v1.0.1 / chapter 13 of 20 / 01 sep 07 / greg goebel / public domain
* Prewar work on a quantum theory of electromagnetism had been stalled by theoretical difficulties and then the distraction of World War II. After the war, the work of Dick Feynman and others led to the construction of a (mostly) satisfactory theory of "quantum electrodynamics (QED)", which would become the model for quantum theories of other forces. It also led to the concept that the vacuum itself is full of energy, though the idea of "zero point energy (ZPE)" is still hotly debated.
* As mentioned earlier, Paul Dirac had more or less discovered the positron in the late 1920s while he was conducting studies to describe the electromagnetic field in a quantum context, with "virtual" photons acting as the carrier of an exchange force binding together or repelling electrically charged particles. His original cumbersome (if entertaining) notion of the existence of a universal sea of negative-energy electrons had been discarded, but progress on a satisfactory theory of quantum electromagnetism proved slow. Heisenberg, Pauli, and Oppenheimer tried to extend Dirac's ideas but kept running into roadblocks in the form of unresolvable infinities, caused by the electromagnetic interaction of the electron with itself. With the coming of World War II, physicists had other things to worry about for a while, and there was also a sense of frustration that it was all a dead end.
The breakthrough took place in 1947, when the American physicist Willis Lamb (born 1923) and his colleague Robert Retherford performed studies of the energy states of the hydrogen atom, showing there was a previously unknown "splitting" of energy states, meaning that where there had been thought to be one energy state there was actually two. The difference between these two states became known as the "Lamb shift". Lamb would share the 1955 Nobel prize in physics with the German-born American physicist Polykarp Kusch (1911:1993), who had performed similar studies in parallel with Lamb. A British researcher had actually discovered the shift earlier, but his professor convinced him that he had made a mistake.
The discovery of the Lamb shift provided a clue to the interactions of light and electrons; as theory stood at the time, there was no provision for it, and simply fitting into the theory showed that the Lamb shift should be infinite. This might have seemed like more frustration, but in fact the value of the Lamb shift opened the door, suggesting that trickery invoked to give the proper value might just get things on the right track. Another contemporary discovery, a much-improved measurement of the magnetic moment of the electron performed in 1948, also provided a useful constraint.
The theoreticians eliminated the infinities through a process called "renormalization" in which one infinity was nulled out by another to give a specific value. Since that is a mathematically ambiguous operation, the equations had to then be constrained by the values of known results to get them to work. It was an ugly approach, but it did have the virtue of getting things to work.
There was still the problem that though the results of the system of equations used were consistent with relativity, each of the individual terms was not, which was regarded as unsatisfactory. In the early 1950s, the Japanese physicist Shinichiro Tomonaga (1906:1979), a university classmate of Hideki Yukawa, and the American physicists Julian Schwinger (1918:1994) and Richard Feynman managed to independently come up with a system of equations that were individually consistent with relativity.
The result became known as "quantum electrodynamics (QED)", and Tomonaga, Schwinger, and Feynman shared the 1965 Nobel prize in physics for it. They had to wait so long because Niels Bohr, who was on the Nobel committee, didn't like QED, and it wasn't until after his death in 1962 that QED made it onto the list for consideration. When the prize was announced, Robert Oppenheimer sent Feynman a telegram that simply said: "ENFIN" -- French for "at last".
Tomonaga and Schwinger took a strictly mathematical approach in their studies of QED, while Feynman took a more easily understood graphical approach. Feynman described the paths of particles through spacetime with what became appropriately known as "Feynman diagrams". Feynman's approach proved the most popular, possibly partly because he was an outstanding lecturer and could sell his ideas much more easily than most other physicists. Later in the 1950s the British-born American physicist Freeman Dyson (born 1923) would show, not too surprisingly, that the Feynman diagrams could be derived from Tomonaga's and Schwinger's equations.
Of course, even with Feynman diagrams, QED is fairly tough going. After Feynman won the Nobel prize, a TV reporter had the bad judgement to ask him to describe the matter in 20 seconds for the viewing audience. Feynman shot back: "If I could describe it 20 seconds, I wouldn't have won the Nobel prize."
* The electromagnetic field is an interaction of electrically charged particles, with the photon acting as the force carrier. The essence of QED is the interaction of photons and electrons, since once that is understood the interaction of photons and other charged particles amounts to variations on the same theme. Dick Feynman pointed out that the interaction of photons and electrons could be understood in terms of three probabilities:
If these probabilities are known, then the interaction of a photon and an electron can be understood. More complicated systems can be understood, at least statistically, as made up of a set of individual interactions.
