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We Will Now Discuss Two Different Experiments That Illustrate “Quantum-Mechanical Weirdness”, and That Continue to Challenge

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We Will Now Discuss Two Different Experiments That Illustrate “Quantum-Mechanical Weirdness”, and That Continue to Challenge I. QUINTESSENTIALLY QUANTUM We will now discuss two different experiments that illustrate “quantum-mechanical weirdness”, and that continue to challenge our basic intuitions even today, in spite of the almost universal acceptance of the laws of quantum physics. A. The Double-Slit Experiment, First Hypothesized and Finally Realized A P Q FIG. 1: A schematic diagram of the double-slit experiment. In 1801, the English physicist Thomas Young introduced the double-slit interferometer. In such a device, a light wave spreads outward from a point source and is allowed to pass through two slits in an opaque barrier; once the wave is beyond those slits, it interferes with itself (in a way, it is more like two waves interfering with each other, one emanating from each slit), and what results is an interference pattern on a distant two-dimensional surface. Even today, this type of device remains one of the most versatile tools for demonstrating interference phenomena for waves of 1 any imaginable sort. Here, we will consider a variation on this theme, involving electrons rather than light. Our hypothetical two-slit experiment (see Figure 1) was originally dreamt up by Richard Feynman in Volume Three of his famous Feynman Lectures on Physics. In Feynman’s thought experiment, deeply inspired by Young’s interferometer, an electron (which, from many experiments over the past century, we have every reason to conceive of as a microscopic dot carrying electric charge) is released at point A towards a screen, and somewhere between point A and the screen there is an impenetrable wall that has two slits in it, at, say, points P and Q. We immediately see that the rightward-moving electron can reach the screen and leave a little mark on it only if it passes through either slit P or slit Q. This simple conclusion is not merely commonsensical, but totally obvious and not worth giving a moment’s thought to. Or at least that is what classical thinking would tell us. But quantum mechanics violates this “obvious” fact, because quantum mechanics tells us that particles — tiny points moving through space like tiny pebbles flying through the sky — do not act like pebbles in the sky but like ripples on water. However, this fact, when first encountered, is very disorienting, to say the least, so let us first spell out what our deep-seated classical intuitions would predict for such a setup. If we were to send a broad stream of electrons from point A toward the screen, we would expect to find two dark splotches building up on the screen as more and more electrons came in for landings, each point-like electron leaving a tiny mark where it landed. This seems absolutely straightforward and obvious. More specifically, we would expect to see splotches gradually building up at exactly two predictable places on the screen — namely, at (or very near) the two points on the screen that are determined by drawing a straight line first from A to P and extending it all the way to the screen, and then from A to Q and likewise extending it to the screen. These two straight lines, determined by the point of release and the two slits in the wall, are the only conceivable trajectories that could carry an electron from point A to the screen, since the wall, aside from slits P and Q, is impenetrable. But commonsensical and even watertight though this conclusion may seem, what we have just described is not what is actually observed on the screen. What is seen on the screen, instead of two isolated splotches where electrons land, is an interference pattern — that is, a blurry pattern all over the screen, which is darker in certain areas and lighter in others — and in no way does it look like two splotches! In fact, oddly enough, the pattern is darkest exactly halfway between 2 the two hypothetical splotches that classical thinking gave us, and a short distance from there it fades to zero, and then a little further away it again becomes dark, and then it fades away to zero again, then darkens and lightens again, and so forth and so on. This pattern of alternating lighter and darker zones — the trademark of an interference pattern, just like those observed by Thomas Young in the early 1800s — is what is symbolized by the wavy line shown to the right side of the screen in Figure 1. The peaks of the wavy graph are the areas where the screen is darkest, and the troughs are where it is lightest. To further reveal the mysteries of the wave–particle duality intrinsic to quantum mechanics, Feynman invited his readers to imagine firing just one single