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 containing 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.
The same reasoning, though mathematically a bit more involved,
applies even if the proton and electron have different masses. If they
are the only two particles produced in the decay of the neutron, their
speeds, and hence their energy and momenta, would be required to
each have unique, fixed values that depend on the ratio of their
respective masses.
As a result, if electrons from beta decay of neutrons come off with
a range of different energies, this would violate the conservation of
energy and momentum. But, as I subtly suggested above, this is only
true if the electron and proton are the only particles produced as
products of the neutron decay.
Again, in 1930, only a few years before the discovery of the
neutron, the remarkable Austrian theoretical physicist Wolfgang
Pauli wrote a letter to colleagues at the Swiss Federal Institute of
Technology, beginning with the immortal header “Dear radioactive
ladies and gentlemen,” in which he outlined a proposal to resolve
this problem, which he also said he didn’t “feel secure enough to
publish anything about.” He proposed that a new electrically neutral
elementary particle existed, which he called a neutron, and that in
͟͟͝
addition to the electron and the proton this new neutral particle was
produced in beta decay so that the electron, proton, and this particle
together could share the energy available in the decay, allowing a
continuous spectrum.
Pauli, who later won the Nobel Prize for his “exclusion principle”
in quantum mechanics, was no fool. In fact, he had no patience for
fools. He was famous for supposedly rushing up to the blackboard
during lectures and removing the chalk from the speaker’s hand if he
felt nonsense was being spouted. He could be scathingly critical of
theories he didn’t like, and his worst criticism was reserved for any
idea that was so vague, as he put it, “it isn’t even wrong.” (A dear old
colleague of mine when I taught at Yale, the distinguished
mathematical physicist Feza Gürsey, once responded to a reporter
who asked what was the significance of an announcement of some
overhyped idea proposed by some scientists seeking publicity by
saying, “It means Pauli must be dead.”)
Pauli realized that proposing a new elementary particle that
hadn’t been observed was speculative in the extreme, and he argued
in his letter that such a particle was unlikely both because it had
never been seen and would therefore have to interact weakly with
matter, and also because it would have to be very light to be
produced along with an electron, given that the energies available in
beta decay were so small compared to the proton’s mass.
The first problem that arose with his idea was the name he chose.
After Chadwick’s 1932 experimental discovery of the particle we
now call the neutron, appropriate for a neutral cousin of the proton
with comparable mass, Pauli’s hypothesized particle needed another
name. The brilliant Italian physicist and colleague of Pauli’s—Enrico
Fermi—came up with a solution in 1934, changing its name to
neutrino, an Italian pun for “little neutron.”
͟͝͠
It would take twenty-six years for Pauli’s neutrino to be
discovered, enough time for the little particle, and its heavier cousin,
the neutron, to force physicists to totally revamp their views on the
forces that govern the cosmos, the nature of light, and even the
nature of empty space.
͟͝͡
C h a p t e
r 1 0
F R O M
H E R E T O
I N F I N I T Y:
S H E D D I N G L I G H T O N T H E
S U N
I have fought a good fight, I have finished my course, I have kept
the faith.
—2 TIMOTHY 4:7
The physicist Enrico Fermi is largely unsung in the public’s
eyes, but he remains one of the greatest twentieth-century physicists.
He, together with Richard Feynman, more than any of the other
remarkable figures from that equally remarkable period in physics,
most influenced my own attitude and approach to the field, as well
as my own understanding of it. I only wish I were as talented as
either of them.
Born in 1901, Fermi died at the age of fifty-three of cancer,
perhaps brought on by his work on radioactivity. In 1954, when he
died, he was nine years younger than I am as I write this. But in his
short life he pushed forward the frontiers of both experimental and
theoretical physics in a way that no one has since repeated, and no
one is ever likely to do again. The complexity of the array of
theoretical tools now used to develop physical models, and the
complexity of machinery now used to test them, are separately too
sophisticated to allow any single individual today, no matter how
talented, to remain on the vanguard of both endeavors at the level
Fermi achieved in his time.
͟͢͝
In 1918, when Fermi graduated from high school in Rome, the
possibilities open to a brilliant young scientific mind were far less
constrained. Quantum mechanics had just been born, new ideas
were everywhere, and the rigorous mathematics necessary to deal
with these ideas had not yet been developed or applied.
Experimental physics had yet to enter the domain of “big science”;
experiments could be performed by individual researchers in
makeshift laboratories, and they could be completed in weeks
instead of months.
Fermi applied to the prestigious Scuola Normale Superiore in
Pisa, which required an essay as part of the entrance exam. The
theme that year was “specific characteristics of sounds.” Fermi
submitted an “essay” that included solving partial differential
equations for a vibrating rod and applying a technique called Fourier
analysis. Even today, these mathematical techniques are not
normally encountered until maybe the third year of an
undergraduate degree, and for some students not until graduate
school. But as a seventeen-year-old, Fermi sufficiently impressed the
examiners to receive first place in the exam.
