The Greatest Story Ever Told—So Far

by Lawrence M. Krauss

This profoundly important result, proven by decades of work by some of the most creative and talented theoretical physicists in the world, established QED as the most precise and preeminent quantum theory of the twentieth century.

  Which made it all the more upsetting to discover that, while this mathematical beauty indeed allowed a sensible understanding of one of nature’s fundamental forces—electromagnetism—other nastiness began when considering the forces that govern the behavior of atomic nuclei.

  Chapter 9

  * * *

  DECAY AND RUBBLE

  There is no new thing under the sun.

  —ECCLESIASTES 1:9

  When I first learned that we human beings are radioactive, it shocked me. I was in high school listening to a lecture by the remarkable polymath and astrophysicist Tommy Gold, who had done pioneering work in cosmology, pulsars, and lunar science, and he informed us that the particles that made up most of the mass of our bodies, neutrons, are unstable, with a mean lifetime of about ten minutes.

  Given, I hope, that you have been reading this book for longer than ten minutes, this may surprise you too. The resolution of this seeming paradox is one of the first and most wonderful of the gorgeous accidents of nature that make our existence possible. As we continue to explore more deeply the question “Why are we here?,” this accident will loom large on the horizon. While the neutron may seem far removed from light, which has been the centerpiece of our story thus far, we shall see that the two are ultimately deeply connected. The decay of neutrons—responsible for the “beta decay” of unstable nuclei—required physicists to move beyond their simple and elegant theories of light and open up new fundamental areas of the universe for investigation.

  But I am getting ahead of myself.

  In 1929, when Dirac first wrote down his theory of electrons and radiation, it looked as if it might end up being a theory of almost everything. Aside from electromagnetism, the only other force in town was gravity, and Einstein had just made great strides in understanding it. Elementary particles consisted of electrons, photons, and protons, together comprising all the objects that appeared necessary to understand atoms, chemistry, life, and the universe.

  The discovery of antiparticles upset the applecart somewhat, but since Dirac’s theory had effectively predicted them (even if Dirac himself had to catch up with the theory), this was more like a speed bump on the road to reality than a roadblock or detour.

  Then came 1932. Up to that time, scientists had presumed that atoms were composed entirely of protons and electrons. This posed a bit of a problem, however, because the masses of atoms didn’t quite add up. In 1911 Rutherford discovered the existence of the atomic nucleus, containing almost all the mass of atoms in a small region one hundred thousand times smaller than the size of the orbits of the electrons. Following that discovery, it became clear that the mass of heavy nuclei was just a bit more than twice the mass that could be accounted for if the number of protons in the nucleus equaled the number of electrons orbiting the nucleus, ensuring that atoms would be electrically neutral.

  The proposed solution to this conundrum was simple. Actually twice as many protons were in the nucleus as electrons surrounding it, but just the right number of electrons were trapped inside the nucleus, so that again the total electric charge of the atom would be equal to zero.

  However, quantum mechanics implied that the electrons couldn’t be confined within the nucleus. The argument is a bit technical, but it goes something like this: If elementary particles have a wavelike character, then if one is going to confine them to a small distance, the magnitude of their wavelength must be smaller than the confinement scale. But the wavelength associated with a particle is, in quantum mechanics, inversely proportional to the momentum carried by the particle, and hence also inversely proportional to the energy carried by the particle. If electrons were confined to a region the size of an atomic nucleus, the energy they would need to possess would be about a million times the energy associated with the characteristic energies released by electrons as they jump between energy levels in their atomic orbits.

  How could they achieve such energies? They couldn’t. For, even if electrons were tightly bound to protons within nuclei by electronic forces, the binding energy that would be released in this process as they “fell” into the nucleus would be more than ten times smaller than the energy needed to confine the quantum mechanical electron wave function to a region contained within the nucleus.

  Here too the numbers just didn’t add up.

