Later, in 1965, physicists discovered, much to their surprise, that certain microscopic processes for elementary particles do have an arrow of time associated with them—namely, the rates for a process and its time-reversed version are slightly different. This result was so surprising that it garnered the Nobel Prize for the experimentalists involved. Nevertheless, while this effect may play an important role in understanding certain features of our universe, including perhaps why we live in a universe of matter and not antimatter, conventional wisdom still suggests that the macroscopic arrow of time is associated with the tendency for disorder to increase, and arises, not from microscopic physics, but from macroscopic probabilities, as Einstein, Feynman, and Wheeler had presumed.
ULTIMATELY ALL THIS Sturm und Drang associated with the interpretation of Feynman and Wheeler’s ideas was misplaced. The theoretical ideas they had proposed ended up being more or less wrong, in that their proposals didn’t ultimately correspond to reality. Electrons do have self-interactions, and electromagnetic fields, including those involving virtual particles, are real. Feynman summed it up well a decade later when he wrote to Wheeler, “So I think we guessed wrong in 1941. Do you agree?” History has recorded no response from Wheeler, but by then the evidence was indisputable.
So what was the point of all of this work? Well, in science almost every significant new idea is wrong, either trivially wrong (there is a mathematical error) or more substantially wrong (as beautiful as the idea is, nature chooses not to exploit it). If that were not the case, then pushing the frontiers of science forward would be almost too easy.
In light of this, scientists have two choices. Either they can choose to follow well-trodden ground and push solid results a tad further with a reasonable assurance of success. Or they can strike out into new and dangerous territory, where there are no guarantees and they have to be prepared for failure. This might seem depressing, but in the process of exploring all the dead ends and blind alleys, scientists build up experience and intuition and a set of useful tools. Beyond this, unexpected ideas resulting from proposals that lead nowhere, at least as far as the original problem is concerned, nevertheless sometimes carry scientists in a direction that was completely unanticipated, and which every now and then can hold the key to progress. Sometimes ideas that don’t work in one area of science end up being just what was needed to break a logjam elsewhere. As we will see, so it was with Richard Feynman’s long journey through the wilderness of electrodynamics.
AMID THE TURBULENT intellectual flow in Feynman’s life during this period, his personal life evolved deeply as well. Ever since he had been a young man, a child almost, he had known, admired, and dreamed about a certain girl, a girl who possessed qualities that weren’t manifest in him: artistic and musical talents, and the social confidence and grace that often accompany them. Arline Greenbaum had become a presence in his life early on in high school. He had met her at a party when he was fifteen and she was thirteen. She must have had everything he was looking for. She played the piano, danced, and painted. By the time he had entered MIT, she had become a fixture in his family life, painting a parrot on the door of a clothes closet for the family, and teaching piano to his sister Joan and then taking her for walks afterward.
We will never know if these kindnesses were Arline’s way of ingratiating herself with Richard, but it was clear that she had decided he was the young man for her, and he too was smitten. Joan later claimed that by the time Richard entered MIT, when he was seventeen, the rest of the family knew that one day they would be married. They were right. Arline had visited him at his fraternity in Boston on weekends during his early years at college, and by the time he was a junior, he had proposed, and she had accepted.
Richard and Arline were soul mates. They were not clones of each other, but symbiotic opposites—each completed the other. Arline admired Richard’s obvious scientific brilliance, and Richard clearly adored the fact that she loved and understood things he could barely appreciate at that time. But what they shared, most important of all, was a love of life and a spirit of adventure.
Arline makes her way into this scientific biography at this point not merely because she was Feynman’s first, and perhaps deepest, love, but because her spirit provided him with the vital encouragement he needed to keep going, to find new roads, to break traditions, scientific and otherwise.
Their correspondence during the five years between the time of his proposal and her death from tuberculosis is remarkably touching and moving. Filled with naive hope, combined with mutual love and respect, they reflect two young people who were determined to make their own way in the world no matter what the obstacles.
In June of 1941, when Richard was well along in his graduate career, and a year before their marriage, Arline wrote to fill him in on her visits to doctors (it took many misdiagnoses before they eventually got her condition correct), but the letter focuses on him, not her:
Richard sweetheart I love you. . . . we still have a little more to learn in this game of life and chess—and I don’t want to have you sacrifice anything for me. . . . I know you must be working very hard trying to get your paper out—and do other problems on the side—I’m awfully happy tho’ that you’re going to publish something—it gives me a very special thrill when your work is acknowledged for its value—I want you to continue and really give the world and science all you can . . . and if you receive criticisms—remember everyone loves differently.
