Exploring the quantum boundary

kw: book reviews, nonfiction, quantum mechanics, quantum theory, popular treatments

When I was about ten, I was disappointed in a picture I'd taken. I had been too far from the person I was "shooting", so he looked like no more than a couple of dots. Having recently learned about enlargements, I suggested getting the middle of the picture enlarged. My father remarked that the photo shop charges a lot for enlargements. Then I suggested putting it under my microscope and taking another picture, then getting that printed—I'd already been setting up a clumsy rig with a tripod holding Dad's camera at the eyepiece and making photos of the cells in thin-sliced carrots and leaves. He said I could try, but it would be very blurry, then explained about the grain in the print and in the negative. I looked, and sure enough, even at 25X the film grain made the picture look like it was printed on sand.

The next year he and I made a small telescope (I still use it), and I learned about diffraction and the magnification limit of an optical system. I realized, even if the film and print grain were a hundred times smaller, and even if the optics of the camera were flawless, diffraction would limit how much I could enlarge the final image.

This is an illustration of the Rayleigh criterion for resolving star images in a telescope. I downloaded it from the Angular Resolution article in Wikipedia. The upper section shows that the Airy Disks of the two stars are fully separated. The Airy Disk is everything inside the first dark ring (first null). The lowest section shows serious overlap, and the middle section shows the Rayleigh criterion, at which point the first null of one Airy Disk passes through the center of the other. This is the accepted resolution limit of a telescope system, or indeed, any optical system, including the eye.

What causes this pattern? It results from the interaction of light from a distant point source (or multiple sources) passing through a circular aperture. Just by the way, if you should get the notion to make a telescope with a rectangular aperture, under high magnification you'll get a diffraction pattern more like this:

Such diffraction patterns, I realized one day, are a visible manifestation of quantum-mechanical effects. If you could solve the Schrödinger Wave Equation for this system, the square of its solution would look like this image. In the SWE, the solution is in complex space, and represents probabilities, while the square of the complex probability at any point is the intensity of, for example, a beam of light or electrons, as it is spread through space by diffraction. One characteristic of the SWE is that, while there will frequently be numerous nulls, or zeroes, in the solution, there is no greatest angle or maximum distance beyond which its solution is always zero. This is why even huge telescopes such as the 10m diameter Keck telescopes in Hawaii still have a diffraction pattern once all other aberrations are accounted for (the atmosphere is a much bigger light scatterer "down here", though).

So, think of it. The yellow-green light that our eyes are most sensitive to has a wavelength of 0.55µ, or 550 nm. That's pretty small, about 1/1800 mm. And, even if we are comfortable with photons, the minimal packets of light, we think of them as having a similar "size". But diffraction patterns show us that a photon can somehow "sense" the entire aperture as it "chooses" by how much to change its direction of travel. A certain experiment that has been done with both photons and electrons proves it:

• Set up a very, very light-tight box with a dimmable light source at one end, a sheet with a hole in it about midway, and either a sheet of film or an array of sensitive detectors (e.g. a digital camera sensor) at the opposite end.
• Let's assume the light source is accompanied by a lens system that makes a uniform beam larger in diameter than the hole in the sheet.
• Set the "brightness" of the light source such that there will very seldom be more than one photon inside the box at any one time. That's pretty dim!
• A 550 nm photon has an energy of 2.254 eV.
• A 1 mw yellow-green laser set to that wavelength (you can do that with dye lasers) emits 2.77 quadrillion photons per second.
• Light traverses a 1-meter box in about 3 ns.
• The 1 mw laser thus emits 8.3 million photons in those 3 ns.
• Thus you must dim the beam by a factor of more than 8 million. That is 23 f/stops, or an ND of 6.9. Two pieces of #9 welding glass is about right.
• Close the box, turn on the light, and wait about 3 hours.
• Develop or download the resulting image. It will have the same diffraction pattern as if you'd left off the filters and shot a picture in 1/1000 sec.

The experiment has been done many times, usually using a two-slit setup. Either way, it shows that both a photon and an electron somehow "self-interfere" as they are influenced by everything along the way from emitter to "final resting place."

All the above serves to get my mind in gear to write about The Quantum Moment: How Planck, Bohr, Einstein, and Heisenberg Taught Us to Love Uncertainty By Robert P. Crease and Alfred Scharff Goldhaber. The authors, professors at Stony Brook University, aim to demonstrate that "quantum stuff" keeps things from either collapsing or flying apart. That we owe our lives to it. Dr. Goldhaber, in particular, draws upon classroom experience, for he teaches a course that uses optics to introduce quantum mechanics.

The book is filled with mini-histories and mini-biographies of the "physics greats" of a century ago who wrestled with the findings of phenomena that revealed that Newtonian mechanics are not up to the task of explaining all the little stuff that underlies our everyday experience. Optical diffraction is just one such phenomenon. If there were no diffraction, you could put a really powerful eyepiece on an ordinary pair of binoculars and see to the end of the universe...if your eyes were sensitive to really, really dim light (telescopes are big mainly to collect more light; high resolution is also good, but is secondary in many cases).

Einstein imagined riding a beam of light from emitter to absorber. Nowhere have I read an explanation that, from the photon's point of view, nothing happens at all. The special theory of relativity, with length compression by Lorentz contraction, and time dilation, only applies to non-photons, and in particular, particles with mass. If you take Lorentz contraction and time dilation to their limits at v=c, the photon travels no distance at all, and does so in zero time. So there is nothing to experience! From a photon's point of view, the entire universe has zero size and time has no meaning; the big bang may as well never have happened!