This all seems fairly straightforward, at least to someone with some familiarity with quantum physics, but to no surprise to someone with such a background, it gets much more devious. Figuring out the probability of a photon going from point A to point B might seem to start with imagining that the photon travels in a straight line between the two points, but Feynman said that what it really involved was figuring the sum of probabilities of the photon going from point A to point B by every possible path, even ones that are ridiculously roundabout and convoluted. This was an application of what quantum physicists now call the "totalitarian theorem": whatever is not forbidden is compulsory, or in other terms, anything that can possibly happen will happen -- at its appropriate level of probability.
Somebody who knew Feynman suggested that Feynman came up with the idea by simply asking himself: "If I were an electron, what would I do?" Feynman later filled in the answer, which gave an answer that would have almost been obvious to anyone who knew him: "The electron does anything it likes. It just goes in any direction at any speed, forward or backward in time, and then you add up all the amplitudes and it gives you [the answer]."
This is called the "path integral" or "sum over histories" approach, the word "history" in this context mean any of the possible paths of the photon. The approach was not without precedent, since centuries before the great Dutch physicist Christiaan Huygens (1629:1695) had explained light interference effects by summing up the interactions of an infinite number of points making up a set of light-emitting sources.
In more modern terms, it makes a certain sort of sense to anyone who understands the paradox inherent in the two-slit interference experiment, which one of the reasons Feynman said that all paradoxes in quantum physics "were like that". If a single photon is fired at the two slits, then the end result, the interference pattern, has to be understood in terms of two possible paths, one through each slit. Go to four slits, there's four possible paths; go to eight, there's eight; until in the limit of no obstruction whatsoever there's an infinity of possible paths. In the sum, however, the probabilities add up so that the photon appears to go from point A to point B by a straight line.
This concept of sum over histories provides an alternative to the Schroedinger equation and the Copenhagen interpretation, and in fact the sum over histories approach has advocates who insist that it is a much easier way to do things. Instead of a photon or electron or other quantum entity represented as a probabilistic wavefunction and not existing until it is measured, sum over histories says that it exists over all possible paths and the measured value is simply a sum of all those paths.
* Feynman's sum over histories seems at first glance a ridiculous complication that ought to be carved away by Occam's Razor, the principle that logical excess baggage should be discarded, but Feynman pointed out that the QED approach does have specific implications, giving results that are consistent with experiment.
Suppose Alice, our physics student, looks at her reflection of a point light source in a mirror, with a barrier in the line of sight between her and the light source. By classical physics, the reflected light will arrive by a single path, with the angle of incidence equal to the angle of reflection. By QED, however, the light is reflected from every point on the glass, with the angles being any required to allow the light to reach her eye. The sum of probabilities of these reflections ends up giving the same result as classical physics, with the most probable path being the single path with the same angle of incidence and reflection. This is the "least time" path, the path that takes the least possible time of all those available.
This doesn't seem to buy anything either, but now suppose a set of opaque stripes is laid down across the mirror. What this does is eliminate some of the cancelling paths, so the light will be seen coming from parts of the mirror where it could not be seen when the stripes weren't present. The cancellation pattern will be different for different wavelengths of light, effectively separating the colors of a white-light source into a rainbow of its components. This describes a diffraction grating.
This analysis assumes that light travels in straight lines from the light source to the mirror and then in straight lines from the mirror to the eye. Actually, as stated before, it takes every crazy possible path available. The end result of the path integral ends up being the same.
* Of course, the interaction between photons and electrons is closer to the heart of QED. Dirac's original work in 1929 described the interactions between an electron and a photon, but he couldn't get the results to agree very well with experiment. In 1948, Schwinger realized that the problem was that the electron could also emit and reabsorb a photon while it was interacting with the first. This was only one of the possible variations on the theme, and to get the right results meant determining them all and adding up the probabilities. After painstaking effort, the results finally began to converge with experimental reality. Modern results give agreement with experimental results down to ten decimal places. This is about equivalent to determining the accuracy of the distance from New York to Los Angeles to a width of a hair.