  Physicists at the time were aware of the problem, but lived with it. I suspect that an agnostic approach was deemed prudent, and physicists were willing to suspend disbelief until they knew more, because the issues involved the cutting-edge physics of quantum mechanics and atomic nuclei. Instead of proposing exotic new theories (there were probably some at the margins that I am not aware of), the community was eventually driven by experiments to overcome its natural hesitation to take the logical next step: to assume nature was more complicated than had thus far been revealed.

  In 1930, about the time that Dirac was coming to grips with the possibility that his antiparticles weren’t really protons, a series of experiments provided just the clues that were needed to unravel the nuclear paradox. The poetry of the discoveries was rivaled only by the drama in the private lives of the researchers.

  Max Planck had helped pioneer the quantum revolution by resolving the paradox of the spectrum of radiation emitted by atomic systems. So it was fitting that Planck should indirectly help resolve the paradoxical makeup of the nucleus. While he didn’t himself spearhead the relevant research, he recognized the talents of a young student of mathematics, physics, chemistry, and music at the University of Berlin, Walther Bothe, and in 1912 Planck accepted him as a doctoral student and mentored him throughout the rest of his career.

  Bothe was spectacularly lucky to be mentored by Planck and, shortly thereafter, by Hans Geiger, of Geiger counter fame. Geiger, in my mind, is one of the most talented experimental physicists to have been overlooked for a Nobel Prize. Geiger had begun his career by doing the experiments, with Ernest Marsden, that Ernest Rutherford utilized to discover the existence of the atomic nucleus. Geiger had just returned from England, where he’d worked with Rutherford, to direct a new laboratory in Berlin, and one of his first acts was to hire Bothe as an assistant. There Bothe learned to focus on important experiments, using simple approaches that yielded immediate results.

  After an “involuntary vacation” of five years, as a prisoner of war in Siberia during the First World War, Bothe returned and built a remarkable collaboration with Geiger, eventually succeeding him as director of the laboratory. During their time together they pioneered the use of “coincidence methods” to explore atomic, and eventually nuclear, physics. Using different detectors located around a target, and using careful timing, they could look for simultaneous events, signaling that the source had to be a single atomic or nuclear decay.

  In 1930 Bothe and his assistant Herbert Becker observed something completely new and unexpected. While bombarding beryllium nuclei with products of nuclear decay called alpha particles (already known to be the nuclei of helium), the two observed the emission of a completely new form of high-energy radiation. This radiation had two unique features. It was more penetrating than the most energetic gamma rays, but like gamma rays, the radiation was composed of electrically neutral particles so that it did not ionize atoms as it passed through matter.

  News of this surprising discovery made its way to other physics laboratories throughout Europe. Bothe and Becker had initially proposed that this radiation was some new sort of gamma ray. In Paris, Irène Joliot-Curie, the daughter of famed physicist Marie Curie, and Irène’s husband, Frédéric, replicated Bothe and Becker’s results and explored the radiation in more detail. In particular, they found that when it bombarded a paraffin target, it knocked out protons with incredible energy.

  This observation made it clear that the radi
ation couldn’t be a gamma ray. Why?

  The answer is relatively simple. If you throw a piece of popcorn at an oncoming truck, you are unlikely to stop the truck or even break a window. That is because the popcorn, even if you throw it with great energy, carries little momentum because the popcorn is light. To stop a truck you have to change its momentum by a large amount because, even if it is moving slowly, it is heavy. To stop a truck or knock a heavy object off the truck, you have to throw a big rock.

  Similarly, to knock out a heavy particle such as a proton from paraffin, a gamma ray, made of massless photons, would have to carry great energy (so that the momentum carried by the individual photons was large enough to kick out a heavy proton), and not enough energy was available, by an order of magnitude at least, in any known nuclear-decay processes for this.

  Surprisingly, the Joliot-Curies (they were modern and both adopted the same hyphenated last name) were probably loath, like Dirac, to propose new elementary particles to explain data—since protons, electrons, and photons were not only familiar, but sufficient up to that time to explain everything known, including exotic quantum phenomena associated with atoms. So, Irène and Frédéric didn’t make the now-obvious proposal that maybe a new neutral massive particle was being produced in the decays that Bothe and Becker had discovered. Unfortunately, a similar timidity caused the Joliot-Curies to fail to claim discovery of the positron—in spite of having actually observed it in their experiments before Carl Anderson reported his own discovery somewhat later.