What if we step back a tiny bit, and imagine the neutrinos that arrived in 1987, heralding the core collapse of an immense star in the Large Magellanic Cloud, Supernova 1987a (SN1987a). I haven't read any analysis of their apparent velocity, but it must have been only the tiniest whisker slower than c. Neutrinos do have some mass, perhaps a few billionths of the mass of an electron, so they tend to have near-c velocities. It is likely that the "clock" of those neutrinos registered only a few minutes during their journey of 187,000 light years, and the distance seemed at most a few hundreds or thousands of kilometers. Now, that is relativistic.

What did Einstein and Planck and Heisenberg do that got everyone (among physicists) all in a dither for the first half of the Twentieth Century? First, Planck applied a minimum limit to the "packets" of energy radiating from a heated object, in order to combine two competing, and incompatible, mathematical models of "black body radiation" into a single formula. Einstein later showed a simpler derivation of that formula. But at first, physicists just thought of it all as a mathematical trick. In between, Einstein had described a good theory of the photoelectric effect, which seemed to require that light be in finite packets, that we now call photons.

Photons are usually small in terms of the energy they convey. As mentioned above, the yellow-green color seen at 550 nm wavelength is carried by photons with an energy of 2.254 eV (electron-Volts). An eV is a 6 billionth-billionths of a joule, and a 1-watt current is defined as one joule per second. But molecules are also small, and the energies that underlie their structure are similarly small. UVb radiation from the sun, just half the wavelength, and thus twice the energy, of "550 nm yellow-green", breaks chemical bonds in your skin, causing damage that can lead to cancer. So use sunscreen! (The middle of the UVb band is close to 275 nm, with a photon energy near 4.5 eV; more than enough to knock a carbon-carbon bond for a loop.)

Book after book is filled with the stories of the founders and discoverers of quantum physics. This book puts it all into a context that the authors call the Quantum Moment. They use the word "moment" the way a historian uses "era". From 1687 until 1927, the Newtonian Moment dominated about 240 years of physics discovery. Once a critical mass of physicists had to accept that quantum phenomena were real, not just mathematical tricks, the Quantum Moment arrived. The stories of the epic battle between Bohr, who formulated the Copenhagen Interpretation, and Einstein, whose work stimulated Bohr and others, but from which Einstein then recoiled, is told here with more feeling and clarity than any other I've read.

Scientists have an emotional bond with their science. For many of them, it is their church, which they defend as keenly as any ardent fundamental Christian defends his church's theology. In the Newtonian Moment, phenomena whose initial state could be perfectly described were thought to be perfectly predictable. The math might be gnarly, but it could, in principle, be done. Quantum theory, and then quantum mechanics, blow by blow cracked open this notion and showed it to be a fantasy.

This is not just the problem of imperfect knowledge, rounding errors, or the need to simplify your equations to make them solvable. Heisenberg's Uncertainty Principle is not just a description of the way a measurement apparatus "kicks" a particle when you are measuring its location or velocity. What is Uncertain is not your measurement, but the actual location and velocity of the particle itself, at least according to Bohr. One implication of this with more recent application is the "no-quantum-cloning" principle, which makes certain applications of quantum computing impossible. However, they also make it very possible to create unbreakable cryptographic codes, which has the governments of the world (or their equivalents of our NSA and CIA) all-aquiver.

Then there's the cat. The authors give us the luscious details of Schrödinger's Cat satire, which he proposed as a slap against the notion of an "observer". Bohr and others needed some instruction from optics: every quantum particle is sensitive to, very literally, everything in the universe. All at once, and with no apparent limitation set by c. Heck, half the time, the cat is the only observer that matters. The other half, the cat is dead, and it ceases to matter to him. But, the authors point out, the air in the box is an "observer": the exchange of oxygen, water and carbon dioxide around a breathing cat are quite different from those near a dead one. So all we can say from outside the box with the cat in it, is that we can't decide the status of the cat without looking inside. We just need to remember that the term "observer" is very squishy.

I recall reading that even a pitched baseball has a "wavelength", according to the deBroglie formula. It is really tiny, only a few thousand times larger than the Planck limit of 10-35 cm, in fact. That means the deBroglie wavelength of a jet aircraft is much, much smaller than the Planck limit, which is why "real world" phenomena are easily treated as continuous for practical matters.

But the Cat, and the Uncertainly limit, show that the boundary between quantum and "classical" worlds is hard to pin down. Since that is the core of the Copenhagen Interpretation, it is seen to be weak at best, and in the eyes of some physicists, simply wrong. But there is no well-attested competing theory.

We must remember that the theories and mathematics of quantum "stuff" describe lots of "what" and a little bit of "how". They tell us nothing about "why". We don't know why there is a Pauli Exclusion Principle, that two electrons, and two only, can coexist in an atomic "s" shell, but only if they have opposite spins (and that "spin" is oddly different from the way a top spins). But we do know, that if it were not so, atoms would collapse in a blast of brightness, almost immediately, and the universe would collapse back into a reverse of the big bang, all at once and everywhere.

