How to Make an Apple Pie from Scratch

by Harry Cliff

  How to explain the peculiar short range of the strong nuclear force? Yukawa’s bright idea was that the force was communicated between protons and neutrons by the exchange of a new type of “heavy particle,” as Yukawa dubbed it. The fact that the proposed particle was heavy was key. The particle’s large mass meant that it could only travel a very short distance,*1 severely limiting the range of the strong nuclear force. Based on measurements of how protons, neutrons, and nuclei bounce off one another, Yukawa calculated that his particle needed to have a mass of 100 MeV; for reference, the electron’s mass is 0.5 MeV, compared to 938 MeV for the proton.

  At first it looked as though Anderson and Neddermeyer had bagged Yukawa’s heavy particle—its mass appeared to be almost precisely in line with Yukawa’s prediction. A surge of excitement swept through the physics community. At last the mysterious nature of the strong nuclear force might be within reach. However, doubts soon began to grow. For one thing, the particle they’d discovered seemed to be able to penetrate much farther through slabs of metal than you’d expect of the particle of the strong nuclear force, which should interact enthusiastically with atomic nuclei and get stopped much more abruptly. What’s more, Anderson and Neddermeyer’s particle lived far longer before decaying than Yukawa had predicted.

  It would take more than a decade to clear up the confusion. In 1947 a group led by Cecil Powell at the University of Bristol used a completely different technique—based on exposing photographic plates to cosmic rays—to discover a new charged particle, which they called the “π meson” but today is usually shortened to just “pion.” Here at last was Yukawa’s predicted carrier of the strong nuclear force! In fact, there were three types of pion, a positive and a negative one, along with an electrically neutral version discovered a few years later. Yukawa was quickly rewarded with a Nobel Prize for his audacious prediction, and Powell for the experimental discovery.

  An enlarged picture of the makeup of matter was emerging. Electrons orbit atomic nuclei made of protons and neutrons, which are bound together in their nuclear prison by the frenetic exchange of three types of pion. Rather pleasingly, this means our apple pie is in part made from pions. Hanging around awkwardly on its own was Anderson and Neddermeyer’s muon, which seemed to look a lot like a heavy and unstable version of the electron but without serving any useful function as far as anyone could tell. The physicist Isidor Rabi famously captured the confusion caused by the muon with the pithy phrase “Who ordered that?” as if it were a pizza delivery that had turned up unexpectedly.

  The appearance of the pions kicked off a flood of new discoveries. In the same year, the Manchester duo of George Rochester and Clifford Butler spotted strange pairs of forking tracks in their cloud chamber that seemed to be produced by the decay of a new particle about a thousand times heavier than the electron. Originally dubbed “V particles” due to their distinctive V-shaped decays, they are now known as “kaons.” Before long physicists were faced with a plethora of proliferating particles: some lighter than protons and neutrons, others heavier.

  What were all these new particles for? No one had the foggiest idea. Such was the confusion that one physicist quipped, “The finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a ten-thousand-dollar fine.” Physics appeared to be in danger of morphing from an elegant subject with only a small number of ingredients governed by a few simple, unifying principles to something more akin to zoology, with a baffling variety of different species jostling for space in an ever growing particle zoo. Physicists, who often wear their inability to remember anything so banal as a list of facts, dates, or names as a badge of honor, were horrified. Enrico Fermi famously harrumphed, “If I could remember the names of all these particles, I would have been a botanist!”

  Amid the chaos, physicists did their best to impose some kind of order. There were a few clues to follow. First off, with the notable exception of the muon, all these new particles experienced the mighty pull of the strong nuclear force. To distinguish them from particles that didn’t—like the electron, muon, or the photon—physicists dubbed this new family of strongly interacting particles “hadrons.” The hadrons could be broadly divided into two further categories: those with masses in between the electron and the proton became known as “mesons,” while those heavier than the proton were classed as “baryons.”

  More could be gleaned by sorting the hadrons according to their essential properties or quantum numbers. One example that we’ve already come across is electric charge; the proton has an electric charge of +1, while Rochester and Butler’s kaon has a charge of 0. Another extremely important one is a particle’s angular momentum, or spin. If momentum is the amount of oomph carried by a particle due to its motion in a straight line, then angular momentum is the amount of oomph due to its rotation. Quantum mechanical spin comes in discrete lumps of size ¹/₂ and can only take values in the sequence 0, ¹/₂, 1, ³/₂, 2, ⁵/₂, and so on. A great deal of effort was spent figuring out the spins of the zoo of particles that continued to appear in experiments. At first the mesons all seemed to have spin 0 and the baryons spin ¹/₂, but before long mesons with spin 1 and baryons with spin ³/₂ were also discovered.

  By the 1950s, physicists were no longer content to wait for particles to arrive in their cloud chambers from outer space. Now the pendulum swung toward huge accelerators, which could produce exotic particles on demand by firing protons or electrons into suitable targets, converting their kinetic energy into new particles in the process. In 1953, a hulking ring-shaped particle accelerator known as the Cosmotron was inaugurated at Brookhaven National Laboratory on Long Island, New York. The first accelerator to break the billion-volt barrier, the Cosmotron used a series of powerful magnets to guide beams of protons around in a circle so that they could be accelerated repeatedly each time they orbited the ring, reaching energies high enough to create the full panoply of particles that had previously only been seen in cosmic rays.