At the university, Fermi first majored in mathematics but
switched to physics and largely taught himself General Relativity—
which Einstein had only developed a few years earlier—as well as
quantum mechanics and atomic physics, which were then emerging
fields of research. Within three years of arriving at the university he
published theoretical papers in major physics journals on subjects
from General Relativity to electromagnetism. At the age of twenty-
one, four years after beginning his university studies, he received his
doctoral degree for a thesis exploring the applications of probability
to X-ray diffraction. At the time a thesis on purely theoretical issues
was not acceptable for a physics doctorate in Italy, so this
ͣ͟͝
encouraged Fermi to ensure his competence in the laboratory as well
as with pen and paper.
Fermi moved to Germany, the center of the emerging research on
quantum mechanics, and then to Leiden, Holland, where he met
with the most famous physicists of the day—Born, Heisenberg, Pauli,
Lorentz, and Einstein, to name a few—before returning to Italy to
teach. In 1925, Wolfgang Pauli proposed the “exclusion principle,”
which disclosed that two electrons could not occupy exactly the
same quantum state at the same time and place, and which laid the
basis of all of atomic physics. Within a year, Fermi applied this idea
to systems of many such identical particles that, like electrons, have
two possible values of spin, angular momentum, which we call spin
up, and spin down. He thus established the modern form of the field
called statistical mechanics, which is at the basis of almost all
materials science, semiconductors, and those areas of physics that
led to the creation of modern electronic components such as
computers.
As I earlier emphasized, there is no intuitive way to picture a
point particle as spinning around some axis. It is simply one of the
ways that quantum mechanics evades our notions of common sense.
Electrons are called spin ½ particles because the magnitude of their
spin angular momentum turns out to be half as big as the lowest
value of angular momentum associated with the orbital motion of
electrons in atoms. Any spin ½ particle such as an electron is called a
fermion, named in Fermi’s honor.
At the tender age of twenty-six Fermi was elected to a new chair
in theoretical physics at the University of Rome and thereafter led a
vibrant group of students, including several subsequent Nobel
laureates, as they explored atomic and then nuclear physics.
In 1933, Fermi was motivated by another proposal of Pauli’s, that
for the new particle produced in the decay of neutrons, which Fermi
ͤ͟͝
labeled a neutrino. But naming the new particle was just an aside.
Fermi had much bigger fish to fry, and he produced a theory for
neutron decay that revealed the possible existence of a new
fundamental force in nature, the first new force known to science
beyond electromagnetism and gravity—which was in its own way
inspired by thinking about light. Although it wasn’t obvious at the
time, this was to be the first of two new forces associated with
atomic nuclei, which together with electromagnetism and gravity,
comprise all the forces known to operate in nature, from the
smallest subatomic scales to the motion of galaxies.
When Fermi submitted his proposal to the journal Nature, the
editor turned it down because it was “too remote from physical
reality to be of interest to readers.” For many of us who have since
had papers rejected by equally high-handed editors at that journal, it
is comforting to know that Fermi’s paper, one of the most important
proposals in twentieth-century physics, also didn’t make the cut.
This inappropriate rejection was undoubtedly frustrating to
Fermi, but it did have a useful side effect. Fermi decided instead to
return to experimental physics, and in short order he began to
experiment with the neutrons discovered by Chadwick two years
earlier. Within several months Fermi had developed a powerful
radioactive source of neutrons and found that he was able to induce
radioactive decays in otherwise stable atoms by bombarding them
with neutrons. Bombarding uranium and thorium with neutrons, he
also witnessed nuclear decays and thought he had created new
elements. In fact, he had actually caused the nuclei to split, or
fission,
into lighter nuclei, which were later found to also emit more
neutrons than they absorbed in the process—as other scientists
discovered in 1939.
Fermi’s segue into experiment turned out to be good for him.
Four years later, in 1938, at the age of thirty-seven, he was awarded
ͥ͟͝
the Nobel Prize for introducing artificial radioactivity, creating new
radioactive elements by neutron bombardment. Yet by 1938 the
Nazis had begun to establish their racial laws in Germany, and Italy
had followed suit, so Fermi’s Jewish wife, Laura, was endangered. So,
after receiving the prize in Stockholm, Fermi and his family didn’t
return to Italy but moved to New York City, where he accepted a
position at Columbia.
When Fermi learned the news about nuclear fission in 1939 in
New York, following a lecture by Niels Bohr at Princeton, Fermi
amended his earlier Nobel acceptance speech to clarify his earlier
error and in short order reproduced the German results. Before long,
he and his collaborators realized that this produced the possibility of
a chain reaction. Neutrons could bombard uranium, causing it to
fission and release energy, and to release more neutrons that could
bombard more uranium atoms and so on.
Soon after, Fermi gave a lecture to the US Navy warning of the
potential significance of this result, but few took him seriously. Later
that year, Einstein’s famous letter made its way to President
Roosevelt and changed the course of history.
Fermi had recognized the potential dangers inherent in releasing
the energy of the atomic nucleus even earlier. A year after getting his
doctorate, in 1923, he wrote the appendix for a book on relativity
and talked of the potential of E = mc2, writing at the time, “It does
not seem possible, at least in the near future, to find a way to release
these dreadful amounts of energy—which is all to the good because
the first effect of an explosion of such a dreadful amount of energy
would be to smash into smithereens the physicist who had the
misfortune to find a way to do it.”
That idea must have been on his mind in 1941 when, as part of
the newly established Manhattan Project, Fermi was assigned the
task of creating a controlled chain reaction—namely creating a
͜͝͠
nuclear reactor. While those in charge were understandably worried
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