  It fell to the physicist James Chadwick to push things further. Chadwick clearly had a great nose for physics, but his political acumen was not so sharp. After graduation from the University of Manchester with a master’s degree in 1913, working with Rutherford, he obtained a fellowship that would allow him to study anywhere. So he went to Berlin to work with Geiger. He couldn’t have picked a better mentor, and he began to do important studies of radioactive decays. Unfortunately, the First World War broke out while Chadwick was in Germany, and he spent the next four years in an internment camp.

  Eventually he returned to Cambridge, where Rutherford had since moved, to complete his PhD under Rutherford’s direction. Following this Chadwick stayed on to work with Rutherford and help direct the Cavendish laboratory there. While he was aware of Bothe and Becker’s results and even reproduced them, only when one of his students informed him of the Joliot-Curies’ results did Chadwick become convinced, using the energy argument I mentioned above, that the radiation that had been observed had to result from a new neutral particle—of mass comparable to that of the proton—that might reside in atomic nuclei, an idea he and Rutherford had been germinating for years.

  Chadwick reproduced and extended the Joliot-Curies’ experiments, bombarding targets other than paraffin to explore the outgoing protons. He confirmed not only that the energetics of the collisions made it impossible for the source to be gamma rays, but also that the interaction strength of the new particles with nuclei was far greater than would be predicted for gamma rays.

  Chadwick didn’t dawdle. Within two weeks of beginning his experiments in 1932, he sent a letter to Nature entitled “Possible Existence of a Neutron” and followed this up with a more detailed article sent to the Royal Society. The neutron, which we now know makes up most of the mass of heavier nuclei, and thus most of the mass in our bodies, had been discovered.

  For his discovery he was awarded the Nobel Prize in Physics three years later, in 1935. In a kind of poetic justice, three of the people whose experiments had made Chadwick’s results possible—but who missed out on identifying the neutron—were awarded Nobel Prizes for other work. Bothe won the Nobel Prize in 1954 for his work on using coincidences between observed events in different detectors to explore the detailed nature of nuclear and atomic phenomena. Both Irène and Frédéric Joliot-Curie, who barely missed out on two other Nobel Prize–winning discoveries, won the Nobel Prize in Chemistry in 1935 for their discovery of artificial radioactivity—which was later an essential ingredient in the development of both nuclear power and nuclear weapons. Interestingly, only after winning the Nobel Prize was Irène awarded a professorship in France. With the two Nobel Prizes for her mother, Marie, the Curie family garnered a total of five Nobel Prizes, the most that have ever been received by a single family.

  After his discovery Chadwick set out to measure the mass of the neutron. His first estimate, in 1933, suggested a mass of slightly less than the sum of the masses of a proton and an electron. This reinforced the idea that perhaps the neutron was a bound state of these two particles, and the mass difference, using Einstein’s relation E = mc2, was due to the energy lost in binding them together. However, after several conflicting measurements by other groups, further analysis a year later by Chadwick using a nuclear reaction induced by gamma rays—which allowed all energies to be measured with great precision—definitely indicated that the neutron was heavier than the sum of the proton and electron masses, even if barely so, with the mass difference being less than 0.1 percent.

  It is said that “close” only matters when tossing horseshoes or hand grenades, but the closeness in mass between the proton and the neutron matters a great deal. It is one of the key reasons we exist today.

  Henri Becquerel discovered radioactivity in uranium in 1896, and only three years later Ernest Rutherford discerned that radioactivity occurred in two different types, which he labeled alpha and beta rays. A year later gamma rays were discovered, and Rutherford confirmed them as a new form of radiation in 1903, when he gave them their name. Becquerel determined in 1900 that the “rays” in beta decay were actually electrons, which we now know arise from the decay of the neutron.