Not at all incidentally, the possible variations on the theme can get extremely baroque. For example, a high-energy gamma-ray photon can spontaneously be converted into an electron and a positron -- pair production. Feynman came up with a description of this process that is conceptually elegant if on the bizarre side. He showed that the pair production caused by the gamma-ray photon was equivalent to a collision between the photon and an electron that sends the electron flying backwards in time, which reverses its charge by a certain "double negative" or "taking away negative charge" logic, turning it into a positron; this reversal is referred to as "charge conjugation". The positron moving backward in time then encounters a gamma-ray photon that causes it to recoil forward in time, turning it back into an electron.
The exact same scenario also applied to electron-positron annihilation, just with the time sense reversed. It also applied to electron scattering by a gamma-ray photon, just with the diagram rotated -- incidentally, since photons have neither charge nor time sense, moving at the speed of light, as far as a Feynman diagram goes they can be regarded as moving in either time direction.
The variations on the theme that caused all the trouble with developing QED involved the production and absorption of photons by a single electron, with the photons possibly turning into an electron-positron pair and then back into a photon, and so on. This is where the infinities arose that plagued the theory. The discovery of the Lamb shift helped drive a solution.
The solution relied on what is known as "perturbation theory", which is more a calculational algorithm than a theory as such, a type of successive approximation method. The self-interaction of the electron could be approximated by assuming the simplest possible and most probable interaction, the emission and reabsorption of a single photon by an electron. This would yield an answer, which could then be adjusted by considering the second simplest and probable interaction, the emission of two photons, and adding in that result. Further if increasingly smaller adjustments could be made by considering successively more complicated interactions -- with the probability of such interactions decreasing rapidly as their complexity increased -- until the result of the "perturbation series" no longer changed at the desired level of decimal places. By the end of the 20th century, the perturbation series had been worked out to the eighth level of interactions, which gave a total of almost a thousand distinct interactions.
Renormalization, the nulling of infinities by infinities, was needed to calculate the terms. Unfortunately, renormalization was the sort of approach that might work, might not, and the only reason it could be said to work was because the results agreed with experiment. Mathematicians hated it; Feynman called renormalization "dippy" and believed, as most physicists still do, that QED will be revised in the future to get rid of it. Although Dirac was the intellectual grandfather of QED, he was too much of a purist to ever like renormalization and was very suspicious of QED as it emerged in the 1950s.
Incidentally, the fact that an electron is surrounded at all times by a cloud of virtual particles means that the charge of the electron that is observed by experiment is not the same as the charge of the electron all by itself. This charge, known as the "bare charge", is the one that must be used in Feynman diagrams, while the actual observed charge is known as the "dressed charge". The same concept applies to the electron mass: it has a "bare mass" that is not quite the same as its "dressed mass".
* As something of a footnote to QED, Feynman's development of the theory showed why he was one of the most intriguing figures in science. He came up with the notion of particles moving backwards and forwards in time when he was a graduate student at Princeton, working under John A. Wheeler. Wheeler liked to assign his students difficult problems and then let them go at them, handing out the occasional hint or suggestion as seemed useful.
In 1940, Feynman was tinkering with the electrodynamics of the solitary electron and trying to figure out how to get rid of the ugly infinities, nobody having thought of renormalization just yet. At first, he thought he might overcome the problem by simply assuming an electron didn't interact with itself, but that was a non-starter. A charged particle, even one in relative isolation, has a certain resistance to motion above its ordinary inertia, and it was troublesome to figure out how this "radiation resistance" could arise if an electron didn't have self-interactions.
Then Feynman switched to the opposite approach, assuming there really wasn't any such thing as an isolated electron. Would electromagnetism actually exist if there was only a single charged particle in the entire Universe? Feynman postulated that there needed to be other charged particles, with exchanges of photons between them creating the electromagnetic force. The problem was this was that radiation resistance was an immediate sort of thing -- push an electron and the resistance is there, with no delay of any sort. If it had something to do with exchanges of photons, and if the only charged particles were a distance away, it would seem that the effects would be delayed by the time it took photons to shuttle back and forth.
Feynman's got a leg up on his next step from John Wheeler, and it was a big step indeed. It was known that at the level of fundamental interactions, physics doesn't generally make any distinction about the direction of time. A video of a collision between two particles makes sense whether it's run forward or backwards. Of course, for systems of particles it's easy to see the direction of time, which is in the direction of increasing disorder or "entropy": if a video is made of a sugar cube dissolving in water, it is very easy to tell if the video is running forward or in reverse.