  One of the Cosmotron’s achievements was helping to pin down yet another property that some particles appeared to possess. Certain members of the particle zoo lived far longer before decaying than theorists naïvely expected, and what’s more these particles always seemed to be produced in pairs. In 1953 the theoretical physicists Kazuhiko Nishijima and Murray Gell-Mann independently proposed that the reason these particles lived an unusually long time was because they carried a new quantum property, which given their strange behavior they called simply “strangeness,” a term that has survived to this day. The Cosmotron could get protons to such high energies that it could recreate all the strange particles discovered so far in cosmic rays, along with a new strange meson that hadn’t been seen before.

  The Cosmotron was aided by the arrival of a brand-new type of detector that allowed physicists to record the cascades of decaying particles in unprecedented detail. These bubble chambers were descendants of the cloud chamber, but instead of gas they were filled with supercooled liquids—usually liquid hydrogen, freon, or propane. The liquid was held just below the boiling point until the physicists were ready to fire a beam of particles into the chamber, at which point the pressure was suddenly reduced, causing little bubbles of gas to erupt along the paths taken by electrically charged particles. At the same instant a flash of light was sent through the chamber, illuminating the beautiful trails of bubbles so that they could be captured by cameras peering in through portholes around the edge of the chamber.

  The winning combination of record-breaking energy and a shiny new bubble chamber allowed the Cosmotron to steal a march on its competitors, but its success triggered a particle accelerator arms race. Ever larger and more powerful machines were soon being built around the world, many of them with excitingly futuristic names. Across the bay from San Francisco at Berkeley, the place where the first circular particle accelerator had been invented at the start of the 1930s, t
he Bevatron smashed the Cosmotron’s record, reaching a beam energy of 6.2 gigaelectron volts (GeV)*2 and discovering the antiproton in 1955. Not to be outdone by its capitalist foe, the Soviet Union soon had its own superbly named Synchrophasotron in Dubna near Moscow, whose peak energy of 10 GeV left the American machines eating its dust. Europe briefly took the lead when it fired up its 28 GeV Proton Synchrotron at CERN in 1959 until it was knocked off the top spot by the United States’ Alternating Gradient Synchrotron (AGS), built at Brookhaven in 1961.

  The race for ever higher energy brought a flood of new particles, transforming these giant accelerator complexes into the boomtowns of particle physics, packed full of ambitious researchers hoping to sift some shiny new nugget from the subnuclear detritus. The particle zoo continued to grow apace, and yet as it did, what at first had seemed like unconnected fragments slowly began to come together to reveal hints of an underlying order. That said, big chunks were still missing, and the relationships between the pieces were clouded by the messiness of the experimental data. It would take a mind of extraordinary vision and clarity to see through the fog and discern the jewel-like symmetry beneath. Luckily, such a mind turned up in the form of Murray Gell-Mann.

  ESCAPE FROM THE ZOO

  Murray Gell-Mann grew up in Manhattan in the 1930s and 40s, the son of Jewish immigrant parents from the Austro-Hungarian Empire. His older brother Ben taught him to read at the age of three using a Sunshine cracker box and introduced him to a love of bird and mammal watching, botany, and insect collecting. As kids, Murray and Ben would wander all over New York City in search of the few surviving fragments of unspoiled nature where they might spy an interesting animal or plant. Murray’s orderly mind delighted in the way you could arrange all of the different living things they came across into species, connected together on the evolutionary tree.

  In 1960 Gell-Mann, already one of the world’s most respected theorists, had a flash of insight that would eventually unravel the mystery of the particle zoo. Like a zoologist sorting different species into genera and families, he began by arranging the known hadrons into their own broad groupings, the spin 0 mesons and the spin ¹/₂ baryons, and then searching for deeper connections between the individual members. Protons and neutrons seemed to make a neat pair, with almost the same mass but different electric charges, and since both had spin ¹/₂ they clearly belonged to the baryons. Then there were the pions, which came in positive, negative, and neutral varieties, and then two strange kaons, positive and negative, all of which were spin 0 mesons.

  As he played his game of particle categorization, Gell-Mann became convinced that a deep symmetry was lurking just below the surface. In search of a structure that might describe the patterns he was seeing, he turned to what had been until recently a relatively neglected area of mathematics known as “group theory.”

  One of group theory’s many applications is its use in describing symmetries. Simply put, a symmetry exists when you can do something to a system that leaves it unchanged. Take for example an ordinary cube. Since a cube has a high degree of symmetry, there are many ways of rotating it so that it ends up looking the same as it did before. These rotations form what is known as a group, which is just the collection of ways of rotating a cube while leaving it looking the same.

  As he puzzled over the hadrons, Gell-Mann thought he spied the imprint of a more abstract mathematical group known as SU(3). Unfortunately, there’s no easy-to-imagine way of describing SU(3) without resorting to mathematics, but the important point is that Gell-Mann realized you could use the symmetries of the SU(3) group to arrange the hadrons on a set of grids according to their spins, electric charges, and strangeness, producing sets of hexagons with a particle at each corner and two in the center.

