where frictional and compressional heating raise temperatures to millions of degrees and cause flashing and flickering at primarily X-ray wavelengths. Such a black hole is called a "stellar black hole" because it formed from the collapse of a single star.

A much larger event or series of events must underlie the formation of the very large black holes at the centers of galaxies. It is very likely that a "supermassive black hole" is at the core of every galaxy. The stars in our own galaxy, the Milky Way, orbit a black hole with a mass of about 4 million Suns, or about 270,000 times the mass of Cyg X-1. Larger galaxies, or galaxies with larger central bulges, and large elliptical galaxies which are all central bulge, have central black holes up to several billion Suns in mass.

Do these galactic black holes also shine or flash like Cyg X-1? Whenever they have a source of infalling matter, they do. Quasars are extremely bright and very tiny (compared to a galaxy) objects that are seen in light, radio, and X-rays caused by large amounts of matter in their accretion disks. "Active galactic nuclei" are dimmer than quasars, from our perspective, but are probably quasars when seen from a special perspective, because the emissions of black holes are directional.

Black holes all spin, and they all have magnetic fields. This is because they were formed from spinning matter (and accretion adds to their spin), and all plasmas in space are magnetic; the magnetic field is retained after collapse within the event horizon. Accreted matter, heated to a plasma, is spun by the spinning magnetic field and is compressed into a pair of jets which emit primarily along the spin axis of the black hole. A quasar is what we see when we are looking "down the barrel" of one of these jets. An active galactic nucleus is seen when we are off to the side. Cyg X-1 is apparently also pointed right at us.

When we read of a quasar that has an apparent brightness of trillions of stars, we must remember that the "trillions" figure is calculated by assuming equal brightness in all directions. The actual beam is a degree or two across, and a sphere has an angular area of more than 41,000 square degrees. So the "trillions" become "billions" or "hundreds of millions", nearly all concentrated into those two beams and so amplified from our viewpoint. That is still really, really bright!

The first quasar had a spectrum too weird to fathom, at first, until it was finally realized that the spectral lines were those of hydrogen, shifted far toward the red end, implying a cosmological distance of about 2 billion light-years. The distance to a quasar is actually rather tricky to calculate, because of three effects (this is just me now; the second and third factors are not mentioned in the book):

1. The cosmological red shift caused by the expansion of space.
2. The gravitational red shift caused by the tremendous gravitational potential close to the event horizon (where the gravitational red shift would be infinite!). This increases the total red shift and by itself will cause us to over-estimate the distance to the quasar.
3. A blue shift caused by the relativistic velocity of the superheated matter beam, which might be as much as 0.2c to 0.5c pointed toward us, and perhaps even more. This counteracts some of the red shift from expansion and gravity.

Of these three factors, it is generally considered that the first is the greatest, but I have not read a definitive analysis of the second and third factors for any particular quasar…and I've been looking.

The book is fascinating and enjoyable. A timeline in an appendix helps tie events together, and traces the contributions of many scientists to the understanding of general relativity and gravitational collapse and its implications. A well-researched and well-written book, it rounds out the scientific story into a fascinating human story.

The Market is People

kw: book reviews, nonfiction, statistics, physics, stock markets

A financial market behaves like a small collection of quantum particles. This is my conclusion after decades of investing (sometimes lucky, sometimes not), and reading about them, from The Emergence of Probability and The Taming of Chance by Ian Hacking, to The Black Swan by Nassim Taleb and Beat the Market by Ed Thorp and Sheen Kassouf, and now The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall. The shine isn't quite off Dr. Weatherall's first PhD yet—it is but half a decade—but already he exhibits a breadth of vision that sets him apart. He actually has two doctorates, in physics and in philosophy, so he has the kind of mind I like, not just thinking outside the box, but leaving all the boxes behind.

So why would he be interested in market analysis? For the same reasons a ton of physicists have had already: that is where the money is. Plus it has the un-ignorable allure of a challenge that is almost impossible, yet not quite. Given that many thousands of smart people have been trying to "beat the market" for, oh, half a millennium at least, a few have gotten rich, at least by chance, but rare indeed are those persons or funds who managed to stay ahead of the pack and get rich by actually betting on predictions that panned out, again and again. A physicist-run hedge fund called Renaissance is claimed to be one of them.

