Through Two Doors at Once

1

THE CASE OF THE EXPERIMENT WITH TWO HOLES

Richard Feynman Explains the Central Mystery

There is nothing more surreal, nothing more abstract than reality.

-Giorgio Morandi

Richard Feynman was still a year away from winning his Nobel Prize. And two decades away from publishing an endearing autobiographical book that introduced him to non-physicists as a straight-talking scientist interested in everything from cracking safes to playing drums. But in November 1964, to students at Cornell University in Ithaca, New York, he was already a star and they received him as such. Feynman came to deliver a series of lectures. Strains of "Far above Cayuga's Waters" rang out from the Cornell Chimes. The provost introduced Feynman as an instructor and physicist par excellence, but also, of course, as an accomplished bongo drummer. Feynman strode onto the stage to the kind of applause reserved for performing artists, and opened his lecture with this observation: "It's odd, but in the infrequent occasions when I have been called upon in a formal place to play the bongo drums, the introducer never seems to find it necessary to mention that I also do theoretical physics."

By his sixth lecture, Feynman dispensed with any preamble, even a token "Hello" to the clapping students, and jumped straight into how our intuition, which is suited to dealing with everyday things that we can see and hear and touch, fails when it comes to understanding nature at very small scales.

And often, he said, it's experiments that challenge our intuitive view of the world. "Then we see unexpected things," said Feynman. "We see things that are very far from what we could have imagined. And so our imagination is stretched to the utmost-not, as in fiction, to imagine things which aren't really there. But our imagination is stretched to the utmost just to comprehend those things which are there. And it's this kind of a situation that I want to talk about."

The lecture was about quantum mechanics, the physics of the very small things; in particular, it was about the nature of light and subatomic bits of matter such as electrons. In other words, it was about the nature of reality. Do light and electrons show wavelike behavior (like water does)? Or do they act like particles (like grains of sand do)? Turns out that saying yes or no would be both correct and incorrect. Any attempt to visualize the behavior of the microscopic, subatomic entities makes a mockery of our intuition.

"They behave in their own inimitable way," said Feynman. "Which, technically, could be called the 'quantum-mechanical' way. They behave in a way that is like nothing that you have ever seen before. Your experience with things that you have seen before is inadequate-is incomplete. The behavior of things on a very tiny scale is simply different. They do not behave just like particles. They do not behave just like waves."

But at least light and electrons behave in "exactly the same" way, said Feynman. "That is, they're both screwy."

Feynman cautioned the audience that the lecture was going to be difficult because it would challenge their widely held views about how nature works: "But the difficulty, really, is psychological and exists in the perpetual torment that results from your saying to yourself 'But how can it be like that?' Which really is a reflection of an uncontrolled, but I say utterly vain, desire to see it in terms of some analogy with something familiar. I will not describe it in terms of an analogy with something familiar. I'll simply describe it."

And so, to make his point over the course of an hour of spellbinding oratory, Feynman focused on the "one experiment which has been designed to contain all of the mystery of quantum mechanics, to put you up against the paradoxes and mysteries and peculiarities of nature."

It was the double-slit experiment. It's difficult to imagine a simpler experiment-or, as we'll discover over the course of this book, one more confounding. We start with a source of light. Place in front of the source a sheet of opaque material with two narrow, closely spaced slits or openings. This creates two paths for the light to go through. On the other side of the opaque sheet is a screen. What would you expect to see on the screen?

The answer, at least in the context of the world we are familiar with, depends on what one thinks is the nature of light. In the late seventeenth century and all of the eighteenth century, Isaac Newton's ideas dominated our view of light. He argued that light was made of tiny particles, or "corpuscles," as he called them. Newton's "corpuscular theory of light" was partly formulated to explain why light, unlike sound, cannot bend around corners. Light must be made of particles, Newton argued, since particles don't curve or bend in the absence of external forces.

In his lecture, when Feynman analyzed the double-slit experiment, he first considered the case of a source firing particles at the two slits. To accentuate the particle nature of the source, he urged the audience to imagine that instead of subatomic particles (of which electrons and particles of light would be examples), we were to fire bullets from a gun-which "come in lumps." To avoid too much violent imagery (what with bombs in the prologue, and a thought experiment with gunpowder to come), let's imagine a source that spews particles of sand rather than bullets; we know that sand comes in lumps, though the lumps are much, much smaller than bullets.

First, let's do the experiment with either the left slit or the right slit closed. Let's take it that the source is firing grains of sand at high enough speeds that they have straight trajectories. When we do this, the grains of sand that get through the slits mostly hit the region of the screen directly behind the open slit, with the numbers tapering off on either side. The higher the height of the graph, the more the number of grains of sand reaching that location on the screen.

Now, what should we see if both slits are open? As expected, each grain of sand passes through one or the other opening and reaches the other side. The distribution of the grains of sand on the far screen is simply the sum of what goes through each slit. It's a demonstration of the intuitive and sensible behavior of the non-quantum world of everyday experience, the classical world described so well by Newton's laws of motion.

To be convinced that this is indeed what happens with particles of sand, let's orient the device such that the sand is now falling down onto the barrier with two slits. Our intuition clearly tells us that two mounds should form beneath the two openings.

Turning the experiment back to its original position, let's dispense with the sand and consider a source that's emitting light, and assume that light's made of Newtonian corpuscles. Informed by our experiment with sand particles, we'd expect to see two strips of light on the screen, one behind the right slit and one behind the left slit, each strip of light fading off to the sides, leading to a distribution of light that is simply the sum of the light you'd get passing through each slit.

Well, that's not what happens. Light, it seems, does not behave as if it's made of particles.