  By ordering the hadrons in this way Gell-Mann did for them what Dmitri Mendeleev had done for the chemical elements a century earlier. Just as Mendeleev had predicted the existence of new elements from gaps in his periodic table, Gell-Mann was able to predict the existence of new hadrons. The symmetries of the SU(3) group required there to be eight spin 0 mesons and eight spin ¹/₂ baryons, but so far only seven spin 0 mesons had been discovered.

  When Gell-Mann published his theory in 1961, he found that another physicist, Yuval Ne’eman of Imperial College in London, had come up with the same idea at almost exactly the same time. However, Ne’eman was a relative unknown, having only recently left the Israeli military to enter the world of physics, while Gell-Mann was already a highly respected figure and an able communicator to boot, which ensured that his version of the theory reached a much wider audience.

  Erudite as well as brainy, and not shy about showing it off, Gell-Mann turned to ancient Buddhist teachings to find a name for his theory, which he dubbed “the Eightfold Way” after the path that liberates those who follow it from the endless cycle of death and rebirth. When just months later the missing eighth meson, named the “eta meson,” was found by the team at Berkeley, physicists began to believe that Gell-Mann might have found the way to hadronic nirvana.

  However, the clincher really came with the discovery of a clutch of new, even heavier particles. As well as predicting octets of spin 0 mesons and spin ¹/₂ baryons, the Eightfold Way required that there should be ten baryons with spin ³/₂. When these spin ³/₂ particles were arranged on the same grid of electric charge versus strangeness, they traced out the shape of a pyramid. At the time that Gell-Mann and Ne’eman published their theories, only four such particles were known, the so-called Delta baryons with 0 strangeness, which presumably made up the base of the pyramid. Then, in July 1962 physicists thronged to a major conference hosted at CERN where particle hunters announced solid evidence for three new Sigma-star baryons with strangeness −1 and a pair of Xi-star baryons with strangeness −2.

  Gell-Mann and Ne’eman knew immediately that these five new particles must form the next two layers of the pyramid. After the discoveries had been announced, Gell-Mann leaped to his feet to predict the existence of the tenth and final missing particle, the capstone of the pyramid with strangeness -3, which he named the “Omega” after the last letter of the Greek alphabet. Ne’eman, who had also raised his hand to speak but was sitting farther back in the hall, could only watch on gloomily as Gell-Mann made the very prediction he had been about to propose.

  Later, over lunch with two young experimenters from Brookhaven, Nicholas Samios and Jack Leitner, Gell-Mann grabbed a napkin and sketched out how the Omega might be found by looking for its likely decay products. The pair took the napkin back to Brookhaven and used it to persuade the lab’s director to give them time on the AGS, the most powerful particle accelerator in the world. After more than a year spent getting the accelerator and bubble chamber into working order, the team began collecting data just before Christmas, working feverishly around the clock into the new year. Poring over tens of thousands of bubble chamber photographs, each crisscrossed by numerous particle tracks, Samios spotted a single image with multiple strange particles all pointing back to a common point of origin, the smoking gun of the Omega.

  The discovery of the Omega sealed the deal for the Eightfold Way. By 1964 there was a powerful sense that another great revolution in our understanding of the subatomic world was underway. At long last the particle zoo was being tamed.

  But what did it all mean? As we’ve seen, the patterns in Mendeleev’s periodic table were the first clues that supposedly indivisible atoms actually have an internal structure, which ultimately determines each chemical element’s unique properties. Could the Eightfold Way be hinting at something similar? Could all these hadrons, including the protons and neutrons that make up the chemical elements, be made of even smaller things?

  Not necessarily. The most popular explanation of the existence of the hadrons at the time did away with the distinction between fundamental particles with no internal structure and composite particles made of smaller things. The Am
erican theoretical physicist Geoffrey Chew instead argued for what he called “nuclear democracy,” where no particle could be thought of as being any more fundamental than any other. According to Chew, each hadron was a mixture of all the others.

  This fantastically counterintuitive idea became known as the “bootstrap model,” as it involved the hadrons effectively pulling themselves into existence, like the nonsensical idiom of pulling yourself up by your own bootstraps. The great hope of the bootstrap theorists was that there might only be one possible set of hadrons that could pull themselves into existence, in which case you’d have a fantastically economical theory explaining all the known particles without any external inputs. Perhaps the Eightfold Way was a consequence of the deeper truth provided by the bootstrap model, which many hoped would soon come into view.

  However, the bootstrap model wasn’t the only show in town. For the past few years Murray Gell-Mann had been playing around with the idea that the symmetries he’d spied in the hadrons could be explained if you thought of them as being made up of smaller bits. He had never taken the idea very far, partly because he thought it was incompatible with the more aesthetically pleasing bootstrap model and partly because he was busy solving other more pressing problems. Also, these smaller bits, whatever they might be, would need to have fractional electric charges of ¹/₃ or ²/₃ that of the electron’s, but so far, the charge of every particle seen in nature was a whole number.