One scientist's work is not mentioned in this book, probably because he wasn't directly involved in the quantum revolution. But his work is pertinent in another way. Kurt Gödel formulated his Incompleteness Theorems in 1931, early in the Quantum Moment. Together, they show that no mathematical system can "solve" every problem that can be stated using its postulates, and that no mathematical system can be used to describe its own limitations. For example, there are rather simple polynomials that can be formulated using Algebra, but can only be solved using Complex Analysis. Even weirder if you know only Algebra, the simple formula X²=1 has two answers (1 and -1), but we tend to think that Xⁿ=-1 has only the answer -1 when n is odd, and is "imaginary" when n is even. But in Complex analysis, when n=3, for example, there are three answers, two of them involving an "imaginary" part.

At present, then, science has three boundaries to infinite exploration:

• Heisenberg Uncertainty. You can't know everything to infinite precision.
• Schrödinger Undecidability: You can't predict quantum phenomena on a particle-by-particle basis. Even if you could escape the Uncertainty Principle, you couldn't do anything of great use with the results (which would fill all the computers in the known universe, just describing a helium atom to sufficient precision).
• Gödel Incompleteness: You can't solve most of the questions being asked in the framework of quantum mechanics, not now, not ever, using the methods of quantum mechanics. QM appears to be the most Gödelian of mathematical systems, in that it asks so few questions that can be answered!

For scientists who grew up in the Newtonian Moment, it is like finding out that your church has no roof, and the rain and raccoons are getting in and taking over the place. No wonder Einstein was upset! We are in the Quantum Moment, nearly 90 years into it, and it may be another century or two before a new Moment supersedes it. Get used to it.

Everything affects everything

kw: book reviews, nonfiction, quantum mechanics, quantum theory, entanglement

A couple of quotes are in order:

"Entanglement is not one but rather the characteristic trait of quantum mechanics." —Erwin Schrödinger

"The Universe is not only queerer than we suppose, but queerer than we can suppose." —J.B.S. Haldane

Mathematics professor Amir D. Aczel, whose books illuminate the mysteries of science and mathematics for "the public", has tackled the fundamental scientific mystery in Entanglement: The Greatest Mystery in Physics. He has taken on the unenviable job to explain something nobody can understand to everybody else. This is truly to unscrew the inscrutable!

"Entanglement" has a specific meaning in physics. Certain processes, such as the mutual annihilation of an electron and a positron, or the two-photon cascade in the decay of "excited" states of many kinds of atoms, produce a pair of photons that have exactly opposite values of certain quantum properties such as spin or polarization. Then, if you measure the property of one of them, you know that the other one has the opposite property. This is most of the aforesaid meaning; to make it complete, two provisos are needed: firstly, that entanglement is possible between more than photons, but also electrons and any other kinds of particles that can be produced in such linked pairs (for example, the Cooper Pairs of electrons that make superconductivity possible); and secondly, that the actual values of the property to be measured exist in superposition on both particles, until a measurement is taken on one of them, and then in some way the other particle takes on the opposite property, instantly, with zero delay. This last proviso, the core of the Copenhagen Interpretation, is what so bothered Einstein, and he went to his grave believing it could not be so. He called it "spooky action at a distance".

Dr. Aczel uses twenty chapters filled with stories, mini-biographies, explanations, and an occasional formula, to tease out the development of the ideas and experiments that have led to the inescapable conclusion that entanglement really occurs, and that there are not some "hidden variables" that determine the values we will measure at the time of our choosing. This is a subtle point, and one I find hard to imagine, let alone describe.

However, superposition of states is not confined to entanglement. It is everywhere. It is the reason we cannot see with infinite clarity. We call it diffraction. Most people never encounter diffraction to any bothersome extent. But anyone who owns a microscope or telescope knows about it. However, you don't even need one of those. A pinhole will do.

Try this. Take three pieces of aluminum foil a few cm in size. For ease of handling, make suitable holes in cardboard and tape the foils over the holes. Pierce one with a 3-penny nail or a sharpened piece of 14-gauge wire. If carefully done, you get a 2mm hole (what works best for me is holding the foil against a piece of Styrofoam to pierce it). Pierce the second with the thinnest pin or needle you can find. With luck, you can make a hole in the range 1/2-3/4 mm in diameter. With the third, hold it against a piece of glass, and just barely poke it with the tip of your sharpest pin. You may need to twist the pin to get the point to just go through. With luck, you will get a hole 1/10 mm in diameter. In a darkened room, shine a flashlight through the largest hole, holding it about half a meter from the wall or a light-colored surface (such as a piece of paper taped to the wall). The light spot will be about the same size as the hole. Then shine the light through the middle-sized hole. The spot will be dimmer, but nearly the same size; definitely larger than the hole itself. Now shine the light through the third, tiny pinhole. You may not see much at first. Move the hole closer to the wall until you can see the spot. Even with it held rather close to the wall, the spot will be much larger than the pinhole, and may be as much as 5mm across.

