Indeed, as we will see, in the quantum world both electric and magnetic forces can be thought of as being caused by the exchange of virtual photons. Because the photon is massless, an emitted photon can carry an arbitrarily small amount of energy. Therefore, as the Heisenberg uncertainty principle tells us, the photon can travel an arbitrarily long distance (taking an arbitrarily long time) between particles before it must be reabsorbed in order that the energy it is carrying is returned back to the electron. It is precisely for this reason that the electromagnetic force between particles can act over long distances. If the photon had a mass, then it would always carry away a minimum energy, E = mc2, where m is its mass, and in order for this violation of energy conservation to remain hidden within quantum uncertainties, the Heisenberg uncertainty principle implies that the photon must be reabsorbed by either the original electron or another electron within some fixed time, or equivalently within some fixed distance.
We are getting ahead of ourselves here, or at least ahead of Feynman at this time in his life, but introducing these complications at this point has a purpose. Because if all of this seems very complicated and hard to picture, join the crowd, especially the crowd in the era before World War II. This was the world of fundamental physics that Richard Feynman entered into as a student, and it was a world where the strange new rules seemed to produce nonsense. The classical infinite self-energy of the electron, for example, remained part of quantum theory, apparently owing to the fact that the electron could emit and reabsorb photons of arbitrarily high energy, as long as it did so over very short timescales.
But the confusion was even worse. The quantum theory fit well overall with experiment results. But whenever physicists tried to calculate predictions precisely to compare to accurate measurements—if they included the interchange of not just one photon between particles, for example, but more than one photon (a process that should happen more rarely than the exchange of a single photon) they found that the additional contribution due to this “higher order” effect was infinite. Moreover, the calculations in the quantum theory needed to explore these infinities were harrowingly difficult and tedious, taking the best minds at the time literally months to perform each such calculation.
While still an undergraduate, Feynman had an idea that he carried with him to graduate school. What if the classical “picture” of electromagnetism, as I have described it, was wrong? What if, for example, there was a “new” rule that a charged particle could not interact with itself? That would, by fiat, get rid of the infinite self-energy of an electron because it could not interact with its own electric field. I emphasize that the infinity this new rule was designed to avoid is present in the pure classical theory, even without considering quantum mechanical effects.
But Feynman was even bolder. What if what we call the electromagnetic field, caused by an exchange of virtual photons between particles, also was a fiction? What if the whole of electromagnetism was due to a direct interaction between charged particles with no field present at all? Classically, electric and magnetic fields are completely determined by the motion of the charged particles producing them, so to Feynman the field was itself redundant. In other words, once the initial configuration of charges and their motion is specified, all of their subsequent motion could in principle be determined simply by considering the direct impact of the charges on one another.
Moreover, Feynman reasoned that if we could dispense with the electromagnetic field in the classical theory, this might solve the quantum problems as well, because if we could dispense with all of the infinite number of photons running around the calculations in the quantum theory and just deal with charged particles, perhaps we could get sensible answers. As he put it in his Nobel address, “Well, it seemed to me quite evident that the idea that a particle acts on itself is not a necessary one—it is a sort of silly one, as a matter of fact. And so I suggested to myself that electrons cannot act on themselves; they can only act on other electrons. That means there is no field at all. There was a direct interaction between charges, albeit with a delay.”
These were bold ideas, and Feynman brought them to graduate school at Princeton, and to John Archibald Wheeler, who was precisely the man to bounce them off of. I knew John Wheeler as a most gentle and cordial soul, polite and considerate to a fault, like a perfect southern gentleman (even though he was from Ohio). But when he talked about physics, he suddenly became bold and fearless. In the words of one of his Princeton colleagues at the time, “Somewhere among those polite facades there was a tiger loose . . . who had the courage to look at any crazy problem.” This kind of fearlessness matched Feynman’s intellectual predilections exactly. I remember causing ripples of laughter when I quoted Feynman once as saying in a letter to a potential young physicist, “Damn the torpedoes. Full speed ahead.” Feynman of course was aping Admiral David Farragut, but that historical fact seemed irrelevant. That phrase applied equally well to both Feynman and Wheeler.
It was a match made in heaven. What followed at Princeton was an intense three-year period of intellectual give-and-take between the two resonant minds—physics as it should be done. Neither man would immediately discount the crazy ideas of the other. As Wheeler later wrote, “I am eternally grateful for the fortune that brought us together on more than one fascinating enterprise. . . . Discussions turned into laughter, laughter into jokes, and jokes into more to-and-fro and more ideas. . . . From more than one of my courses he knew my faith that whatever is important is at bottom utterly simple.”
When Feynman first brought his crazy idea to Wheeler, it was not met with derision. Instead, Wheeler immediately pointed out its flaws, reinforcing the axiom “Fortune Favors the Prepared Mind,” for Wheeler too had been thinking along very similar lines.