The bulk of the book is a history of statistical thought, as it developed over the past few hundred years, frequently in response to the desire to understand price fluctuations in markets for currency, commodities, or stocks and options of various kinds. The tools used for this began with the Normal (AKA Gaussian) distribution, the familiar Bell Curve. All kinds of additive phenomena obey Gaussian statistics, such as average height for men or women of a given ethnicity, or most famously, IQ. A particular Normally distributed population is completely described by a Mean (µ) and a Standard Deviation (σ). The shape is scalable, wider for large σ and narrow for small σ, but is otherwise fixed, so that 68% of the population is found within the range µ-σ to µ+σ, called the 1-sigma range; and the 2-sigma range encompasses 95% of the population. So, for IQ, at least among Euro-Americans, µ is standardized at 100 and σ at 15. Thus the range [70-130] includes 95% of these folks, and 68% are found in [85-115]. Public education was originally aimed at the 1-sigma group, and the rest were left to fend for themselves, until Special Education and Gifted Education movements arose to help out those in the "tails", whether duller or brighter.

Is the Normal distribution a good model of market fluctuations? Not at all. First, we must realize that human perception is involved. A $1 change in a $10 stock feels just as large as a $5 change in a $50 stock, particularly if you have 500 shares of the first one or 100 shares of the other. Both changes are 10% of your $5,000 investment. The chart below shows the day-to-day change of closing price for Coca-Cola common stock, since the beginning of 1986, expressed as a % of the prior day's closing price.

If we sort these numbers and plot them against a "Probability Ordinate", really an inverse Normal ordinate (I use the NORM.S.INV function in Excel 2010), we would get a scatter plot that closely follows a straight line if the distribution were Normal. But here is what we get instead:

If we extend a line tangent to the central part of the distribution, to -4σ or +4σ, it strikes at a 5% change, indicating that variations greater than this ought to be rare indeed (there are 7,101 daily changes plotted here). But what do we see instead? Going back to the original data sheet, I find 42 days on which the stock increased by 5% or more, up to nearly +20%, and 33 days on which it fell 5% or more, to nearly -25%. How'd you like to own a million shares of this stock and have it lose 1/4 of its value on a single day? So early on, the Normal distribution was found wanting.

Normal analysis was based on the concept of a random walk, also called the drunkard's walk. Its additive nature will always result in a distribution of final locations, say after ten staggers, that is Normal. So a different distribution with extra-wide excursions is needed. In an entertaining section, Dr. Weatherall describes a drunken firing squad. They have a target upon a very long wall, but being too drunk to point well, might shoot in any direction at all. Give them lots of ammunition (and hide somewhere until they run out), and the pattern of bullet holes will follow a Cauchy distribution. It looks a little like the Normal distribution, but has a pointier top, and most importantly, "fat tails"; that is, many points that are farther—or much farther—from the middle than a Normal distribution would predict. The distribution above is also fat-tailed, having lots of numbers outside the range we'd expect from a Normal distribution. To test a distribution for Cauchy behavior, plot it against a Tangent function evenly distributed in the range -π/2 to +π/2. For my 7,101 points, the Tangent function ranges from nearly -5,000 to +5,000, so the chart is thus:

The Cauchy distribution is clearly a bit too much, its tails are "too fat", compared to the tails of Coca-Cola daily price fluctuations. This kind of conundrum was tackled by many bright people, from Fischer Black to Benoit Mandelbrot. Mandelbrot probably came closest with fractal analysis, which wasn't wedded to integer exponents. But I got another thought as I read along.

The Normal and Cauchy distributions are related, being examples of Stable distributions. In one formulation, a parameter called α has a value of 2.0 for a Normal distribution, and a value of 1.0 for a Cauchy distribution. The fattest tails possible are at α=0, the Uniform distribution of infinite width. Mandelbrot had used fractal analysis to calculate a distribution with α of 1.7, closer to Normal but still with a fat tail. I realized that the most familiar distribution with at least one long tail is Lognormal, but it is confined to positive only values. Does it have a complex square root, perhaps? I sorted the squares of the KO daily changes and charted them against a Normal ordinate on a logarithmic scale. But there was a problem. On 245 days there was no change in price. Prior to the 1970s stocks were valued in 8ths of a dollar (12.5¢), and in pennies thereafter, though dividend allocations can be calculated to 0.0001¢ increments. Trades are reported to the nearest cent. Anyway, you can't take the logarithm of zero, so in my spreadsheet I used a value a little smaller than the smallest calculated nonzero value for those 245. They form the line at bottom left on this chart:

If trades were made with a continuous range of values, not limited by the minimum value, I would expect the left portion of the chart to be as linear as the rightmost. Quantization errors have artificially depressed the daily motion for about 15% of the trades. In the other charts, the two extreme values, -25% and +20%, seemed like outliers. Here, as the two rightmost data points, they are seen to be at most slightly larger than one might expect.