It is a matter of ratio. The width of the spot divided by the distance between the hole and the wall is the same as the diameter of the hole divided by the wavelength of the light. A 1/10 mm hole is 100 microns. Yellow light has a wavelength of 0.6 microns, so the ratio is about 160:1. If the hole and light are held 500mm from the wall, the spot's size will be about 500/160 or 3mm. Now, why are tiny photons, with a wavelength of 0.6 microns, disturbed as they pass through a hole so much larger than they are? Amazingly, even the Hubble Space Telescope, orbiting above the blurring atmosphere, with a mirror whose diameter is 2.4m, disturbs the photons entering its aperture such that it cannot see with infinite clarity, but has a "figure of merit" of about 1/25 arc second at visible wavelengths. It cannot record an image with details smaller than that. Thus, when it looks at a galaxy a billion light years distant, the smallest features seen in the images it records are nearly 200 light years across.

The quantum mechanical explanation for diffraction is that the photon (or any other moving particle) has a rather diffuse "edge". Though it's wavelength is less than a micron, it has an extension and can "feel" the size of a hole it is passing through. The full consequence of diffraction is that there is no limit to the size of the "hole" that a moving particle can "feel". This has also been confirmed with electrons. An electron microscope makes much sharper pictures, and thus can be used at much greater magnification, than an optical microscope. However, even electrons with a wavelength (called the de Broglie wavelength; it depends on mass and velocity) of 1/10,000 micron are diffracted as they pass through the aperture in the magnetic lens of an electron microscope, so it takes rather clever (and large) design to make an electron microscope that can directly see atoms. But this has been done.

Suppose there were no diffraction at all? Then, even a small telescope could see to the ends of the Universe. The Hubble, being above the atmosphere, would be able to see aliens walking on the surface of planets anywhere in the visible Universe, depending only on the cost of making lenses that could increase its angular magnification by a factor of a few million or billion. In fact, your 1/10 mm pinhole could be a telescopic camera. Just put film a meter or so away from the hole (in a dark box), put it on a stable mount (with a clock drive if you are looking at stars), and expose for a long, long time, because you are gathering so little light. No matter how far away you put the film from the pinhole, the spot would be 1/10 mm across, so for higher resolution, just go longer. But even a "pinhole telescope" one meter long would have an effective f/ratio of 10,000. It would take a very long exposure even to make an image of the sun! That's the main reason professional telescopes are wide, to gather more light.

Diffraction implies that every moving particle is affected by everything in the Universe! On page 127 of Entanglement, an illustration shows an electron passing by a closed cylinder. There is a magnetic field inside the cylinder, but not outside. Still, the electron's motion is affected by the magnetic field. Some part of the electron's wave nature still enters the cylinder, even though it may pass by some distance away (the distance used in the experiment is not stated, but is likely to be a few mm).

I think you can see from the above discussion that I view the essence of quantum mechanics to be non-locality. Every photon, every electron, every atom or molecule in an "atomic beam" experiment, even every Buckyball (C60 molecule) in an experiment Aczel describes on p24, is "spookily" connected to the entire Universe!! Entanglement is simply one rather puzzling embodiment of such connections.

OK, why doesn't a jogger's direction get "disturbed" while running between two buildings? The jogger's de Broglie wavelength is about 10-³⁶m. The ratio is so huge, that the runner, aiming for the middle of the sidewalk half a block ahead, will only "miss" by a trillion-trillionth of a mm. Not enough to notice. And the jogger will take a few dozen steps in that same half block. The disturbance of each step, and ensuing corrections by the jogger, make the only effective difference.

There is another large-scale effect that shows why Star Trek teleportation is unlikely. Quantum entanglement makes it possible to "teleport" certain quantum properties, such as spin or polarization, from one particle to another, effectively making particle #2 identical to particle #1 (while destroying that property for #1), but in a different location. In effect, particle #1 jumps from the first location to the other, instantaneously. What about multi-particle systems, such as a human body? The number of protons and neutrons and electrons in a human body of, say 50kg mass (my wife's size), is about 6x10²³ times 50,000, times 1.7 (for the electrons), or about 5x10²⁸. That is, 50,000 trillion trillion particles. You have to measure not just spin or polarization, but identity (proton, neutron, or electron), location (to the nearest nanometer, or maybe to the nearest femtometer, I am not too sure), and velocity for each and every one of them, and take no more than about a millionth of a second to do so, then perform the quantum transportation to that number of particles at your target location. The measurement operation would effectively focus many quadrillions of quadrillions of watts of energy on that 50kg body, and vaporize it in much less than the millionth of a second it takes to make the measurement. It would be greater than a multi-megaton nuclear explosion. Neither the Enterprise nor the planet you were sending Captain Kirk to visit would survive intact.

The explanations in the book are clear, or as clear as possible for our limited mind to take in. To be sure, the experiments that confirm that entanglement really takes place do not give us any indication how or why it occurs, they just confirm that it does. Practically speaking, "why" is a theological question anyway. Science describes, and to some extent it can predict (that is what theories are for). And, to a lesser extent, it can enable technological achievements. Will a "quantum computer" or "quantum encryption" become practical, using equipment smaller than a battleship, or perhaps a kitchen stove? Possibly. Unlikely in my view.

Schrödinger's camera

kw: observations, physics, quantum theory

OK, I reckon most folks know the thought experiment called Schrödinger's cat: A cat is put in a box with a glass jar of cyanide and a hammer that will be dropped on the jar if a signal is received by a Geiger counter. A radioactive source is used that has a 50% chance of emitting a particle into the receiving window of the Geiger counter within the next hour. After one hour the radioactive source is removed and the box is opened. Is the cat alive or dead? Before you opened the box, was the cat either alive or dead, or in some combination of states?