Feynman had realized earlier one glaring fault with his idea. It is well known that it takes more work to accelerate a charged particle than a neutral one, because in the process of acceleration a charged particle emits radiation and dissipates energy. Thus a charged particle does seem to act on itself by producing an extra resistance (called radiation resistance) to being pushed around. Feynman had hoped that somehow he could resolve this problem by considering the reaction back on the particle, not by itself, but by the induced motion of all of the other charges in nature that would be affected by their interactions with the first particle. Namely, the force from the first particle on the other particles would cause them to move, and their motion would produce electric currents that could then react back on the first particle.
When he first heard about these ideas, Wheeler responded by pointing out that if this were the case, the radiation resistance produced by the first particle would depend on the location of these other charges, which it doesn’t, and moreover would be delayed because no signal could travel faster than the speed of light. It would hence take time for the first particle to interact with the second (some distance away) and even more time for the second particle to then interact back with the first particle—resulting in a back reaction that would be considerably delayed in time compared to the initial motion of the first particle.
But then Wheeler suggested an even crazier idea: what if the return action by these other charges somehow acted backward in time? Then instead of the back reaction of these particles on the first particle occurring well after the first particle had started to move, it might occur at the exact same time the first particle started to move. At this point a sensible novice might say, “Hold on there, isn’t that crazy? If particles can react backward in time, then doesn’t this violate sacred principles of physics like causality, which requires causes to happen before effects?”
But while allowing for backward back-reaction opens up such a possibility in principle, to find out if it really causes problems, physicists must be more precise and actually perform the calculations first. And this is what Feynman and Wheeler did. They were playing around to see if they could fix their problems without
creating new ones, and they were willing to suspend disbelief until their results required them not to.
First off, based on his prior thinking about these issues, Wheeler was able to work out with Feynman almost immediately that in this case the radiation reaction could be derived to be independent of the location of the other charges, and could also in principle be made to occur at the appropriate time, and not at some later, delayed, time.
Wheeler’s proposal had its own problems, but it got Feynman thinking, and calculating. He worked through the details and determined precisely how much of the backward-in-time reaction between particles was needed to make things work out just right, and as was typical of Feynman, he then also checked a lot of different examples to make sure that this idea would not produce crazy phenomena that are not observed, or violations of common sense. He challenged his friends to find an example that might stump him, and he showed that as long as in every direction in the universe there was 100 percent certainty that one would ultimately encounter a charged particle that could interact back with the original particle, one could never use these crazy backward-in-time interactions to produce a device that could turn on before the on button is pushed, or anything like that.
AS HUMPHREY BOGART might have said, it was the beginning of a beautiful friendship. Whereas Feynman had mathematical brilliance and startlingly good insight, Wheeler had experience and perspective. Wheeler was able to quickly shoot down some of Feynman’s misconceptions and suggest improvements, but he had an open mind and encouraged Feynman to explore and to gain calculational experience that was adequate to match his talents. Once Feynman combined the two, he would be almost unstoppable.
CHAPTER 3
A New Way of Thinking
An idea which looks completely paradoxical at first, if analyzed to completion in all its details and in experimental situations, may in fact not be paradoxical.
—RICHARD FEYNMAN
Despite the assurances of Richard’s undergraduate professors, Melville Feynman did not lay his concerns about his son’s future to rest. After Richard had begun his working relationship with John Archibald Wheeler in graduate school, Melville made the trek to Princeton to check once more on his progress and prospects. Once again, he was told that Richard had a brilliant future ahead of him, independent of his “simple background” or possible “anti-Jewish prejudice,” as Melville phrased things. Wheeler may have been sugarcoating reality, or merely reflecting his own ecumenical bent. While still a student he had been the founder and president of the Federation of Church and Synagogue Youth.
Nevertheless, even any lingering anti-Semitism in academia would not have been sufficient to halt Richard Feynman’s march forward. He was simply too good and having too much fun. Only a fool would not recognize his genius and his potential. As they would continue to throughout his life, Feynman’s fascination with physics, and his ability to solve problems others couldn’t, stretched across the spectrum of the physical world, from the esoteric to the seemingly mundane.
Everywhere there were glimpses of his playful intensity. The Wheeler children used to love his visits, when he would often amuse them with tricks. Wheeler remembered one afternoon when Feynman asked for a tin can and told the children that he could tell whether solid or liquid was inside without even opening it or looking at the label. “How?” came a chorus of young voices. “By the way it turns when I toss it up in the air,” he answered, and sure enough, he was right.
Feynman’s own childlike excitement about the world meant that his popularity with children remained unabated, as reflected in a letter written in 1947 by the physicist Freeman Dyson, who was a graduate student at Cornell when Feynman was an assistant professor there. Describing a party at the home of the physicist Hans Bethe in honor of a distinguished visitor, Dyson remembered that Bethe’s five-year-old son, Henry, kept complaining that Feynman was not there, saying, “I want Dick. You told me Dick was coming.” Ultimately Feynman arrived, dashed upstairs, and then proceeded to play noisily with Henry, stopping all conversation down below.