Maxwell's equations, which defined the action of electromagnetism, are time-symmetric, meaning that a video made of the interactions defined by those equations worked as well in forward as in reverse, though it required reversing electric charge -- leading to the concept of charge conjugation discussed in the previous section. One day Wheeler bounced a wild idea off of Feynman, saying: "I know why all the electrons have the same charge and same mass."
"Why?"
"Because they're all the same electron." The idea was that there was only a single electron in all the Universe, bouncing back and forth through time. It was an interesting notion, but the problem was that it implied an equal number of electrons and positrons in our Universe, which didn't seem to be the case even at the time, and which nobody seriously believes now.
In addition, the avenue that Feynman was moving down had been established by Dirac with one goal of consistency with Einstein's theory of relativity. According to relativity, time slows down for an object as it approaches the speed of light. Since light itself of course moves at the speed of light, time doesn't exist for light. From the point of view of a photon, any consideration of time was irrelevant, and so any consideration of the direction of time was irrelevant as well.
Feynman was now able to describe the radiation resistance of an electron as due to interactions with other charged particles, no matter how distant, by assuming an electron emitted photons both forward and backward in time. The photons moving forward in time are known as "retarded waves", since there is a delay between the emission and reception, while the photons moving backward in time are similarly known as "advanced waves".
In early 1941, Feynman gave a lecture on the "Wheeler-Feynman absorber theory", as it was named, to the physics department of Princeton. At the time, Princeton's physics faculty included Pauli and Einstein. Pauli expressed mild, by his standards, skepticism about the notion, but Einstein was intrigued: "No, the theory seems possible." It was grand praise for a graduate student. Feynman's doctoral thesis of 1942 was built around the concept; he then went off to Los Alamos to work on the atomic bomb project, and the evolution of absorber theory into QED would have to wait until the war was over.
* QED might sound muddled and mystical, and in fact when Feynman first told Freeman Dyson about the sum-over-histories notion, Dyson replied: "You're nuts." Feynman himself called it "the strange theory of light and matter." It is "strange" and anybody doing ordinary practical work in optics or electromagnetics or chemistry has little or no use for it. However, it is the "theory of light and matter" that provides a solid theoretical foundation for such work, as well as almost every other phenomena observed in the macroscale except those involving gravity. Such is the power of its methods that it is regarded as one of the "crown jewels" of theoretical physics.
Feynman had an outgoing, egotistical personality and an extravagant sense of humor; he became well-known to the public through a set of books that described his personal adventures and misadventures, such as his hobby of safecracking when he was at Los Alamos during the war. The stories were clearly egocentric and in some cases seem to have had a tenuous relationship to reality. Some regarded Feynman as flamboyant, fun-loving, and direct, while others found him showoffy, volatile, confrontational, and obnoxious. Some of his students were downright terrified of him. Almost everyone admitted he was brilliant: "Like Dirac, only human" -- was how Eugene Wigner, Dirac's brother-in-law, described Feynman.
Freeman Dyson saw both sides of Feynman at the very start, his initial impression of Feynman being that he was "half genius and half buffoon". Dyson would find that the buffoonery was more superficial than the genius. Feynman later bought a 1975 Dodge van and had Feynman diagrams painted on it for all to see. When asked why he had done so, he answered: "Because I'm Dick Feynman."
Although Feynman and Julian Schwinger had a lot in common -- both Jewish, both from the New York City metro area, both the same age -- and fought out their ideas on QED against each other, there was a certain comical clash of styles between the two. Physicists, particularly those at the genius level, are not necessarily "ordinary folks" and may have difficulties being accepted as such by their neighbors. If so, they have a choice of either charging forward regardless or keeping a low profile. Feynman charged. He was extroverted in the extreme, cocky, outspoken, gregarious, casual, and had a knack for communicating his ideas. Schwinger kept a low profile. He was shy, quiet, cool, aloof, was almost always dressed in expensive tailored suits, and drove an immaculate Cadillac.
Schwinger usually rose at noon and worked nights to ensure his privacy, and as a mathematical prodigy from a young age -- one who knew him called him a "Mozart of mathematics", as a high-schooler reading papers by Dirac -- he loved mathematical complexity for its own sake. Schwinger was inclined to make up his own mathematical notations, as if trying to make it harder for people to understand him -- it became known as "Schwingerese" and was a bit of a handicap for his students when they had to deal with the rest of the world -- and he actually disliked Feynman diagrams because they were easier to understand, preferring his own more strictly mathematical approach. In practice, physicists prefer to use Feynmann diagrams for teaching and for investigating ideas, while using Schwinger's equations when "heavy lifting" is required.