Even before Newton's time, there were observations that challenged his theory of the particle nature of light. For example, light changes course when going from one medium to another-say, from air to glass and back into air (this phenomenon, called refraction, is what allows us to make optical lenses). Refraction can't be easily explained if you think of light as particles traveling through air and glass, because it requires positing an external force to change the direction of light when it goes from air to glass and from glass to air. But refraction can be explained if light is thought of as a wave (the speed of the wave would be different in air than in glass, explaining the change in direction as light goes from one type of material to another). This is exactly what Dutch scientist Christiaan Huygens proposed in the 1600s. Huygens argued that light is a wave much like a sound wave, and since sound waves are essentially vibrations of the medium in which they are traveling, Huygens argued that light too is made of vibrations of a medium called ether that pervades the space around us.

This was a serious theory put forth by an enormously gifted scientist. Huygens was a physicist, astronomer, and mathematician. He made telescopes by grinding lenses himself, and discovered Saturn's moon Titan (the first probe to land on Titan, in 2005, was named Huygens in his honor). He independently discovered the Orion nebula. In 1690, he published his TraitŽ de la Lumire (Treatise on Light), in which he expounded his wave theory of light.

Newton and Huygens were contemporaries, but Newton's star shone brighter. After all, he had come up with the laws of motion and the universal law of gravitation, which explained everything from the arc of a ball thrown across a field to the movement of planets around the sun. Besides, Newton was a polymath of considerable renown (as a mathematician, he gave us calculus, and even ventured into chemistry, theology, and writing biblical commentaries, not to mention all his work in physics). It was no wonder that his corpuscular theory of light, despite its shortcomings, overshadowed Huygens's ideas of light being wavelike. It'd take another polymath to show up Newton when it came to understanding light.

Thomas Young has been called ÒThe Last Man Who Knew Everything.Ó In 1793, barely twenty years of age, he explained how our eyes focus upon objects at different distances, based partly on his own dissection of an oxÕs eyes. A year later, on the strength of that work, Young was made a Fellow of the Royal Society, and in 1796 he became Òdoctor of physic, surgery, and midwifery.Ó When he was in his forties, Young helped Egyptologists decipher the Rosetta stone (which had inscriptions in three scripts: Greek, hieroglyphics, and something unknown). And in between becoming a medical doctor, getting steeped in Egyptology, and even studying Indo-European languages, Young delivered one of the most intriguing lectures in the history of physics. The venue was the Royal Society of London, and the date, November 24, 1803. Young stood in front of that august audience, this time as a physicist describing a simple and elegant homespun experiment, which, in his mind, had unambiguously established the true nature of light and proved Newton wrong.

"The experiments I am about to relate . . . may be repeated with great ease, whenever the sun shines," Young told the audience.

Whenever the sun shines. Young wasn't overstating the simplicity of his experiment. "I made a small hole in a window-shutter, and covered it with a piece of thick paper, which I perforated with a fine needle," he said. The pinhole let through a ray of light, a sunbeam. "I brought into the sunbeam a slip of card, about one-thirtieth of an inch in breadth, and observed its shadow, either on the wall, or on other cards held at different distances."

If light is made of particles, Young's "slip of card" would have cast a sharp shadow on the wall in front, because the card would have blocked some of the particles. And if so, Newton would have been proved right.

If, however, light is made of waves, as Huygens claimed, then the card would have merely impeded the waves, like a rock impedes flowing water, and the wave would have gone around the card, taking two paths, one on either side of the card. The two paths of light would eventually recombine at the wall opposite the window shutter to create a characteristic pattern: a row of alternating bright and dark stripes. Such stripes, also known as interference fringes, are created when two waves overlap. Crucially, the central fringe would be bright, exactly where you'd expect a dark shadow if light were made of particles.

We know about interference from our everyday experience of waves of water. Think of an ocean wave hitting two openings in a coastal breakwall. New waves emerge from each opening (a process called diffraction) and travel onward, where they overlap and interfere with each other. In regions where the crests of both waves arrive at the same time, there's constructive interference and the water is at its highest (analogous to bright fringes of light); and in regions where the crest from one wave arrives at the same time as the trough of the other, there's destructive interference and the water is at its lowest (corresponding to dark fringes).

Young saw such optical interference fringes. Specifically, since he was working with sunlight, which contains light of all colors, he saw a central region that was flanked by fringes of colors. The central region, upon closer inspection, was seen to be made of light and dark fringes. The numbers of these fringes and their widths depended on how far away the pinhole in the window shutter was from the screen or wall. And the middle of the central region was always white (a bright fringe). He had shown that light is wavelike.

There must have been disbelief in the audience, for Young was going against Newton's ideas. Even before Young's lecture, articles written anonymously in the Edinburgh Review had been heavily critical of his work. The author, who turned out to be a barrister named Henry Brougham (he became Lord Chancellor of England in 1830), was scathing, calling Young's work "destitute of every species of merit" and "the unmanly and unfruitful pleasure of a boyish and prurient imagination."

It was anything but. Soon enough, Young's ideas got further support from other physicists. His experiment led to what's now called the double-slit experiment and was in fact the first formulation of it-the very same experiment whose virtues Feynman extolled during his lecture at Cornell. In the more standard double-slit experiment, Young's sunbeam is replaced by a source of light. And instead of a "slip of card" placed in the sunbeam's path to create two paths for the light, the double-slit experiment creates two paths of light by letting the light fall on an opaque barrier with two narrow slits or openings through which the light can pass. And on the screen on the far side, you see an interference pattern, essentially fringes similar to what Young saw on the wall opposite the window shutter (if the screen is a photographic plate, or a piece of glass coated with photosensitive material, then the image can be thought of as a film negative: dark regions will form where the film is being exposed to light). You don't see just two strips tapering away, which you'd expect if light behaved as if it came in lumps. It's behaving like a wave.