Even as Feynman entertained Wheeler’s children, he and Wheeler continued to amuse each other as they worked throughout the year to explore their exotic ideas on ridding classical electromagnetism of the problem of infinite self-interaction of charged particles, via strange backward-in-time interactions with external absorbers located out in an infinite universe.
Feynman’s motivation for continuing this work was straightforward. He wanted to solve a mathematical problem in classical electromagnetism with the hope of ultimately addressing the more serious problems that arose in the quantum theory. Wheeler, on the other hand, had an even crazier notion he wanted to develop to explain the new particles that were being observed in cosmic rays and ultimately in nuclear physics experiments: maybe all elementary particles were just made of different combinations of electrons, somehow interacting differently with the outside world. The notion was crazy, but at least it helped maintain his own enthusiasm for the work they were doing.
Feynman’s own playful attitude toward the inevitable frustrations and stumbling blocks associated with theoretical work in physics is exemplified by one of the earliest letters he wrote his mother, shortly after starting graduate school and before his work with Wheeler had moved in the direction of reexamining electromagnetism:
Last week things were going fast and neat as all heck, but now I’m hitting some mathematical difficulties which I will either surmount, walk around, or go a different way—all of which consumes all my time—but I like to do very much and am very happy indeed. I have never thought so much so steadily about one problem—so if I get nowhere I really will be very disturbed—However, I have already gotten somewhere, quite far—and to Prof. Wheeler’s satisfaction. However, the problem is not at completion although I’m just beginning to see how far it is to the end and how we might get there (although aforementioned mathematical difficulties loom ahead)—SOME FUN!
Feynman’s idea of fun included prevailing over mathematical difficulties—one of the many attributes that probably separated him from the man on the street.
After an intense few months of give-and-take with Wheeler in the fall and winter of 1940–41 working on their new ideas for electromagnetism, Wheeler finally gave Feynman a chance to present these ideas, not to graduate students, but to professional physicists, through the Princeton physics department seminar. But this was not to be just any group of colleagues. Eugene Wigner, himself a later Nobel Prize winner, ran the seminar and invited, among others, a special cast of characters: the famous mathematician John von Neumann; the formidable Nobel Prize winner and one of the developers of quantum mechanics, Wolfgang Pauli, who was visiting from Zurich; and none other than Albert Einstein, who had expressed an interest in attending (perhaps egged on by contact with Wheeler).
I have tried to imagine myself in Feynman’s place, as a graduate student speaking among such a group. This would not be an easy crowd to please, independent of their eminence. Pauli, for example, was known to jump up and take the chalk out of the hands of speakers with whom he disagreed.
Feynman nevertheless prepared his talk and once he began, the physics took over and any residual nervousness disappeared. As expected, Pauli objected, concerned about whether the use of the backward-in-time reactions might have implied that one was simply working backward mathematically from the correct answer and not actually deriving anything new. He was also concerned about the “action-at-a-distance” aspect of the ideas, once one had dispensed with the fields that usually transport the forces and information, and he asked Einstein whether this might be incompatible with his own work on general relativity. Amusingly, Einstein humbly responded that there might be a conflict, but after all his own theory of gravitation (which the rest of the physics community has regarded as the most significant single piece of work since Newton) was “not so well established.” Actually, Einstein was sympathetic to the no
tion of using backward-in-time as well as forward-in-time solutions, as Wheeler later recalled, when he and Feynman went to visit Einstein at his Mercer Street home to talk further about their work.
The problem is that one of the most obvious features of the physical world, manifest from the moment we wake up each day, is that the future is different from the past. This is true not only for human experience, but also for the behavior of inanimate objects. When we put milk in our coffee and stir it, we will never see that milk at some point in the future coalesce into separate droplets like it appeared when we first poured it into the coffee. The question is: does this apparent temporal irreversibility in nature arise because of an asymmetry in microscopic processes, or is it only appropriate for the macroscopic world we experience?
Like Feynman and Wheeler, Einstein believed that the microscopic equations of physics should be independent of the arrow of time—namely, the apparent irreversibility of phenomena in the macroscopic world arises because certain configurations are far more likely to arise naturally when many particles are involved than are other configurations. In the case of Feynman and Wheeler’s ideas, as Feynman had shown to his fellow graduate student, physics behaved sensibly in the bulk—that is, the future was different from the past in spite of the weird backward-in-time interaction he and Wheeler included. This was precisely because the probabilities associated with the behavior of the rest of the presumably infinite number of other charges in the universe responding to the motion of the charge in question produced the kind of macroscopic irreversibility we are used to seeing in the world around us.
Quantum Man: Richard Feynman's Life in Science Page 4