Schrödinger intended this as a bitter joke, but it has deep philosophical implications, according to physicists. It emphasizes the rôle of the "observer" in quantum events. According to the dogma I was taught, until a quantum event, or an event governed by a quantum event, is "observed", all possibilities exist in some superposition of states, and only when an observation is made does this superposition "collapse" upon one of the possible final states, in a random fashion. Does that mean that the cat in the box doesn't either live or die until an observer opens the box? More to the point, is the cat an observer? Or does observation require human intelligence, or that very loosely defined quality, "sentience"? (or the equally fuzzy "consciousness" … I think cats are conscious, but …)

Let's go further. Suppose the box is to be opened automatically, and a camera takes a picture of the inside. Hours later the experimenter develops the camera's film (or, if it is digital, puts the picture in a computer to look at it). Does the dead/alive superposition persist until the experimenter (or any other conscious being) looks at the picture?

I resolve the dilemma this way. Consider diffraction. When light passes an edge, some is scattered into the shadowed area. By using a laser beam and a razor blade you can verify this for yourself. Not only that, with a sensitive detector, you can determine that some tiny amount of light is diffracted even if the visible beam entirely misses the edge of the blade. The amount depends on the magnitude of the "miss". Now consider the diffraction pattern itself. Perhaps it is just seen on a screen, or a scan by a detector yields a string of numbers representing the brightness of the beam at various points. Is the same diffraction pattern there if the detector, and you, are absent? If a specific small area is seen to receive 0.001% of the laser beam, does it continue to do so when you and your detector are absent? I happen to think it does.

This shows that the "observer" rôle must be conferred upon any object that is capable of affecting the path of the photons of the light beam. Since the quantum wave function is typically nowhere zero, that means that every particle in the universe is an observer. The universe doesn't need us or other "conscious" or "sentient" observers. It observes itself, and it does what it does whether we exist or not.

Thus I contend that there is no superposition of states to collapse. Every particle, whether lepton or boson (or mysterious dark matter particle), is continually influenced by every other particle in existence, and not just by its gravitational force. The probability that a particular influence will make a measurable effect on the particle's position and velocity at some future time is proportional to the distance between them, and to the sensitivity of the measurement, with the understanding that the measuring apparatus also influences the particle. For example, when you move a razor blade closer to or farther from a laser beam, the blade is part of the measurement, and so are you. Your position in the room influences things, though your detector may not be sensitive enough to record it. And just by the way, the laser "beam" is simply the brightest part of a photonic phenomenon that fills all space, or will if given time enough.

Going further than this leads to madness. I'm glad I got that off my mind.

Is an observer needed?

kw: science, quantum theory

After writing yesterday's review of The Age of Entanglement, I continued thinking about the issues raised by entanglement and the "observer problem" that is at the root of the disagreements over the philosophy of quantum theory.

One of the thought experiments that probes the issue is Schrodinger's Cat. A live cat is placed in a box that contains a tiny bit of radioactive material, a detector, and some means of the detector triggering the release of poison gas when the detector detects a radioactive decay. The amount of radioactive material and the placement of the detector are designed such that there is a 50% chance the device will trigger within one hour.

When the box is opened after one hour, is the cat alive or dead? Just before you open the box, in what state is the cat? According to some interpretations of quantum mechanics, the cat is in a superposition of states, both dead and alive. Opening the box to observe the cat "collapses the wavefunction" (is there meaning in those three words?) and produces either a dead cat or a living cat, out of an ambiguous state.

Then there is an extension of the matter, the "Wigner's friend" version: Wigner steps out of the lab, and while he is gone, his friend performs the experiment. Well after the hour has passed, Wigner returns, to be told the result by his friend. Now we are one step removed. Before Wigner returns, is his friend in an ambiguous state, a mixture of happy over a live cat and sad over a dead one? Does some wavefunction collapse when Wigner returns?

I always ask, "How about the cat? Is it an observer?" I guess the answer is, "Not to a physicist." But to me, the detector is an observer! It observes the radioactive decay (or not) and takes action accordingly. You could replace it with a piece of sensitive film, and develop the film. There will be a spot, or there will not be a spot. Does the spot exist before the film is developed? When does the wavefunction collapse? Whatever that might mean, I say it collapses when the particle's motion is diverted or stopped.

Consider interference, whether carried out with light (photons) or electrons, or even with viruses (this has been done!). Let's use electrons. A beam of electrons passes trough one very small hole, which leaves a coherent, spreading beam. This then strikes a plate that contains two holes or slits. A photographic film placed a suitable distance beyond the two slits is exposed for a while, enough time for many thousands of electrons to strike it. Then it is removed and developed. The banded pattern that shows up on the developed film indicates interference, that the electrons behaved as waves when passing through the slits.

It is easy to figure out how to lower the current in the electron beam such that the electrons arrive one at a time; indeed, such that there is never more than one electron anywhere in the whole beam, from emitter to film, at any particular time. It takes a long time to gather thousands of "hits" on the film, but what do we see when the film is developed? We see the same banded pattern. This has been done. It seems to prove that each electron somehow goes through both slits and interferes with itself! Yet the banded pattern is made up of many tiny dots, each indicating where an electron struck the film. They just didn't strike the film in the "low" bands, and they did strike in great numbers in the "high" bands.