Arline knew Richard as no one else did, and in so doing she had the power both to embarrass him and to drive him forward to hold true to his beliefs. Most important among these were honesty and the courage to make his own choices. The title of one of his famous autobiographical books, “What Do You Care What Other People Think?” is the question she often repeated when she caught him in a timid or insecure moment, such as when she sent him a box of pencils, each engraved with the phrase “Richard darling, I love you! Putsie” (Putsie was his pet name for her), and caught him slicing off the words in case Professor Wheeler might see them when they were working together. If Feynman had the courage of his convictions, and ultimately the courage to go his own way in the world, both intellectually and otherwise, it was in no small part due to Arline and his memory of her.
While Melville Feynman was concerned about his son’s career direction, Richard’s mother, Lucille, was equally concerned about his personal one. She surely loved Arline, but she wrote to him, late in his graduate career, like many a Jewish mother, concerned that Arline would be a drag on his ability to work and gain a job and on his finances. Arline’s illness would require special care, and time and money, and Lucille was worried that Richard didn’t have enough of any of these things.
Richard responded, within weeks of receiving his PhD and marrying Arline, in June of 1942, remarkably dispassionately:
I’m not dopey enough to tie up my whole life in the future because of some promise I made in the past—under different circumstances. . . . I want to marry Arline because I love her—which means I want to take care of her. That is all there is to it. . . .
I have, however, other desires and aims in the world. One of them is to contribute as much to physics as I can. This is, in my mind, of even more importance than my love for Arline.
It is therefore especially fortunate that, as I can see (guess) my getting married will interfere very slightly, if at all with my main job in life. I am quite sure I can do both at once. (There is even the possibility that the consequent happiness of being married—and the constant encouragement and sympathy of my wife will aid in my endeavor—but actually in the past my love hasn’t affected my physics much, and I don’t really suppose it will be too great an assistance in the future.)
Since I feel I can carry on my main job, and still enjoy the luxury of taking care of someone I love—I intend to be married shortly.
Whether or not his love affected his physics, Arline had
clearly reinforced his determination to follow his ideas wherever they might lead. She had helped ensure his intellectual integrity, and if the words in his letter seem somewhat cold and dispassionate, Arline might have been encouraged by them had she ever read them, because they reflected the kind of rational thinking she so wanted to foster in the man she so loved and admired.
She might have been equally moved by a heart-wrenching event that happened much later, on the dark day of her death, June 16, 1945, six weeks before the atomic bomb Richard had worked to build was exploded over Hiroshima. After she breathed her last breath in the hospital room, he kissed her, and the nurse recorded the time of death as 9:21 p.m. He later discovered that the clock by her bedside had stopped at precisely the same time. A less rational mind might have found this cause for spiritual wonder or enlightenment—the kind of phenomena that makes people believe in a higher cosmic intelligence. But Feynman knew the clock was fragile. He had fixed it several times and he reasoned that the nurse must have picked it up and disturbed it to check the time of Arline’s death. He would display the same kind of intellectual focus and determination to continue down a road he began in 1941, one that would ultimately, profoundly, and irrevocably change the way we think about the world.
THE WRITER LOUISE Bogan once said, “The initial mystery that attends any journey is: how did the traveler reach his starting point in the first place?” For Feynman’s journey, like many epic voyages, the beginning was simple enough. He and Wheeler had completed their work demonstrating that classical electromagnetism could be cast in a form that involved only direct interactions, albeit forward and backward in time, between different charged particles. In so doing, one could obviate the problem of the infinite self-energy of any individual charged particle. The next challenge was to see if this theory could be brought into accord with quantum mechanics, and possibly resolve the thornier mathematical problems that resulted in a quantum theory of electromagnetism.
The only problem was that their rather exotic theory— which was rigged with interactions at different times and places in order to be equivalent in its predictions with the results of classical electromagnetism, and which had electric and magnetic fields that transmitted these interactions—required a mathematical form that quantum mechanics couldn’t handle at the time. The problem originated because of the interactions between particles at different times, or as Feynman later put it, “The path of one particle at a given time is affected by the path of another at a different time. If you try to describe, therefore, things . . . telling what the present conditions of the particles are, and how these present conditions will affect the future—you see it is impossible with particles alone, because something the particles did in the past is going to affect the future.” Up to that point quantum mechanics was based on a simple principle. If we somehow knew or were told the quantum state of a system at one time, the equations of quantum mechanics allowed us to determine precisely the subsequent dynamical evolution of the system. Of course, knowing precisely the dynamical evolution of the system is not the same as predicting exactly what we would subsequently measure. The dynamical evolution of a quantum system involves determining exactly, not the final state of the system, but rather a set of probabilities that tells us what the likelihood is the system being measured will be in some specific state at a later time.
The problem is that electrodynamics as formulated by Feynman and Wheeler required knowing the positions and motion of many other particles at many different times in order to determine the state of any one given particle at any given time. In such a case, the standard quantum methods for determining the subsequent dynamical evolution of this particle failed.
Feynman had succeeded during the fall and winter of 1941–42 in formulating their theory in a host of different, if mathematically equivalent, ways. During the process he had discovered that he could rewrite the theory completely in terms of the very principle that he had so renounced while an undergraduate.