Incidentally, although Freeman Dyson never reached a level of influence in his field close to that of the towering Dick Feynman, Dyson wrote a set of highly readable and sparkling popular books, full of brilliantly imaginative speculations, that gave him a comparable level of visibility with the public. Dyson himself commented on the irony that he will almost certainly be much more remembered for his speculative concepts -- such as the "Dyson sphere", in which an advanced civilization dismantles a planet to build a shell around a sun to provide more living space -- than his professional work. A person could do a lot worse for himself.
* One of the implications of QED is that what we think of as empty space isn't really empty at all. Pairs of virtual particles and antiparticles are being created and destroyed all the time, popping in and out of existence so fast that they can't be detected, at least not directly. One of the implications is that there is an energy, known as "zero point energy (ZPE)", inherent in the vacuum itself.
The zero point energy can be detected indirectly, if just barely. The Lamb shift that led to the development of modern QED is due to the ZPE, as is the unavoidable "quantum noise" that becomes a fundamental barrier to sensitivity in electronic and optical equipment. The best known of the phenomena that illustrate the existence of zero point energy is the "Casimir effect", discovered in 1948 by Dutch physicist Hendrik B.G. Casimir (1909:2000).
If two metal plates are set up in a vacuum, they will act as a resonant chamber for virtual photons, and this will result in a faint but measurable net force on the plates. The reason is that in the region between the plates, the electromagnetic waves manifested by the zero point energy cannot have wavelengths longer than the spacing between the plates. This constrains the possible wavelengths of the trapped electromagnetic waves, while electromagnetic waves outside of the two panels are not constrained.
The imbalance results in a very tiny force. Measurements have been conducted using a "torsion pendulum" mounted in a vacuum chamber, with the force exerted between two plate moving the pendulum. The motion was so slight that it had to be measured by using a precision laser system; it was about equivalent to the gravitational force exerted by the entire Earth on an amoeba.
There is a faction of ZPE enthusiasts, including a cadre of science-fiction fans, that still believe there are enormous energies available from the vacuum. In any volume of space, the ZPE could support electromagnetic waves with an infinite number of frequencies, and so could conceivably provide access to an infinite amount of energy. Skeptics believe the infinities are mathematical artifacts that will eventually be eliminated. The presence of infinite amounts of energy built into space itself implies, through Einstein's E=M*C^2 mass-energy relation, a mass of the Universe far greater than that which is implied by observations of the expansion of the Universe, and correspondingly requires a number of awkward assumptions to make observations fit with theory. One critic of the ZPE advocates has countered mildly: "One has to keep an open mind, but the concepts I've seen so far would violate energy conservation."
The uncertainty principle says that the greater the energy of a virtual
particle, the shorter the time it exists, and it is hard to figure out any
way of getting around this obstacle. However, some physicists have
speculated that under the right circumstances a virtual event might propagate
into an entire Universe of its own, as long as the energies balanced out.
Given the Heisenberg uncertainty relation:
delta_energy * delta_time = hbar
-- then if the net energy or "delta_energy" of the Universe is close to zero,
the lifetime or "delta_time" could be be very long. The idea of the
spontaneous creation of the Universe from a fluctuation of the vacuum was
apparently first suggested in a 1973 paper by Edward Tryon of the City
University of New York, in which he dryly concluded: "I offer the modest
proposal that our Universe is simply one of those things which happens from
time to time." He later added: "This proposal struck people as
preposterous, enchanting, or both."
This notion has since been expanded into a vision, most prominently associated with the Russian-American physicist Andrei Linde (born 1948) but not unique to him, of branching trees of universes giving rise to new universes, possibly with different laws of physics, performing an evolution in which some universes survive and others are stillborn. In this view, while our own Universe clearly had a beginning and will eventually have an end, the branching tree of the "multiverse" may have had no beginning and may not have an end.
It might be even possible to force the generation of a new universe, and so it is conceivable that a physicist might be able to play God in an uncomfortably strong sense. Even the most militant atheist might have hesitations about such a course of action, but that issue can be sidestepped for now, since nobody expects to have the capability of performing an experiment along such lines any time soon.