  In beta decay a neutron splits into a proton and an electron, which, as I describe below, would not be possible if the neutron weren’t slightly heavier than protons. What is surprising about this neutron decay is not that it occurs, but that it takes so long. Normally the decay of unstable elementary particles occurs in millionths or billionths of a second. Isolated neutrons live, on average, more than ten minutes.

  One of the chief reasons that neutrons live so long is that the mass of the neutron is only slightly more than the sum of the masses of a proton plus an electron. Thus, there is only barely enough energy available, via the neutron’s rest mass, to allow it to decay into these particles and still conserve energy. (The other reason is that a neutron doesn’t decay into only a proton plus an electron. It decays into three particles . . . stay tuned!)

  While ten minutes may be an eternity on atomic timescales, it is pretty short compared to a human life or the lifetime of atoms on Earth. Returning to the puzzle I mentioned at the beginning of this chapter, what gives? How can we be largely made up of neutrons if they decay before the first commercial break in a thirty-minute TV show?

  The answer again lies in the extreme closeness of the neutron and proton masses. A free neutron decays in ten minutes or so. But consider a neutron bound inside an atomic nucleus. Being bound means that it takes energy to kick it out of the nucleus. But that means that it loses energy when it gets bound to the nucleus in the first place. But, Einstein told us that the total energy of a massive particle is proportional to its mass, via E = mc2. That means that, if the neutron loses energy when it gets bound in a nucleus, its mass gets smaller. But since its mass when it is isolated is just a smidgen more than the sum of the masses of a proton and an electron, when it loses mass, it no longer has sufficient energy to decay into a proton and an electron. If it were to decay into a proton, it would have to either release enough energy to also eject the proton from the nucleus, which, given standard nuclear-binding energies, it would not have, or else release enough energy to allow the new proton to remain in a new stable nucleus. Since the new nucleus would be that of a different element, adding one additional positive charge to the nucleus also generally requires more energy than the minute amount available when a neutron decays. As a result, the neutron and most atomic nuclei containi
ng neutrons remain stable.

  The entire stability of the nuclei that make up everything we see, including most of the atoms in our body, is an accidental consequence of the fact that the neutron and proton differ in mass by only 0.1 percent, so that a small shift in the mass of the former, when embedded in nuclei, means it can no longer decay into the latter. That is what I learned from Tommy Gold.

  It still amazes me when I think about it. The existence of complex matter, the periodic table, everything we see, from distant stars to the keyboard I am typing this on—hinges on such a remarkable coincidence. Why? Is it an accident, or do the laws of physics require it for some unknown reason? Questions such as these drive us physicists to search deeper for possible answers.

  The discovery of the neutron, and the subsequent observation of its decay, introduced more than one new particle into the subatomic zoo. It suggested that perhaps two of the most fundamental properties of nature—the conservation of energy and the conservation of momentum—might break down on the microscopic-distance scales of nuclei.

  Almost twenty years before discovering the neutron, James Chadwick had observed something strange about beta rays, well before he or anyone else knew that they originated from decaying neutrons. The spectrum of energy carried by electrons emitted in neutron decay is continuous, going from essentially zero energy up to a maximum energy, which depends on the energy available after the neutron has decayed—for a free neutron this maximum energy is the energy difference between the mass of the neutron and the sum of the masses of the proton and electron.

  There is a problem with this, however. It is easiest to see the problem if we imagine for the moment that the proton and the electron have equal masses. Then, if the proton carries off more energy than the electron after the decay, it would be moving faster than the electron. But if they have the same mass, then the proton would also have more momentum than the electron. But if the neutron decays at rest, then its momentum before the decay would be zero, so the momentum of the outgoing proton would have to cancel that of the outgoing electron. But that is impossible unless they have equal momenta, going in opposite directions. So the magnitude of the proton’s momentum could never be greater than that of the electron. In short, there is only one value for the energy and the momentum of the two particles after the decay if they have equal masses.