Where is the observer in this? Is it the person who develops the film? Is it the film itself? Crucially for this setup, if no film is put into the path of the beam, do the electrons still pass through space as a fan of narrow beams that would produce a banded pattern if film were ever put into place? I say they do, but some interpreters of quantum theory say that there is no pattern unless something is there to record it. And that shows just how crazy this all can get.

Actually, there are a few things that are already "observing" the electrons! The first hole, that spreads the beam and makes it coherent, has "observed" the positions of electrons and selected only certain ones in a narrow range of positions. This, by Heisenberg's Uncertainty Principle, deflects them, though they have not, it seems, "touched" the edges of the hole. In actuality, they must have done so, their wave nature "feeling" the size of the hole so they'll "know" just how much to spread out! Sorry for the anthropomorphism here, but it is by far the briefest way to describe what is going on.

Then there are the two holes or two slits that turn a portion of the beam into two beams that can interfere with one another. They also "observe" electrons, and select certain ones which are in the "right" range of positions to pass onward.

This leads to my conclusion: anything that disturbs a particle's motion can be considered an observer. The universe was ticking along quite nicely for a long, long time before there were brainy macroanimals about who could think they were somehow privileged to be "the observers".

And one more consequence of the Uncertainty Principle: no particle is ever at rest. When a barrier "stops" a particle, that particle is either destroyed or it takes up a different kind of motion within the material of the barrier. Typically, bosons such as photons, if they are not reflected or refracted, are destroyed and turn into phonons (heat), while fermions such as electrons or protons "join" the material of the barrier, where they either travel through the bulk thereof or become bound in some way and take up vibratory motion that accords with the temperature of the material (they also release some of their kinetic energy as phonons). Even at "absolute zero" (0K), a little jitter remains, having the value of Planck's Constant divided by two pi. So I conclude that a particle has no existence unless it is in motion. Perhaps a "particle" is simply kinetic energy objectified.

Light behaving badly

kw: book reviews, nonfiction, science, quantum theory, biographies

I could never be a quantum mechanic. I have read and studied the subject on and off for more than forty years, and while I have become comfortable with many of the concepts, a number of things simply elude me. To approximate something Niels Bohr said, "If quantum theory doesn't seem crazy to you, you don't understand it."

The Age of Entanglement: When Quantum Physics Was Reborn, by Louisa Gilder, has clarified a point or two for me, but made the subject seem crazier than ever. I wonder how crazy it would seem if I did understand!

The focus of the book is, as the title states, the continuing struggle to understand entangled quanta, a fierce, emotional, eventually nearly no-holds-barred battle between those who, following Einstein (and the "EPR" paper by Einstein, Podolsky and Rosen) consider quanta to have real positions, velocities, and other "quantum states", which are partly hidden to our clumsy means of measuring them; and those who follow Bohr and consider that such quantities do not exist until they are measured. This latter is the Copenhagen Interpretation.

The question is not yet fully answered, decades after the deaths of the original knights in this battle. But as the book relates, physicists are closer to an answer since the work of John Stewart Bell and his "Bell's Inequality", the clearest statement of what must be true if "hidden variables" genuinely exist.

This is the machine that first peeled back the covers a bit to indicate that Bell's Inequality is violated. We'll see in just a minute how crazy that is. It is a pity that Bell did not live to see these results; he died at age 62.

The small mechanism at the center produces a stream of very thin Calcium gas, which a lamp illuminates to send an electron in each of many of the atoms "up" two levels, which then drops back "down", one level after another, releasing two photons as a quick cascade. The illuminating light is ultraviolet (high energy), and the "cascade" photons are green and blue, with energies that add up to that of the original UV photon. The principle of conservation of angular momentum requires that the two photons be polarized at right angles to one another.

The big tapered sections contain glass plates that gradually polarize the light before each photon is counted by a large phototube at each end. In this case that means that certain photons get through, and others are blocked. The Heisenberg Uncertainty principle means you can't measure everything you'd like to with sufficient precision on a single pair of photons, so the experimenters (Clauser and Freedman), had to gather statistics from many pairs of photons. Depending which way the polarizers were set, Bell's Inequality predicted there should be certain ratios of photons of each color detected.

The rival theory, based on the Copenhagen (Bohr's) interpretation, predicted that the ratios ought to be larger at certain angles, compared to the Bell prediction. This is how the experiment turned out! Now let us see how crazy that is.

Suppose you have a room full of people, with plenty of diversity. Pick three "variables" that can be expressed in pairs: male/female, tall/short (cutoff at, say, 1.66m for both men and women), and right/left handed. This groups everyone in the room into one of eight groups: MTR, MTl, MsR, Msl, fTR, fTl, fsR, fsl. Bell's Inequality states that, for three quantum variables, A(not b) + B(not c) is greater than or equal to A(not c). Using "x" to refer to an unknown state, and >= to mean greater than or equal to, we can state the People Inequality thus:

Msx + xTl >= Mxl, or "Short men plus all tall, left-handed people will equal or outnumber the left-handed men." It sounds obvious, perhaps, and perhaps not. But it is proven thus:

Msx = MsR + Msl
xTl = MTl + FTl
Mxl = MTl + Msl

Look carefully: The left side includes both MTl and Msl, plus two other groups, while the right side includes just MTl and Msl. Only if MsR and FTl are zero will this be equal, otherwise the left side is certain to be greater. It cannot be less.