So, all you quants out there, working out the best formula for calculating risk. Give a little attention to the square root of the Lognormal distribution! Now, back to the book.

A key theme of the book is both the value and the danger of numerical models. A physicist understands that a model is always simplified, and cannot be appropriately used outside its range of application. When the people using models of financial systems, to set option prices and other instruments, are physicists, they will know this and avoid over-extending the model. People without physics education will not. When you have a black box program that seems to work magic, it is easy to use it everywhere (the parable of the man whose only tool was a hammer comes to mind).

There have been several major crashes in the past century, and only the one in 1929 was free of the influence of sophisticated statistical modeling tools. I say "sophisticated" because there were statistical tools in use a century earlier, but they were back-of-the envelope estimates at best. All of the more recent ones show at least traces of "broken model" influence, but the October 1987 crash was an overt "robo-trading" crash. This brings up another principle that physicists, at least, ought to keep in mind: the observer effect.

I am not just talking about Heisenberg Uncertainty. Rather, most observations of physical phenomena disturb the system being measured. I remember my father telling me not to check the air pressure in my bike tires so often, because each measurement caused some air to be lost. Later, working in electronics (in a time when the components were visible and manipulable by hand) I learned how to use a Wheatstone Bridge to measure DC voltage the most accurately, because it uses a counter-voltage to keep from bleeding extra current from the circuit. It is only good for very steady DC, of course. Thermometers change the temperature of the pot roast, but only a tiny bit; still the effect is not zero. But now imagine that you have half a million people whose livelihood depends on knowing the temperature in your pot roast, and they all insist on using their own thermometer. There won't be much left of the roast! THAT's what happened in October 1987.

The use of new tools changes the way markets work. What worked in September 1987 doesn't work today; what worked in 1997 or 2007 doesn't work now, and so forth. This pretty much negates the notion of an efficient market. It can only be efficient under two conditions:

1. The traders have no supercomputers available.
2. All traders are coldly rational.

Fat chance, right?

The "efficient market" works like this: In comparatively quiet times, the asking price of a stock or whatever incorporates all the current knowledge about things that might affect its value in the future. To profit from trading that instrument, you either guess it might be underpriced, because of unknown or little-known information, or you try to learn something nobody else knows. The most common source of such knowledge is cadging or coercing it out of an insider, which happens a lot even though it is illegal. Quantitative analysis attempts to find patterns in price fluctuations that signal a change you can profit from. When someone finds a useful pattern, he or his company will profit from it for a while, until others catch on, then pretty soon everyone can do it, and the market is "efficient" again. So quants' work is a continual arms race. Thus, the tools used to test the market change the market.

But the markets are not that efficient. In the medium term they might be, but the momentary trading picture is much more emotional, and tiny bits of information or rumor disguised as information can sway a trader's estimate of value. If that trader is influential, and others see him (usually male) make a move they didn't contemplate before, some will follow. It can cascade into a large market move, that might last a matter of an hour or less, but might last a day or more, and then there is the potential for quite a swing, either towards a bubble or a crash.

The fragility of any market lies in the tendency for all the quantitative trading firms to use the same models, or models based on the same math, with the same or very similar trigger points. Certain rules instituted after 1987 can calm the flurry to some extent, but the events of 2007 to early 2009 present a case in which the agony was simply drawn out over the space of more than a year, rather than taking place in a month or less.


With the contents of this book under my belt, I ask myself, "What is the ordinary investor to do?" We don't have supercomputers and armies of physics PhD's running sophisticated options evaluation software, trading 10-a-minute on our behalf. Dr. Weatherall doesn't tell us what to do. It isn't his business to do so. He is instead advocating for a kind of financial Manhattan Project to set an appropriate, physics-based replacement for the Consumer Price Index, whose flaws are politically grounded, very much on purpose (Oh, you thought it was objective?). As I said, his PhD's are still shiny and new. His next PhD needs to be in human nature, particularly the nature of the political human.

In the meantime, if you dare to invest in stocks, the advice of Will Rogers is still the best:

1. Buy a stock.
2. When it goes up, sell it.
3. If it isn't going to go up, don't buy it.