electron toward the screen (rather than a beam comprised of many electrons), and then marking the position where it strikes the screen, and then repeating this one-electron experiment over and over again. After many electrons have been fired, the marks on the screen will still comprise an interference pattern, which shows that each electron on its own was interfering with itself. In other words, each electron on its own somehow went, in a ghostly manner (or at least in a wavy manner!), through both slits, rather than through just one or the other of the slits (which is what we would expect of a particle that manifests itself as a tiny dot wherever it hits the screen). If we now cover up, say, slit A, so that each electron can pass only through slit B, then no interference pattern will appear on the screen — just a splotch directly behind slit B will build up over time. This agrees with our classical intuitions, and shows us that the intuition-defying interference pattern arises only when we give each electron the chance to pass through both slits. When an electron is given that chance, it will always take it, and so, as one electron after after gets released from point A, the interference pattern gradually takes shape on the screen! Before Feynman dreamt up his thought experiment (in the early 1960s), experiments of this sort using double-slit setups had been done, and they indeed showed the interference pattern we have just described, but they all used a beam of electrons rather than just one electron at a time. Because of this, these experiments did not establish a crucial point of Feynman’s thought experiment — namely, that an individual electron traveling by itself will behave like a wave. Single-electron double-slit diffraction was first demonstrated in 1974 by Giulio Pozzi and colleagues at the University of Bologna in Italy, who passed single electrons through a biprism — an electronic optical device that serves the same function as a double slit — and they observed the predicted build-up of an inteference pattern. A similar experiment was also carried out in 1989 by Akira Tonomura and colleagues at the Hitachi research lab in Japan. The actual Feynman-style 3 double-slit experiment, in which the arrivals of individual electrons in a double-slit situation were recorded one at a time, was finally realized only in 2012 by Pozzi and colleagues. Perfecting the double-slit experiment with a single electron continues to obsess many physicists even today. The double-slit interference pattern with a single electron makes one dizzy irrespective of whether we imagine the electron to be a particle or a wave. If we ask, “Did the electron pass through slit P or slit Q?”, the answer is, “Neither — it passed through them both.” This is because an electron is a wavelike entity, and we have to imagine it spreading through space like ripples moving on the surface of a pond — or if you wish to have a three-dimensional image, then like sound waves propagating through the air (of course, since sound waves are invisible, they are harder to imagine than ripples). The weird thing is that although each electron wears its “wave hat” while propagating through space (that is, while moving away from point A, passing through the slits, and approaching the screen), it doesn’t keep that hat on at the very end. Instead, when it finally lands on the screen, it doffs its “wave hat”, puts its “particle hat” back on, and deposits a little dot in just one single point on the screen. Why and how does this weird hat-trick take place? No one can say. This unfathomable mystery lies at the very heart of quantum mechanics. As Richard Feynman said, “Nobody can explain quantum mechanics.” Or as Albert Einstein once wistfully remarked, toward the end of his life, “I have been trying to understand the nature of light for my entire life, but I have not yet succeeded.” B. The Ehrenberg-Siday-Aharonov-Bohm Effect Two examples of quantum phenomena that have no analogues in classical physics are Heisenberg’s uncertainty principle and quantum tunneling, both discovered in the early days of quantum mechanics, and both quite famous, even outside of physics. There are also less famous quantum phenomena that were discovered later, such as the so-called Aharonov–Bohm effect, dating from 1959, and the Berry phase, dating from 1984, both of which were discovered in Bristol, England, although 25 years apart. In Chapter Eight, we will discuss the Berry phase, but here we will discuss the Aharonov–Bohm effect, published in 1959 by David Bohm and his student Yakir Aharonov. Shortly after their article was published, Bohm and Aharonov learned that Raymond Siday and Werner Ehrenberg had published exactly the same result a decade earlier. This must have been a great shock to them, but David Bohm, to his credit, always referred to the 4 B=0 B >0 FIG.
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