The violation of Bell's Inequality is like this: Suppose out of 30 people, those in Msx + xTl number 12. Then you ask just the Mxl people to gather, and you count 14! How did that happen? In the case of people, somebody lied (at least two people). But for photons, that is what the experimenters claim happened. I told you it is crazy!

This is supposed to prove entanglement, that measuring one of the photons forces the other one to have a particular state when it is measured, with greater probability than if "hidden variables" were determining the result. Quite a number of experiments, with better apparatus, and lasers and so forth, have been done since the contraption above was built in 1969. The result has been verified. Not only so, entangled photons are now routinely sent opposite ways through kilometer-long light fibers, and practical use will soon be made of them to encrypt messages in ways that cannot be broken. Entanglement is also behind the attempts to produce "quantum computers", which will be able to crack any encryption technique that doesn't depend on quantum entanglement. They will also be able, perhaps, to solve other "NP complete" problems that currently could not run on any conceivable "ordinary" computer in less than millions of years.

My mind boggles. Fortunately, being boggled was a pleasant experience in this case. I confess, when I started the book, I read the author's introduction, that she had written many conversations in a semi-fictionalized way, reconstructing them from letters between the persons, and I thought I would quickly get tired of that and give up after a while. However, the writing drew me in; the author doesn't overuse such conversations, and she really does give us a flavor of the way science is carried on among brilliant, passionate advocates for various points of view.

The book, centered on the breakthrough by Bell and his followers, and on the experiments that tested his work, helps me (a little bit) to understand the total weirdness of quantum theory. I can now better accept that certain difficult ideas are so, but I still cannot say why. Then again, neither can anyone else!

Switching in less than a jiffy

kw: observations, science, physics, light, quantum theory

I'm reading a book about the historical development of quantum mechanics and entanglement. A review will appear in a couple more days; science histories take a while to read. I found fascinating the passionate debates engaged in by Bohr, Einstein, Schrodinger, Born, Ehrenfest, Heisenberg and others about what is really going on with quanta such as photons or electrons. Until deBroglie showed that the electron had a wave nature, it was not even considered a quantum.

As an objectivist (but not of the Rand variety), I am most compelled by things that actually happen. At root, a quantum behaves according to the kind of observation made upon it. The wave nature of photons, for example, is responsible for their ability to diffract when passing near an edge, to produce interference patterns, and to be refracted at the interface between differing media. The particle nature of photons is responsible for their ability to be detected by a photocell, a grain of silver chloride in photographic film, or even the retina of the eye.

The photons of light that form an image in your eye are focused as they enter the eye through the cornea, diffracted more or less by passing through a pupil of variable size, and focused more by the lens in the eye. For all these interactions, their wave nature prevails. Then, the energy of each photon is deposited in a dye molecule in a rod or cone cell, where it causes an electron to change its energy level. The electron then releases this energy into a nerve cell, which is now in a form that the brain can detect. The interaction with the electron depends on the photon's particle nature.

At one spot, the photon is behaving as a wave; at another less than 20mm away, it is behaving as a particle. At the speed photons travel through the eye (about 3/4 of their speed in vacuum), the "wave" interaction happens about 90 trillionths of a second before the "particle" interaction.

But that is from our point of view. What about the photon's "experience"? According to the theory of relativity, since a photon always travels at the speed of light, it experiences no passage of time; its "clock" is always stopped. From the time it is emitted, through its travels that possibly include reflections and refractions, until it is absorbed and moves one or more electrons about, the photon cannot experience anything but a timeless instant…speaking with gross anthropomorphism, of course! No matter "where" the points of emission and absorption may be, however far they may be separated, emission and absorption plus everything between are a single event.

There are several mysteries here, and though Heisenberg, Schrodinger and others developed ways of describing them mathematically, mysteries they remain. Yet the vision of every sighted creature (plus many other phenomena) depend on them, particularly on the dual nature of the photons.

Quantum giants humanized

kw: book reviews, nonfiction, quantum theory, scientists

A "simple" thought experiment: Suppose the Universe consisted of four items, two moving particles, an edge, and a sensitive screen. The first particle moves past the edge and strikes the screen. The second particle, moving in exactly the same path as the first as it approaches the edge, moves past the edge and strikes the screen.

The salient question: Does the second particle strike the screen at the same spot as the first? This question cannot be answered. Suppose both particles do strike the same spot on the screen. We must first ask, How can we know whether the two particles actually followed the same path?

The concept known as Heisenberg's Uncertainty Principle states that we cannot measure both the position q and the momentum p (including direction) of any object with infinite precision. Heisenberg quantified his insight: pq≥ћ, where ћ is Planck's Constant, a very small quantity that has popped up everywhere since Planck first derived it to describe the quantization of "blackbody" radiation.

The philosophical question: does the attempt to measure either q or p by itself affect both quantities so that we can't be sure of their values, or do these quantities have a built-in "fuzziness" that attempts at measurement simply unveil?

In 1926 and 1927 Neils Bohr and a number of the giants of theoretical physics wrestled with the implications of quantum mechanics and quantum theory, and produced the Copenhagen Interpretation, which decided in favor of the latter, and furthermore, requires the presence of an "observer" to discern the result.

My own dissent against the Copenhagen Interpretation is this: In the thought experiment above, the Edge is "observer" enough. Its presence affects the path of the particle. No matter how far the particle "misses" the edge, its path will be changed, it will not continue as if there were no edge.

