Reading the recent article Electrons Act Like Waves (from the Physical Review Focus series, a highly recommended, lay[wo]man-friendly feed for your newsreader), i've discovered one of those peculiar stories that make the history of physics even more enjoyable than it would be by its purely scientific side alone.
The article tells the story of Davisson and Germer's discovery of the so-called wave-like nature of electrons. As explained in every textbook, they set up an experiment consisting in scattering electrons through a (nickel) crystal, and observed the familiar fringes that one obtains when a wave crosses a gratting with alternating slots in a wall.
It was 1927, and i always pictured Davisson and Germer as intrepid experimenters boldly trying to confirm de Broglie's 1924 ideas about the wave nature of matter . (Justly enough, an idealisation of this experiment has become the de facto standard presentation of the quantum mechanical world!.) The funny thing is that this romantic picture has nearly nothing to do with what really happened. As it comes, D&G were looking for evidence of the atomic structure of metals and knew nothing about de Broglie. After the experiment had been going on for a somewhat sterile period, one of their widgets broke and overheated the nickel plaits, which crystalised and made (when used again for scattering electrons) the interference patterns apparent. The experimenters were all but bewildered, and only after Davisson discussed his results with other colleagues during a holiday in England, did they realize the importance of their discovery.
That's serendipity at its best. And, of course, it was not the first nor the last time that serendipity gave physicists a helping hand. The Oxford Dictionary gives a precise definition of this beautiful word:
serendipity noun the occurrence and development of events by chance in a happy or beneficial way.
or, even better, this one from Julius H. Comroe (as quoted by Simon Singh)
Serendipity is looking for a needle in a haystack and finding the Farmer's Daughter.
and its all too apt etymology:
ORIGIN 1754: coined by Horace Walpole, suggested by The Three Princes of Serendip, the title of a fairy tale in which the heroes “were always making discoveries, by accidents and sagacity, of things they were not in quest of.”
which in my opinion captures extremely well the kind of discoveries we're discussing. They were by chance, that's true, but not just chance: one needs to be in the quest of something, to begin with.
Another famous (and probably better known) example of serendipity at work is Penzias and Wilson's discovery of the cosmic microwave background. As explained by Ivan Kaminow,
He [Ivan] joked that Penzias was an unusually lucky guy. "Arno Penzias and Bob Wilson were trying to find the source of excess noise in their antenna, where pigeons were roosting," he said. "They spent hours searching for and removing the pigeon dung. Still the noise remained, and was later identified with the Big Bang."He laughed, "Thus, they looked for dung but found gold, which is just opposite of the experience of most of us."
The experiment was being conducted at Bell's Labs and its aim was to tune an ultra-sensitive microwave receiving system to study radio emissions from the Milky Way. It was only after Penzias talked with Robert H. Dicke (see also this nice memorial (PDF) for more on Dicke) that the misterious radiation was recognized as the relics of the Big Bang hypothesized by George Gamow some time before. I read the whole story for the first time in Weinberg's marvelous book (required reading), and I've always found a bit unfair that the Nobel prize went only to Penzias and Wilson.
My third serendipitous example comes also from the skies. In summer of 1974, Russell Hulse was a 23-year-old graduate student compiling data from the Arecibo Observatory radio telescope in Puerto Rico. The job was a little bit tedious: he was trying to detect periodic radio sources that could be interpreted as a pulsar . One of the pulsar's earmarks is its extraordinary regularity (a few nanoseconds deviation per year for a period of about a second). Around 100 pulsars were known back then, all with a stable period with a extremely slow tendency to increase. At the end of the day, the data obtained by the telescope was processed by a computer program written by Russell, which selected candidate signals based on the stability of their period. Those were correlated with later or former observations of the same sky zone, to rule out earth-based, spurious sources. One night, Russell boringly noticed a very weak candidate, so weak that, had it been a mere 4 percent fainter, it would have passed unnoticed. On top of that, its period was too short (about 0,06 seconds) and, even worst, it was variable. Russell was on the verge of discarding it more than once during the following weeks, but eventually he persevered and, helped by his supervisor, Joe Taylor (a.k.a. K1JT), correctly interpreted the observation as a binary pulsar. The rest is history, and a Nobel prize  one. Russell tells the amazing story in his delicious Nobel lecture (PDF), which starts with these telling words:
I would like to take you along on a scientific adventure, a story of intense preparation, long hours, serendipity, and a certain level of compulsive behavior that tries to make sense out of everything that one observes.
I specially like this instance of serendipity, for it shows that, many a time, lucky strikes befall on those who work hard enough to get hit.
Update: I've just found an excellent article by Alan Lightman, Wheels of Fortune, which gives some very nice examples of serendipitous discoveries, as well as a nice discussion. After reading Michael post on serendipity in HEP, i was wondering about non-experimental lucky strikes, and Lightman gives an excellent example: Steve Weinberg's electroweak theory:
Serendipitous discovery strikes not only in the photographic plates, test tubes, and petri dishes of the laboratory. It also can strike in the pencil-and-paper world of theoretical scientists. In the fall of 1967, theoretical physicist Steven Weinberg was working out a new theory of the so-called “weak force,” one of the four fundamental forces of nature, when he discovered, to his surprise, that his new theory was actually two theories in one. Weinberg was approaching the weak force with the seminal idea that pairs of particles it acted upon, electrons and neutrinos for example, might be identical as far as the force is concerned, just as yellow and white tennis balls are identical as far as the game of tennis goes. When he cast this idea into the mathematical language of quantum physics, Weinberg found that his theory necessarily included the electromagnetic force as well as the weak force. The mathematics required the union of the two forces. As he later remarked, “I found in doing this, although it had not been my idea at all to start with, that it turned out to be a theory not only of the weak forces, based on an analogy with electromagnetism; it turned out to be a unified theory of the weak and electromagnetic forces.”
 As an aside, i find the constant chatter about matter being some sort of schizophrenic mix between particles and waves misleading, if not outright wrong. As stressed (to no avail, it seems) by Feynman (see and hear him on this and much more in his Vega Lectures, for instance), electrons (and photons, for that matter) are particles. You never detect half an electron, or a pi-fold-photon. There's always ticks in a detector (a photo-multiplier, a photographic plate, or trails in a Wilson chamber, for instance). The wave function is not real (neither in the physical nor in the mathematical sense of real), and it 'oscillates' in an imaginary space which is not even 3-dimensional when more than a particle is described. The interference patterns observed (which arise from the addition of complex amplitudes which are squared afterwards) are not associated with single electrons, the only thing wavelike (with a twist) about them being the statistics of their hits on the wall. Even if you believe in Bohm's pilot waves, the particles are still particles! Of course, there's ample room for analogy, but i still find the typical discussions misleading.
 The discovery of pulsars had also its share of serendipity. They were found, also unexpectedly, by Jocelyn Bell and Anthony Hewish while they were looking studying scintillating radio signals from compact sources. Jocelyn has written a lively report of their discovery, including the funny story of how they were on the verge on attributing the signals to extraterrestrials, and jokingly use monikers starting with the prefix LGM (for little green men) to name the misterious radio sources. There's also a good review of the tale over at the Hitchhiker's Guide to the Galaxy funny website.
 The pulsar discovery also won a Nobel in 1974. But, curiously enough, the undergraduate hero of the story (Jocelyn Bell) was not awarded this time. One wonders.
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