Quantum Man: Richard Feynman's Life in Science (4 page)

There are other such “Heisenberg pairs,” like energy and time. If we measure the quantum mechanical state of a particle or an atom for a very short time, then there will be a big uncertainty in the measured energy of the particle or atom. In order to measure the energy accurately, we have to measure the object over a long time interval, in which case we cannot say precisely when the energy was being measured.

If this weren’t bad enough, the quantum world gets even weirder once we add Einstein’s theory of special relativity into the mix, in part because relativity puts mass and energy on the same footing. If we have enough energy available, we can create something with mass.

So, if we put all of these things together—quantum multiplexing, the Heisenberg uncertainty principle, and relativity—what do we get? We get a picture of electrons that is literally infinitely more confusing than the one presented by the classical theory, which already led to an infinite self-energy for the electron.

For example, whenever we try to picture an electron, it doesn’t have to be just an electron! To understand this, let’s return back to classical electromagnetism. One of the key features at the heart of this theory is the fact that if we shake an electron, it will emit elecromagnetic radiation, like light, or radio waves. This great discovery resulted from the groundbreaking nineteenth-century experiments of Michael Faraday, Hans Christian Oersted, and others, and the groundbreaking theoretical work of James Clerk Maxwell. Quantum mechanically, this observed phenomenon must still be predicted because if quantum mechanics is to properly describe the world, its predictions had better agree with observations. But the key new feature here is that quantum mechanics tells us to think of the radiation as being made up of individual
quanta
, or packets of energy, called photons.

Now let’s return to the electron. The Heisenberg principle tells us that if we measure the electron for some finite time, there remains some finite uncertainty in knowing its exact energy. But if there is some uncertainty, how do we know we are measuring only the electron? For example, if the electron emits a photon carrying very little energy, the total energy of the system will change, albeit very slightly. But if we don’t know the exact energy of the system, then we cannot say whether it has or hasn’t emitted a low-energy photon. So what we are measuring really could be the energy of the electron plus a photon that it has emitted.

But why stop there? Perhaps the electron has emitted an infinite number of very-low-energy photons? If we watch the electron for long enough, we can both measure its energy very accurately and put a photon counter nearby to see if there are any photons around. In this case, what will have happened to all the photons that were traveling along with the electron in the interim? Simple: the electron can absorb all those photons before we get a chance to measure them.The kind of photons that an electron can emit and reabsorb on a timescale so short that we cannot measure them are called
virtual particles
, and as I will describe later, Feynman recognized that when we include the effects of both relativity and quantum mechanics, there is no getting away from the existence of these particles. So when we think of an electron moving around, we now have to think of it as a pretty complicated object, with a cloud of virtual particles surrounding it.

Virtual particles play another important role in the quantum theory of electromagnetism. They change the way we think of electric and magnetic fields and the forces between particles. For example, say an electron emits a photon. This photon can then in turn interact with another particle, which can absorb it. Depending on the energy of the photon, this will result in a transfer of energy and momentum from one electron to another. But that is what we normally describe as the manifestation of the electromagnetic force between these two charged particles.

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 = m
c
2
, 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.

A
S
H
UMPHREY
B
OGART
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.