There is also some finite probability that the screen may record nothing. That is, the equation that describes diffraction near an edge has a sinusoidal shape of decreasing magnitude, but while that magnitude is zero for a series of angles, it is nonzero at all points except that specific series of angles, even near 180º.

Well, I may rant about these things further some day. These are some thoughts that arose after I finished reading Faust in Copenhagen: A Struggle for the Soul of Physics by Gino Segré. This book actually says little about such things. Segré presents to us the persons involved.

It is a combined biography, first of seven giants of quantum physics (Niels Bohr, Paul Ehrenfest, Lise Meitner, Werner Heisenberg, Wolfgang Pauli, Paul Dirac, and Max Delbrück), then to a lesser extent, of their collaborators, including Albert Einstein, Max Planck, and Enrico Fermi.

I'd always thought Bohr something of a jerk. I just knew the stories of his notorious tendency to argue until his opponent collapsed. Indeed, once when Heisenberg fled to his bed, Bohr sat at his bedside and argued him into insensibility. I never wondered why they tolerated it and came back for more. They loved him...no, they adored him. They knew he loved them even more.

The author, nephew of Nobel laureate Emilio Segré, a lesser giant among these titans, shows Bohr as a family man (he and Margrethe had six children, including a son who won a Nobel of his own), one whose "family" included dozens of physics students. Niels Bohr is the prototype of the scientist who needs others to do his science. He simply had to discuss in order to think. So if you went skiing with him, you could be sure of plenty of physics with your evening toddy.

Even the more, this collective biography shows that genius isn't the unique possession of any personality type. Paul Dirac was the nearest thing to a Vulcan, Paul Ehrenfest was insecure and eventually suicided, and Wolfgang Pauli could be as caustic as Jackie Leonard, yet was almost as beloved as Bohr.

The human side of science is clearly shown in books written in 1929-30 by Heisenberg, Pauli, and Dirac. Their subject and goal is the same, and their understanding of the subject was equivalent, but only Dirac's The Principles of Quantum Mechanics is still in print and in use. What they say is much the same, but the way they each connect with the reader differs. It is paradoxical that Dirac, the least personable, has the clearest writing style.

And what of the book's title? The last major meeting that the seven were supposed to attend (Pauli had to miss it) was Bohr's Copenhagen conference of April 1932. Those attending wrote and produced a skit, as they had before. This one was based on Goethe's Faust, in which the Lord (Bohr) and Mephistopheles (Pauli) dispute the fate of Faust (Ehrenfest). Quotes from Goethe's play are found throughout the book.

By 1932 the Copenhagen Interpretation was considered settled truth by most (Einstein was a notable exception). The skit was a loving look back at the wrangling that produced it, a chance to blow off some steam and mend fences.

World War II scattered the attendees, and many of them became developers of the nuclear bomb, which made their choice of Faust for their last revel all the more striking.

The second annus mirabilis

kw: book reviews, nonfiction, biographies, physics, relativity, quantum theory

In his famous 1926 protest, Albert Einstein wrote,

"Quantum mechanics is certianly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but it does not really bring us any closer to the secrets of the "Old One." I, at any rate, am convinced that He is not playing dice."

From this comes the title of a valuable, but flawed, book.

Reading Secrets of the Old One: Einstein, 1905 by Jeremy Bernstein was frustrating. I have a pretty good understanding of special relativity (very little, thought, of general relativity, but it wasn't in view here), the photoelectric effect, and statsitical mechanics. The author attempts to make the almost unbelievable work that Albert Einstein did in 1905 accessible to a lay audience. I don't find it illuminating.

The value that Dr. Bernstein brings to this mini-biography—of the 1905 work, not so much the man—is his direct connection to the people involved, his review of the discoveries that did and didn't influence Einstein, and the milieu in which Einstein's work was received. The illustration shows many of those whose work I remember studying decades ago.

After a chapter outlining the history of physics, particularly electrodynamics and mechanics, the three articles Einstein submitted in mid-1905 are discussed, first the paper on Special Relativity (the third in order submitted) plus a small fourth paper that first elucidates E = mc2; second the paper on Brownian Movement, in which he demonstrated the appropriate statistics to show that atomic rather than continuous matter best explained the phenomenon; and third the paper on Blackbody Radiation and the Photoelectric Effect, which won him the 1921 Nobel prize.

A minor frustration with the book is that it was poorly proofread. Both Bernstein and his editor (was there one?) seem to think that the past and past participle of "lead" is "lead", rather than "led". This mistake is quite consistent. Comma misuse and sentence fragmentation is rampant. I corrected very few items; in most books I read, I correct all; the volume was too distracting.

The major frustration is a great tendency to assert results with little or no justification. For example, in several pages of explanation of the simultaneity versus non-simultaneity experienced between to systems in relative motion, the reasons for the difference in perception are only sketchily described, where a simple statement that, for example, "For the signals from two events to be perceived as simultaneous in System 2, they would have had to occur at equal distances from the receiver. The geometry as seen from System 1 shows that they occur at different distances." Throughout that chapter, the rotation of axes that causes geometry and time to influence one another is poorly explained.

Thus, whereas I began hoping to learn more of Einstein's thought, I instead learned more of his social circle, which is not in itself a bad thing.