Lawrence Krauss - The Greatest Story Ever Told--So Far

by Why Are We Here (pdf)

D E C AY A N D R U B B L E

  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

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  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

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  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.

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  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

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  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 radiation 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.

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  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

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  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.

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  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 tha
t “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.

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  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