Remember that Feynman had learned in high school that there was a formulation of the laws of motion which was based not on what was happening at a single time, but what happened at all times: the formalism of Lagrange and his principle of least action.
Recall also that the least action principle tells us that in order to determine the actual classical trajectory of a particle, we can consider all possible paths of the particle between its beginning and end points and then determine which one has the smallest average value for the action (defined as the differences between two different parts of the total energy of the particle—the so-called kinetic and potential energies—appropriately summed over each path). This was the principle that was too elegant for Feynman, who preferred to calculate trajectories by considering forces at every point and using Newton’s laws. The idea that he had to worry about the entire path of a particle in order to calculate its behavior at any point seemed unphysical to Feynman at the time.
But Feynman the graduate student had discovered that his theory with Wheeler could be recast completely in terms of an action principle, described purely by the trajectories of charged particles over time, with no need to consider electric and magnetic fields. In retrospect it seems clear why such formalism, which focused on the paths of particles, was appropriate to describe the Feynman-Wheeler theory. After all, such paths are essentially what defined their theory, which depended completely on the interactions of particles moving along different trajectories in time. Therefore, to build a quantum theory, Feynman decided he would need to figure out how to do quantum mechanics for a system like the one he and Wheeler were considering, whose classical dynamics could be determined by such an action principle, but not by more conventional methods.
Physics, or at least the physics that Feynman and Wheeler were imagining, had driven Feynman to a place he never would have expected to be a half-dozen years earlier. The transformation in his thinking following his intensive efforts to explore their new theory had been dramatic. He was now convinced that focusing on events at a fixed time was not the way to think, and that the action principle, based on exploring complete trajectories through space and time, was. As he later wrote, “We have in [the action principle] a thing that describes the character of the path throughout all of space and time. The behavior of nature is determined by saying her whole-space-time path has a certain character.” But how could this principle be translated into quantum mechanics, which thus far depended so crucially on defining a system at one time in order to calculate what would happen at later times? For Feynman, the key to the answer came from a fortuitous beer party in Princeton. But to appreciate this key, we first have to make a short detour to revisit our picture of the mysterious quantum world that Feynman was about to change.
CHAPTER 4
Alice in Quantumland
The Universe is not only queerer than we suppose, but queerer than we can suppose.
J. B. S. HALDANE, 1924
While the distinguished British scientist J. B. S. Haldane was a biologist and not a physicist, his statement about the universe could not be more apt, at least to the realm of quantum mechanics that Richard Feynman was about to conquer. For, as we have seen, at the small scales where quantum mechanical effects become significant, particles can appear to be in many different places at once, while also doing many different things at the same time in each place.
The mathematical quantity that can account for all of this apparent lunacy is the function discovered by the famous Austrian physicist Erwin Schrödinger, who derived what became the conventional understanding of quantum mechanics during a busy two-week period in which he too was doing many different things at the same time—in the midst of trysts with perhaps two different women while holed up in a mountain chalet. It probably was the perfect atmosphere to imagine a world where all of the classical rules of behavior would ultimately be broken.
This function of Schrödinger’s is called the wave function of an objec
t, and it accounts for the mysterious fact, at the heart of quantum mechanics, that all particles behave in some sense like waves, and all waves behave in some sense like particles—the difference between a particle and a wave being that a particle is located at a specific point, whereas a wave is spread out over some region.
So, if a particle, which isn’t spread out, is to be described by something that behaves like a wave and is spread out, the wave function must accommodate this fact. As Max Born later demonstrated, this was possible if the wave function, which itself might behave like a wave, did not describe the particle itself but rather the probability of finding the particle at any given place in space at a specific time. If the wave function, and hence the probability of finding a particle, is nonzero at many different places, then the particle acts like it is in many different places at any one time.
So far so good, even if the notion itself seems crazy. But there is one more crucial bit of craziness at the heart of quantum mechanics, and I should stress that physicists do not have a fundamental understanding of why nature behaves this way, except to say that it does. If the laws of quantum physics determine the behavior of the wave function, then physics tells us that given the wave function of a particle at one time, quantum mechanics in principle allows us to calculate, in a completely deterministic way, the wave function of the particle at a later time. Up to this point it is just like Newton’s laws, which tell us how the classical motion of a baseball evolves in time, or Maxwell’s equations, which tell us how electromagnetic waves evolve in time. The difference is that in quantum mechanics the quantity that evolves in time in a deterministic manner is not directly observable, but rather is a set of probabilities for making certain observations, in this case for determining the particle to be at a certain place at a certain time.
This is strange enough, but it further turns out that the wave function itself does not directly describe the probability of finding a particle at a given place at some time. Instead it is the square of the wave function that gives the probabilities. This one fact is responsible for all of the strangeness of the quantum mechanical world because it explains why particles can behave precisely as waves, as I will describe now.
Quantum Man: Richard Feynman's Life in Science Page 5